Browse Course Material

Course info, instructors.

  • Prof. Hazel Sive
  • Prof. Tyler Jacks
  • Dr. Diviya Sinha

Departments

As taught in.

  • Biochemistry
  • Cell Biology
  • Developmental Biology
  • Molecular Biology

Learning Resource Types

Introductory biology, teaching students to solve problems.

In this section, Prof. Hazel Sive describes this course’s focus on problem solving.

Problem Solving at MIT

I think the unofficial motto of MIT is “We solve problems.” Everything that we do here is to prepare our students to be problem solvers in the world. This idea permeates all the disciplines at MIT: engineering; science; business; architecture and urban planning; and humanities, arts, and social sciences. No matter what degree students earn at MIT, they leave with the ability to solve hard problems. When faced with a new problem, they know how to understand it, think about ways to solve it, try those ways, and ultimately get some kind of solution. That kind of philosophical and also real power gives students a big edge when they leave MIT and enter the workforce, go to graduate school, or go to medical school and become a physician.

It’s a difficult way to learn, but it’s a fantastic way to learn. I believe that learning should be a struggle; without struggle, you don’t get anywhere new. I think the courses at MIT are very challenging, and the introductory courses here are much harder than the introductory courses at most other universities.

Learning Terminology and Facts in Order to Solve Problems

Our course does include some rote learning, but the purpose of this rote learning is for our students to develop enough background to be able to speak the subject and understand and tackle challenging problems. They have to know what DNA is, what a gene is, and what a cell is. Very often, I’ll give them a term and I’ll say, “This is the scientific term. You should know it because it’s in your book, it’s in the scientific literature, and you’ll hear it on the news. But what’s most important is the concept underlying the term.” If you look at our problem sets and exams, you’ll see that there are no questions where students have to label a diagram, give a definition, or regurgitate facts.

Learning to Problem Solve through Practice

"It’s a terrific moment when a student realizes that this is different from any way they’ve been taught before, and they’re going to be challenged in ways in which they never knew they could be challenged."

In this course, students learn to solve problems through practice. Every two weeks, we give the students a problem set with six long problems. The problems are all about problem solving. The students look at the problems and realize that this isn’t just a matter of taking the lecture material and giving it back to us; we assume they know that information, and they’re expected to build from there. It’s very challenging for the students.

This is a shock to many of our students. In most high schools and even universities, biology is about learning facts. This was the case for me. I went to a very good university in South Africa. I learned all about the anatomy of the skull. I learned all about bones. I could classify fish. I learned many things that are very useful, but no one ever taught me how to solve a problem. Many of our students arrive at MIT having gotten the highest possible mark on the Advanced Placement ® biology exam, and when they get the first problem set in our course, they are stunned. They haven’t encountered biology as a kind of detective story where there’s a problem that they need to understand and solve. We explain that biology is a rigorous problem solving discipline; in fact, biology is all about using information to solve problems. It’s a terrific moment when a student realizes that this is different from any way they’ve been taught before, and they’re going to be challenged in ways in which they never knew they could be challenged.

The first problem set has to do with biochemistry. By the time they get the problem set, we’ve taught them about the various classes of molecules and macro-molecules that are found in living cells. We give them a problem set where not only do they have to be able to recognize something about the macro-molecules we present to them, they also have to recognize something about how the macro-molecules are put together, about bonding between the different parts of the macro-molecules, and about what that means for the structure of the macro-molecule, especially proteins. We do that both on paper and then also using a visualization program that was developed in the biology department called StarBiochem . In this program, the students are given a 3-dimensional structure of a protein, and they have to be able to understand what they’re looking at and what it means for the actual function of the protein, which is usually an enzyme that can catalyze a particular reaction. As soon as they see that problem set, they realize that this is going to be different from their high school biology experience.

As another example, when students learn about medical disorders, we don’t ask them to regurgitate the typical symptoms. Instead, we might say, “Here’s a patient that’s presenting with a funny disorder, and if she tries to move too quickly, she collapses. Her muscles look normal. Her nerves look normal, but if you do certain tests to them, you can see they’re not firing properly. Here’s what the trace of their firing pattern looks like. Suggest what’s wrong with the patient.”

The Problem Set Process

I tell the students that they have to practice these problems on their own. We can give pointers about how to solve the problems, but they need to think through the material. I tell them that when I’m thinking hard, I get a headache. For them, it might come as some other manifestation, but they should be getting their own personal version of a headache when they’re doing their problem sets. It shouldn’t be easy, but once they learn how to do a problem and get somewhere with a problem, it’s powerful. It empowers them to then go and tackle another one.

"Through this process, students show themselves that they can triumph over the work, and they come out actually having some power over the material."

For each problem set, I tell the students to print out three copies. First, students should take one copy and attempt the problem set all by themselves, without their notes and without help from others. They can identify what they don’t understand right away. They might get halfway through the problem set and panic upon realizing that they don’t know very much, that they went to lecture but didn’t absorb a lot of the material.

At that point, they can review their notes and their textbook, or go to the library, or search for information on the web. They learn what they can, then try the second problem set copy. Again, this is without help from other people; they need to personally struggle with the material. They always get farther the second time. The headache, the struggle, and then the triumph with bits of the problems is really powerful. Through this process, students show themselves that they can triumph over the work, and they come out actually having some power over the material.

Usually there will still be some holes in what they’re able to do and understand. Then, they can go and talk to their friends, their teaching assistants, and me or my co-instructor. They have to hand in their own work, in their own words, but they can work together and their work can have all these inputs. If they work as a group initially, they may miss getting that headache because they’re relying on their friends and people who may get it more quickly or in a different way than they do. I really discourage them from working together initially because I think they just don’t learn the material properly that way. They need to learn by doing. As they do more and more problems, they get better at addressing these questions. Students get substantial practice throughout the semester, and they come out really knowing something about how to solve problems in this particular area of life science.

Crafting Good Problems for 7.013

A critical part of our job as teachers is crafting good problems. We aim to create problems that have the following characteristics:

  • Rooted in problem solving . A good problem should challenge students to think and to apply their knowledge in novel ways.
  • Clearly written and easily understandable . The point of the problem should be clear.
  • Built upon multiple aspects of the course material . Although the course is taught in a modular way, students cannot forget the earlier material as they learn new material. The early, fundamental material is used for all of the later lectures and problem sets. The best problems not only address the current module that they’re learning, but also draw upon and integrate past modules. For example, while learning about neurobiology, students should still remember that proteins only function properly if they’re put in the correct place in a cell.
  • Informed by current literature . When possible, we like to draw upon real, current examples from the news and/or scientific literature. We usually take just one aspect of it and use it in a problem. When possible, we try to pick topics that we think students can relate to. This way, our problems are fresh, current, and interesting, and we never run out of ideas for problems.

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Step by Step: Biology Undergraduates’ Problem-Solving Procedures during Multiple-Choice Assessment

  • Luanna B. Prevost
  • Paula P. Lemons

Department of Integrative Biology, University of South Florida, Tampa, FL 33620

Search for more papers by this author

Department of Biochemistry and Molecular Biology, University of Georgia, Athens, GA 30602

This study uses the theoretical framework of domain-specific problem solving to explore the procedures students use to solve multiple-choice problems about biology concepts. We designed several multiple-choice problems and administered them on four exams. We trained students to produce written descriptions of how they solved the problem, and this allowed us to systematically investigate their problem-solving procedures. We identified a range of procedures and organized them as domain general, domain specific, or hybrid. We also identified domain-general and domain-specific errors made by students during problem solving. We found that students use domain-general and hybrid procedures more frequently when solving lower-order problems than higher-order problems, while they use domain-specific procedures more frequently when solving higher-order problems. Additionally, the more domain-specific procedures students used, the higher the likelihood that they would answer the problem correctly, up to five procedures. However, if students used just one domain-general procedure, they were as likely to answer the problem correctly as if they had used two to five domain-general procedures. Our findings provide a categorization scheme and framework for additional research on biology problem solving and suggest several important implications for researchers and instructors.

INTRODUCTION

The call to reform undergraduate education involves shifting the emphasis in science classes away from rote memorization of facts toward learning core concepts and scientific practices ( National Research Council [NRC], 2003 ; American Association for the Advancement of Science [AAAS], 2011 ). To develop instruction that focuses on core concepts and scientific practices, we need more knowledge about the concepts that are challenging for students to learn. For example, biology education research has established that students struggle with the concepts of carbon cycling (e.g., Anderson et al. , 1990 ; Hartley et al ., 2011 ) and natural selection (e.g., Nehm and Reilly, 2007 ), but we know much less about students’ conceptual difficulties in ecology and physiology. Researchers and practitioners also need to discover how students develop the ability to use scientific practices. Although these efforts are underway (e.g., Anderson et al. , 2012 ; Gormally et al. , 2012 ; Dirks et al. , 2013 ; Brownell et al. , 2014 ), many research questions remain. As research accumulates, educators can create curricula and assessments that improve student learning for all. We investigate one key scientific practice that is understudied in biology education, problem solving ( AAAS, 2011 ; Singer et al. , 2012 ).

For the purposes of this article, we define problem solving as a decision-making process wherein a person is presented with a task, and the path to solving the task is uncertain. We define a problem as a task that presents a challenge that cannot be solved automatically ( Martinez, 1998 ). Problem-solving research began in the 1940s and 1950s and focused on problem-solving approaches that could be used to solve any problem regardless of the discipline ( Duncker and Lees, 1945 ; Polya, 1957 ; Newell and Simon, 1972 ; Jonassen, 2000 , 2012 ; Bassok and Novick, 2012 ). Despite the broad applicability of these domain-general problem-solving approaches, subsequent research has shown that the strongest problem-solving approaches derive from deep knowledge of a domain ( Newell and Simon, 1972 ; Chi et al. , 1981 ; Pressley et al. , 1987 ). Domain is a term that refers to a body of knowledge that can be broad, like biology, or narrow, like ecosystem structure and function. This body of literature has developed into a theoretical framework called domain-specific problem solving. We situate our research within this theoretical framework.

THE THEORETICAL FRAMEWORK OF DOMAIN-SPECIFIC PROBLEM SOLVING

Domain-specific problem solving has its origins in information-processing theory (IPT; Newell and Simon, 1972 ). IPT focuses on the cognitive processes used to reach a problem solution and emphasizes the general thinking processes people use when they attempt problem solving, such as brainstorming ( Runco and Chand, 1995 ; Halpern, 1997 ) and working backward by beginning with the problem goal and working in reverse toward the initial problem state ( Newell et al. , 1958 ; Chi and Glaser, 1985 ). Despite the empirical evidence for general thinking processes, one of IPT’s shortcomings as a comprehensive view of human cognition ( Dawson, 1998 ) is that the knowledge base of the problem solver is not considered.

Domain-specific problem solving expands IPT to recognize that experts in a particular domain have a relatively complete and well-organized knowledge base that enables them to solve the complex problems they face (e.g., Chase and Simon, 1973 ). One of the landmark studies showing the differences between the knowledge base of experts and nonexperts, or novices, was conducted in science, specifically in physics. Chi and colleagues (1981) compared the classification of physics problems by advanced physics PhD students (i.e., experts) and undergraduates who had just completed a semester of mechanics (i.e., novices), identifying fundamental differences. Chemistry researchers built on Chi’s work to identify differences in how experts and novices track their problem solving and use problem categorization and multiple representations ( Bunce et al ., 1991 ; Kohl and Finkelstein, 2008 ; Catrette and Bodner, 2010 ). Biology researchers built upon this work by conducting similar problem-solving studies among experts and novices in evolution and genetics ( Smith, 1992 ; Smith et al. , 2013 ; Nehm and Ridgway, 2011 ). Taken together, these studies established that experts tend to classify problems based on deep, conceptual features, while novices classify problems based on superficial features that are irrelevant to the solution.

Domain-specific problem-solving research within biology also has revealed important individual differences within groups of problem solvers. These studies show that wide variation in problem-solving performance exists. For example, some novices who solve problems about evolution classify problems and generate solutions that are expert-like, while others do not ( Nehm and Ridgway, 2011 ). This research points to the importance of studying variations in problem solving within novice populations.

Given the centrality of the knowledge base for domain-specific problem solving, it is necessary to describe the components of that knowledge base. Domain-specific problem-solving research recognizes three types of knowledge that contribute to expertise. Declarative knowledge consists of the facts and concepts about the domain. Procedural knowledge represents the how-to knowledge that is required to carry out domain-specific tasks. Conditional knowledge describes the understanding of when and where to use one’s declarative and procedural knowledge ( Alexander and Judy, 1988 ). Note that the field of metacognition also uses this three-type structure to describe metacognitive knowledge, or what you know about your own thinking ( Brown, 1978 ; Jacobs and Paris, 1987 ; Schraw and Moshman, 1995 ). However, for this paper, we use these terms to describe knowledge of biology, not metacognitive knowledge. More specifically, we focus on procedural knowledge.

Procedural knowledge consists of procedures. Procedures are tasks that are carried out automatically or intentionally during problem solving ( Alexander and Judy, 1988 ). Procedures exist on a continuum. They can be highly specific to the domain, such as analyzing the evolutionary relationships represented by a phylogenetic tree, or general and applicable to problems across many domains, such as paraphrasing a problem-solving prompt ( Pressley et al. , 1987 , 1989 ; Alexander and Judy, 1988 ).

APPLYING DOMAIN-SPECIFIC PROBLEM SOLVING TO MULTIPLE-CHOICE ASSESSMENT IN BIOLOGY

We used domain-specific problem solving to investigate the most common form of assessment in the college biology classroom, multiple-choice assessment ( Zheng et al ., 2008 ; Momsen et al ., 2013 ). College biology and science, technology, engineering, and mathematics (STEM) courses rely on multiple-choice assessment due to large enrollments, limited teaching assistant support, and ease of scoring. Outside the classroom, multiple-choice assessment is used on high-stakes exams that determine acceptance to professional schools, like the Medical College Admissions Test and Graduate Record Exam. To our knowledge, the framework of domain-specific problem solving has not been applied previously to investigate multiple-choice assessment in college biology.

It has become common practice within the biology education community to think about assessment, including multiple-choice assessment, by determining the Bloom’s taxonomy ranking of assessment items (e.g., Bissell and Lemons, 2006 ; Crowe et al. , 2008 ; Momsen et al. , 2010 , 2013 ). Bloom’s Taxonomy of Educational Objectives was built to facilitate the exchange of test items among faculty; it was not based primarily on the evaluation of student work ( Bloom, 1956 ; Anderson and Krathwohl, 2001 ). Bloom’s taxonomy helps educators think about the range of cognitive processes they could ask their students to perform and has served as an invaluable resource enabling educators to improve alignment between learning objectives, assessments, and classroom curricula (e.g., Crowe et al. , 2008 ). When applying Bloom’s taxonomy to assessment items, items are ranked as remembering, understanding, applying, analyzing, evaluating, and synthesizing. Items ranked as remembering and understanding are grouped as lower-order items; and items ranked as applying, analyzing, evaluating, and synthesizing are grouped as higher-order items ( Zoller, 1993 ; Crowe et al. , 2008 ). Despite the value of Bloom’s taxonomy for instructors, what is not known is the relationship between the procedural knowledge of domain-specific problem solving and the Bloom’s ranking of biology assessments. This is a critical gap in the literature, because efforts to improve student learning in college science classrooms may be stymied if critical insights about student work from domain-specific problem solving are not linked to our understanding of assessment and curricular design.

What are the domain-general and domain-specific procedures students use to solve multiple-choice biology problems?

To what extent do students use domain-general and domain-specific procedures when solving lower-order versus higher-order problems?

To what extent does the use of domain-general or domain-specific procedures influence the probability of answering problems correctly?

Setting and Participants

We recruited participants from a nonmajors introductory biology course at a southeastern public research university in the Spring 2011 semester. One of the authors (P.P.L.) was the course instructor. The course covered four major areas in biology: evolution, ecology, physiology, and organismal diversity. The instructor delivered course content using lecture interspersed with clicker questions and additional opportunities for students to write and discuss. Students also completed five in-class case studies during the semester; students completed cases in self-selected small groups and turned in one completed case study per group for grading. In addition to group case studies, the instructor assessed student learning via individual exams. Students also received points toward their final grades based on clicker participation.

In the second week of the semester, the instructor announced this research study in class and via the course-management system, inviting all students to participate. Students who volunteered to participate by completing an informed consent form were asked to produce written think-alouds for problems on course exams throughout the semester. One hundred sixty-four students completed an informed consent form. Of the 164 consenting students, 140 students actually produced a written think-aloud for at least one of 13 problems; of the 140 students, 18 did written think-alouds for all 13 problems. The remainder of students did written think-alouds for one to 13 problems. On average, research participants provided written think-alouds for 7.76 problems.

The 164 consenting students represented 73.9% of the course enrollment ( n = 222). The 164 consenting students included 70.8% females and 29.2% males; 20.4% freshmen, 40.9% sophomores, 24.1% juniors, and 13.9% seniors. The 164 students were majoring in the following areas: 3.7% business, 1.5% education, 4.4% humanities, 11.0% life and physical sciences, 5.9% engineering, and 72.3% social sciences.

This research was conducted under exempt status at the University of Georgia (UGA; IRB project 201110340).

Data Collection

Problem development..

We wrote 16 multiple-choice problems to include in this study. All problems related to material dealt with during class and focused specifically on ecosystems, evolution, and structure–function relationships. On data analysis, three problems were excluded, because most students were confused by the wording or visual representations or were able to solve the problem correctly with a superficial strategy. Each problem was preceded by a prompt for students to provide their written think-aloud (see Written Think-Alouds section). Each problem was also labeled with a preliminary Bloom’s taxonomy categorization ( Anderson and Krathwohl, 2001 ). A summary of all problems, including a description, the preliminary Bloom’s ranking, and the faculty consensus Bloom’s ranking, is provided in Table 1 . As an example, one of the final 13 problems is shown in Figure 1 . All other problems are shown in Supplemental Figure S1.

FIGURE 1.

FIGURE 1. Sample problem from the domain of evolution used to probe students’ problem-solving procedures. The preliminary ranking that students saw for this question was Applying and Analyzing based on Bloom’s taxonomy. Experts ranked this problem as Analyzing. The correct answer is E. Images of benthic and limnetic males are courtesy of Elizabeth Carefoot, Simon Fraser University.

For each problem, a description is included along with the preliminary Bloom’s ranking, and the final consensus Bloom’s ranking. The actual problems are included in Supplemental Figure S1.

Ranking of Problems by Bloom’s Level.

We wanted to investigate the use of domain-general or domain-specific procedures in lower-order versus higher-order problems. We asked three biology faculty members who were not investigators in this study to rank the Bloom’s levels of the problems we developed. The biology faculty members were selected because they have extensive teaching experience in college biology and also have experience ranking assessment items using Bloom’s taxonomy. The faculty used a protocol similar to one described previously ( Momsen et al. , 2010 ). To assist with Bloom’s ranking, we provided them with class materials relevant to the problems, including lecture notes and background readings. This is necessary, because the ranking of a problem depends on the material that students have encountered in class previously. The faculty members independently ranked each problem. Interrater reliability of independent rankings was determined using an intraclass coefficient (0.82). The faculty members met to discuss their rankings and settled disagreements by consensus. The preliminary Bloom’s rankings and the faculty consensus Bloom’s rankings for problems are reported in Table 1 . For the remainder of the paper, we use the consensus Bloom’s rankings to describe problems as either lower order or higher order.

Administration of Problems to Students.

The 13 problems included in this study were administered to students on exams 1, 2, 3, and the final exam as follows: three on exam 1, three on exam 2 four on exam 3, and three on the final exam. Students’ multiple-choice responses were part of the actual exam score. They received 0.5 extra-credit points for providing satisfactory documentation of their thought processes. Students did not receive extra credit if we judged their documentation to be insufficient. Insufficient responses were those in which students made only one or two brief statements about their problem-solving process (e.g., “I chose C”). Students could answer the multiple-choice problem and opt not to provide documentation of their thinking for extra credit. Students could receive up to 6.5 points of extra credit for documentation of the problem set. The total points possible for the semester were 500, so extra credit for this research could account for up to 1.3% of a student’s grade.

Written Think-Alouds.

We developed a protocol to capture students’ written descriptions of their thought processes while solving problems on exams based on a think-aloud interview approach. In the think-aloud interview approach, research participants are given a problem to solve and are asked to say aloud everything they are thinking while solving the problem ( Ericsson and Simon, 1984 ; Keys, 2000 ). In the written think-aloud, students are asked to write, rather than say aloud, what they are thinking as they solve a problem. To train students to perform a written think-aloud, the course instructor modeled the think-aloud in class. She then assigned a homework problem that required students to answer a multiple-choice problem and construct written think-alouds recounting how they solved the problem. We then reviewed students’ homework and provided feedback. We selected examples of good documentation and poor documentation and published these anonymously on the online course-management system. After this training and feedback, we included four problems on every exam for which we asked students to provide a written think-aloud description. We collected 1087 written think-alouds from 140 students (63% of course enrollment, n = 222) for 13 problems. Figure 2 shows a typical example of a student written think-aloud.

FIGURE 2.

FIGURE 2. Written think-aloud from an introductory biology student who had been instructed to write down her procedures for solving a multiple-choice biology problem. This document describes the student’s procedures for solving the problem shown in Figure 1 .

Data Analysis

We analyzed students’ written think-alouds using a combination of qualitative and quantitative methods. We used qualitative content analysis ( Patton, 1990 ) to identify and categorize the primary patterns of student thinking during problem solving. We used quantitative analysis to determine the relationship between use of domain-general, hybrid, and domain-specific procedures and problem type and to investigate the impact of domain-general/hybrid and domain-specific procedure use on answering correctly.

Qualitative Analyses of Students’ Written Think-alouds.

The goal of our qualitative analysis was to identify the cognitive procedures students follow to solve multiple-choice biology problems during an exam. Our qualitative analysis took place in two phases.

Phase 1: Establishing Categories of Student Problem-Solving Procedures.

Independently, we read dozens of individual think-alouds for each problem. While we read, we made notes about the types of procedures we observed. One author (P.P.L.) noted, for example, that students recalled concepts, organized their thinking, read and ruled out multiple-choice options, explained their selections, and weighed the pros and cons of multiple-choice options. The other author (L.B.P.) noted that students recalled theories, interpreted a phylogenetic tree, identified incomplete information, and refuted incorrect information. After independently reviewing the written think-alouds, we met to discuss what we had found and to build an initial list of categories of problem-solving procedures. Based on our discussion, we built a master list of categories of procedures (Supplemental Table S1).

Next, we compared our list with Bloom’s Taxonomy of Educational Objectives ( Anderson and Krathwohl, 2001 ) and the Blooming Biology Tool ( Crowe et al. , 2008 ). We sought to determine whether the cognitive processes described in these sources corresponded to the cognitive processes we observed in our initial review of students’ written think-alouds. Where there was overlap, we renamed our categories to use the language of Bloom’s taxonomy. For the categories that did not overlap, we kept our original names.

Phase 2: Assigning Student Problem-Solving Procedures to Categories.

Using the list of categories developed in phase 1, we categorized every problem-solving procedure articulated by students in the written think-alouds. We analyzed 1087 documents for 13 problems. For each of the 13 problems, we followed the same categorization process. In a one-on-one meeting, we discussed a few written think-alouds. While still in the same room, we categorized several written think-alouds independently. We then compared our categorizations and discussed any disagreements. We then repeated these steps for additional think-alouds while still together. Once we reached agreement on all categories for a single problem, we independently categorized a common subset of written think-alouds to determine interrater reliability. When interrater reliability was below a level we considered acceptable (0.8 Cronbach’s alpha), we went through the process again. Then one author (either L.B.P. or P.P.L.) categorized the remainder of the written think-alouds for that problem.

At the end of phase 2, after we had categorized all 1087 written think-alouds, we refined our category list, removing categories with extremely low frequencies and grouping closely related categories. For example, we combined the category Executing with Implementing into a category called Analyzing Visual Representations.

Phase 3: Aligning Categories with Our Theoretical Framework.

Having assigned student problem-solving procedures to categories, we determined whether the category aligned best with domain-general or domain-specific problem solving. To make this determination, we considered the extent to which the problem-solving procedures in a category depended on knowledge of biology. Categories of procedures aligned with domain-general problem solving were carried out without drawing on content knowledge (e.g., Clarifying). Categories aligned with domain-specific problem solving were carried out using content knowledge (e.g., Checking). We also identified two categories of problem solving that we labeled hybrids of domain-general and domain-specific problem solving, because students used content knowledge in these steps, but they did so superficially (e.g., Recognizing).

Supplemental Table S1 shows the categories that resulted from our analytical process, including phase 1 notes, phase 2 categories, and phase 3 final category names as presented in this paper. Categories are organized into the themes of domain-general, hybrid, and domain-specific problem solving (Supplemental Table S1).

Quantitative Analyses of Students’ Written Think-Alouds.

To determine whether students used domain-general/hybrid or domain-specific problem solving preferentially when solving problems ranked by faculty as lower order or higher order, we used generalized linear mixed models (GLMM). GLMM are similar to ordinary linear regressions but take into account nonnormal distributions. GLMM can also be applied to unbalanced repeated measures ( Fitzmaurice et al. , 2011 ). In our data set, an individual student could provide documentation to one or more problems (up to 13 problems). Thus, in some but not all cases, we have repeated measures for individuals. To account for these repeated measures, we used “student” as our random factor. We used the problem type (lower order or higher order) as our fixed factor. Because our independent variables, number of domain-general/hybrid procedures and number of domain-specific procedures, are counts, we used a negative binomial regression. For this analysis and subsequent quantitative analyses, we grouped domain-general and hybrid procedures. Even though hybrid procedures involve some use of content knowledge, the content knowledge is used superficially; we specifically wanted to investigate the impact of weak content-knowledge use compared with strong content-knowledge use. Additionally, the number of hybrid procedures in our data set is relatively low compared with domain-general and domain-specific.

To determine whether students who used more domain-general/hybrid procedures or domain-specific procedures were more likely to have correct answers to the problems, we also used GLMM. We used the number of domain-general/hybrid procedures and the number of domain-specific procedures as our fixed factors and student as our random factor. In this analysis, our dependent variable (correct or incorrect response) was dichotomous, so we used a logistic regression ( Fitzmaurice et al. , 2011 ). We also explored the correlations between the average number of domain-general/hybrid and domain-specific procedures used by students and their final percentage of points for the course.

In this section, we present the results of our analyses of students’ procedures while solving 13 multiple-choice, biology problems ( Figure 1 and Supplemental Figure S1). We used the written think-aloud protocol to discover students’ problem-solving procedures for all 13 problems.

Students Use Domain-General and Domain-Specific Procedures to Solve Multiple-Choice Biology Problems

We identified several categories of procedures practiced by students during problem solving, and we organized these categories based on the extent to which they drew upon knowledge of biology. Domain-general procedures do not depend on biology content knowledge. These procedures also could be used in other domains. Hybrid procedures show students assessing multiple-choice options with limited and superficial references to biology content knowledge. Domain-specific procedures depend on biology content knowledge and reveal students’ retrieval and processing of correct ideas about biology.

Domain-General Procedures.

We identified five domain-general problem-solving procedures that students practiced ( Table 2 ). Three of these have been described in Bloom’s taxonomy ( Anderson and Krathwohl, 2001 ). These include Analyzing Domain-General Visual Representations, Clarifying, and Comparing Language of Options. In addition, we discovered two other procedures, Correcting and Delaying, that we also categorized as domain general ( Table 2 ).

The procedures are categorized as domain-general, hybrid, and domain-specific. Superscripts indicate whether the problem-solving procedure aligns with previously published conceptions of student thinking or was newly identified in this study: a Anderson and Krathwohl (2001) ; b identified in this study; c Crowe et al . (2008) .

During Correcting, students practiced metacognition. Broadly defined, metacognition occurs when someone knows, is aware of, or monitors his or her own learning ( White, 1998 ). When students corrected, they identified incorrect thinking they had displayed earlier in their written think-aloud and mentioned the correct way of thinking about the problem.

When students Delayed, they described their decision to postpone full consideration of one multiple-choice option until they considered other multiple-choice options. We interpreted these decisions as students either not remembering how the option connected with the question or not being able to connect that option to the question well enough to decide whether it could be the right answer.

Hybrid Procedures.

We identified two problem-solving procedures that we categorized as hybrid, Comparing Correctness of Options and Recognizing. Students who compared correctness of options stated that one choice appeared more correct than the other without giving content-supported reasoning for their choice. Similarly, students who recognized an option as correct did not support this conclusion with a content-based rationale.

Domain-Specific Procedures.

In our data set, we identified six domain-specific problem-solving procedures practiced by students ( Table 2 ). Four of these have been previously described. Specifically, Analyzing Domain-Specific Visual Representations, Checking, and Recalling were described in Bloom’s taxonomy ( Anderson and Krathwohl, 2001 ). Predicting was described by Crowe and colleagues (2008) . We identified two additional categories of domain-specific problem-solving procedures practiced by students who completed our problem set, Adding Information and Asking a Question.

Adding Information occurred when students recalled material that was pertinent to one of the multiple-choice options and incorporated that information into their explanations of why a particular option was wrong or right.

Asking a Question provides another illustration of students practicing metacognition. When students asked a question, they pointed out that they needed to know some specific piece of content that they did not know yet. Typically, students who asked a question did so repeatedly in a single written think-aloud.

Students Make Errors While Solving Multiple-Choice Biology Problems

In addition to identifying domain-general, hybrid, and domain-general procedures that supported students’ problem-solving, we identified errors in students’ problem solving. We observed six categories of errors, including four that we categorized as domain general and two categorized as domain specific ( Table 3 ).

The errors are presented in alphabetical order, described, and illustrated with example quotes from different students’ documentation of their solutions to the problem shown in Figure 1 (except for Misreading, which is from problem 13 in Supplemental Figure S1).

The domain-general errors include Contradicting, Disregarding Evidence, Misreading, and Opinion-Based Judgment. In some cases, students made statements that they later contradicted; we called this Contradicting. Disregarding Evidence occurred when students’ failed to indicate use of evidence. Several problems included data in the question prompt or in visual representations. These data could be used to help students select the best multiple-choice option, yet many students gave no indication that they considered these data. When students’ words led us to believe that they did not examine the data, we assigned the category Disregarding Evidence.

Students also misread the prompt or the multiple-choice options, and we termed this Misreading. For example, Table 3 shows the student Misreading; the student states that Atlantic eels are in the presence of krait toxins, whereas the question prompt stated there are no krait in the Atlantic Ocean. In other cases, students stated that they arrived at a decision based on a feeling or because that option just seemed right. For example, in selecting option C for the stickleback problem ( Figure 1 ), one student said, “E may be right, but I feel confident with C. I chose Answer C.” These procedures were coded as Opinion-Based Judgment.

We identified two additional errors that we classified as domain specific, Making Incorrect Assumptions and Misunderstanding Content. Making Incorrect Assumptions was identified when students made faulty assumptions about the information provided in the prompt. In these cases, students demonstrated in one part of their written think-aloud that they understood the conditions for or components of a concept. However, in another part of the written think-aloud, students assumed the presence or absence of these conditions or components without carefully examining whether they held for the given problem. In the example shown in Table 3 , the student assumed additional information on fertility that was not provided in the problem.

We classified errors that showed a poor understanding of the biology content as Misunderstanding Content. Misunderstanding Content was exhibited when students stated incorrect facts from their long-term memory, made false connections between the material presented and biology concepts, or showed gaps in their understanding of a concept. In the Misunderstanding Content example shown in Table 3 , the student did not understand that the biological species concept requires two conditions, that is, the offspring must be viable and fertile. The student selected the biological species concept based only on evidence of viability, demonstrating misunderstanding.

To illustrate the problem-solving procedures described above, we present three student written think-alouds ( Table 4, A–C ). All three think-alouds were generated in response to the stickleback problem; pseudonyms are used to protect students’ identities ( Figure 1 ). Emily correctly solved the stickleback problem using a combination of domain-general and domain-specific procedures ( Table 4A ). She started by thinking about the type of answer she was looking for (Predicting). Then she analyzed the stickleback drawings and population table (Analyzing Domain-General Visual Representations) and explained why options were incorrect or correct based on her knowledge of species concepts (Checking). Brian ( Table 4B ) took an approach that included domain-general and hybrid procedures. He also made some domain-general and domain-specific errors, which resulted in an incorrect answer; Brian analyzed some of the domain-general visual representations presented in the problem but disregarded others. He misunderstood the content, incorrectly accepting the biological species concept. He also demonstrated Recognizing when he correctly eliminated choice B without giving a rationale for this step. In our third example ( Table 4C ), Jessica used domain-general, hybrid, and domain-specific procedures, along with a domain-specific error, and arrived at an incorrect answer.

Different types of problem-solving processes are indicated with different font types: Domain-general problem-solving steps: blue lowercase font; domain-specific problem-solving steps: blue uppercase font, hybrid problem-solving steps: blue italics; domain-general errors: orange lowercase font; domain-specific errors: orange uppercase font. The written think-alouds are presented in the exact words of the students. A, Emily, all domain-general and domain-specific steps; correct answer: E; B, Brian, domain-general and hybrid steps, domain-general and domain-specific errors; incorrect answer: C; C, Jessica, domain-general, hybrid, and domain-specific steps; domain-specific errors; incorrect answer: C.

Domain-Specific Procedures Are Used More Frequently for Higher-Order Problems Than Lower-Order Problems

To determine the extent to which students use domain-general and domain-specific procedures when solving lower-order versus higher-order problems, we determined the frequency of domain-general and hybrid procedures and domain-specific procedures for problems categorized by experts as lower order or higher order. We grouped domain-general and hybrid procedures, because we specifically wanted to examine the difference between weak and strong content usage. As Table 5, A and B , shows, students frequently used both domain-general/hybrid and domain-specific procedures to solve all problems. For domain-general/hybrid procedures, by far the most frequently used procedure for lower-order problems was Recognizing ( n = 413); the two most frequently used procedures for higher-order problems were Analyzing Domain-General Representations ( n = 153) and Recognizing ( n = 105; Table 5A ). For domain-specific procedures, the use of Checking dominated both lower-order ( n = 903) and higher-order problems ( n = 779). Recalling also was used relatively frequently for lower-order problems ( n = 207), as were Analyzing Domain-Specific Visual Representations, Predicting, and Recalling for higher-order problems ( n = 120, n = 106, and n = 107, respectively). Overall, students used more domain-general and hybrid procedures when solving lower-order problems (1.43 ± 1.348 per problem) than when solving higher-order problems (0.74 ± 1.024 per problem; binomial regression B = 0.566, SE = 0.079, p < 0.005). Students used more domain-specific procedures when solving higher-order problems (2.57 ± 1.786 per problem) than when solving lower-order problems (2.38 ± 2.2127 per problem; binomial regression B = 0.112, SE = 0.056, p < 0.001).

Procedures are presented from left to right in alphabetical order. A color scale is used to represent the frequency of each procedure, with the lowest-frequency procedures shown in dark blue, moderate-frequency procedures shown in white, and high-frequency procedures shown in dark red.

Most Problem-Solving Errors Made by Students Involve Misunderstanding Content

We also considered the frequency of problem-solving errors made by students solving lower-order and higher-order problems. As Table 6 shows, most errors were categorized with the domain-specific category Misunderstanding Content, and this occurred with about equal frequency in lower-order and higher-order problems. The other categories of errors were less frequent. Interestingly, the domain-general errors Contradicting and Opinion-Based Judgment both occurred more frequently with lower-order problems. In contrast, the domain-specific error Making Incorrect Assumptions occurred more frequently with higher-order problems.

Categories of errors are presented from left to right in alphabetical order. A color scale is used to represent the frequency of each type of error, with the lowest-frequency errors shown in dark blue, moderate-frequency errors shown in white, and high-frequency errors shown in dark red.

Using Multiple Domain-Specific Procedures Increases the Likelihood of Answering a Problem Correctly

To examine the extent to which the use of domain-general or domain-specific procedures influences the probability of answering problems correctly, we performed a logistic regression. Predicted probabilities of answering correctly are shown in Figure 3 for domain-general and hybrid procedures and Figure 4 for domain-specific procedures. Coefficients of the logistic regression analyses are presented in Supplemental Tables S2 and S3. As Figure 3 shows, using zero domain-general or hybrid procedures was associated with a 0.53 predicted probability of being correct. Using one domain-general or hybrid procedure instead of zero increased the predicted probability of correctly answering a problem to 0.79. However, students who used two or more domain-general or hybrid procedures instead of one did not increase the predicted probability of answering a problem correctly. In contrast, as Figure 4 shows, using zero domain-specific procedures was associated with only a 0.34 predicted probability of answering the problem correctly, and students who used one domain-specific procedure had a 0.54 predicted probability of success. Strikingly, the more domain-specific procedures used by students, the more likely they were to answer a problem correctly up to five procedures; students who used five domain-specific procedures had a 0.97 probability of answering correctly. Predicted probabilities for students using seven and nine domain-specific codes show large confidence intervals around the predictions due to the low sample size ( n = 8 and 4, respectively). Also, we examined the extent to which the use of domain-general or domain-specific procedures correlates with course performance. We observed a weak positive correlation between the average number of domain-specific procedures used by students for a problem and their final percentage of points in the course (Spearman’s rho = 0.306; p < 0.001). There was no correlation between the average number of domain-general/hybrid procedures used by students for a problem and their final percentage of points in the course (Spearman’s rho = 0.015; p = 0.857).

FIGURE 3.

FIGURE 3. Predicted probability of a correct answer based on the number of domain-general and hybrid procedures.

FIGURE 4.

FIGURE 4. Predicted probability of a correct answer based on the number of domain-specific procedures.

We have used the theoretical framework of domain-specific problem solving to investigate student cognition during problem solving of multiple-choice biology problems about ecology, evolution, and systems biology. Previously, research exploring undergraduate cognition during problem solving has focused on problem categorization or students’ solutions to open-response problems ( Smith and Good, 1984 ; Smith, 1988 ; Lavoie, 1993 ; Nehm and Ridgway, 2011 ; Smith et al. 2013 ). Our goal was to describe students’ procedural knowledge, including the errors they made in their procedures. Below we draw several important conclusions from our findings and consider the implications of this research for teaching and learning.

Domain-Specific Problem Solving Should Be Used for Innovative Investigations of Biology Problem Solving

Students in our study used a variety of procedures to solve multiple-choice biology problems, but only a few procedures were used at high frequency, such as Recognizing and Checking. Other procedures that biology educators might most want students to employ were used relatively infrequently, including Correcting and Predicting. Still other procedures that we expected to find in our data set were all but absent, such as Stating Assumptions. Our research uncovers the range of procedures promoted by multiple-choice assessment in biology. Our research also provides evidence for the notion that multiple-choice assessments are limited in their ability to prompt some of the critical types of thinking used by biologists.

We propose that our categorization scheme and the theoretical framework of domain-specific problem solving should be applied for further study of biology problem solving. Future studies could be done to understand whether different ways of asking students to solve a problem at the same Bloom’s level could stimulate students to use different procedures. For example, if the stickleback problem ( Figure 1 ) were instead presented to students as a two-tier multiple-choice problem, as multiple true–false statements, or as a constructed-response problem, how would students’ procedures differ? Additionally, it would be useful to investigate whether the more highly desired, but less often observed procedures of Correcting and Predicting are used more frequently in upper-level biology courses and among more advanced biology students.

We also propose research to study the interaction between procedure and content. With our focus on procedural knowledge, we intentionally avoided an analysis of students’ declarative knowledge. However, our process of analysis led us to the conclusion that our framework can be expanded for even more fruitful research. For example, one could look within the procedural category Checking to identify the declarative knowledge being accessed. Of all the relevant declarative knowledge for a particular problem, which pieces do students typically access and which pieces are typically overlooked? The answer to this question may tell us that, while students are using an important domain-specific procedure, they struggle to apply a particular piece of declarative knowledge. As another example, one could look within the procedural category Analyzing Visual Representations to identify aspects of the visual representation that confuse or elude students. Findings from this type of research would show us how to modify visual representations for clarity or how to scaffold instruction for improved learning. We are suggesting that future concurrent studies of declarative and procedural knowledge will reveal aspects of student cognition that will stay hidden if these two types of knowledge are studied separately. Indeed, problem-solving researchers have investigated these types of interactions in the area of comprehension of science textbooks ( Alexander and Kulikowich, 1991 , 1994 ).

Lower-Order Problems May Not Require Content Knowledge, While Higher-Order Problems Promote Strong Content Usage

Because of the pervasive use among biology educators of Bloom’s taxonomy to write and evaluate multiple-choice assessments, we decided it was valuable to examine the relationship between domain-general and domain-specific procedures and lower-order versus higher-order problems.

For both lower-order and higher-order problems, domain-specific procedures were used much more frequently than domain-general procedures ( Table 5, A and B ). This is comforting and unsurprising. We administered problems about ecosystems, evolution, and structure–function relationships, so we expected and hoped students would use their knowledge of biology to solve these problems. However, two other results strike us as particularly important. First, domain-general procedures are highly prevalent ( Table 5A , n = 1108 across all problems). The use of domain-general procedures is expected. There are certain procedures that are good practice in problem solving regardless of content, such as Analyzing Domain-General Visual Representations and Clarifying. However, students’ extensive use of other domain-general/hybrid categories, namely Recognizing, is disturbing. Here we see students doing what all biology educators who use multiple-choice assessment fear, scanning the options for one that looks right based on limited knowledge. It is even more concerning that students’ use of Recognizing is nearly four times more prevalent in lower-order problems than higher-order problems and that overall domain-general procedures are more prevalent in lower-order problems ( Table 5A ). As researchers have discovered, lower-order problems, not higher-order problems, are the type most often found in college biology courses ( Momsen et al ., 2010 ). That means biology instructors’ overreliance on lower-order assessment is likely contributing to students’ overreliance on procedures that do not require biology content knowledge.

Second, it is striking that domain-specific procedures are more prevalent among higher-order problems than lower-order problems. These data suggest that higher-order problems promote strong content usage by students. As others have argued, higher-order problems should be used in class and on exams more frequently ( Crowe et al. , 2008 ; Momsen et al. , 2010 ).

Using Domain-Specific Procedures May Improve Student Performance

Although it is interesting in and of itself to learn the procedures used by students during multiple-choice assessment, the description of these categories of procedures begs the question: does the type of procedure used by students make any difference in their ability to choose a correct answer? As explained in the Introduction , the strongest problem-solving approaches stem from a relatively complete and well-organized knowledge base within a domain ( Chase and Simon, 1973 ; Chi et al. , 1981 ; Pressley et al. , 1987 ; Alexander and Judy, 1998). Thus, we hypothesized that use of domain-specific procedures would be associated with solving problems correctly, but use of domain-general procedures would not. Indeed, our data support this hypothesis. While limited use of domain-general procedures was associated with improved probability of success in solving multiple-choice problems, students who practiced extensive domain-specific procedures almost guaranteed themselves success in multiple-choice problem solving. In addition, as students used more domain-specific procedures, there was a weak but positive increase in the course performance, while use of domain-general procedures showed no correlation to performance. These data reiterate the conclusions of prior research that successful problem solvers connect information provided within the problem to their relatively strong domain-specific knowledge ( Smith and Good, 1984 ; Pressley et al. , 1987 ). In contrast, unsuccessful problem solvers heavily depend on relatively weak domain-specific knowledge ( Smith and Good, 1984 ; Smith, 1988 ). General problem-solving procedures can be used to make some progress in reaching a solution to domain-specific problems, but a problem solver can get only so far with this type of thinking. In solving domain-specific problems, at some point, the solver has to understand the particulars of a domain to reach a legitimate solution (reviewed in Pressley et al. , 1987 ; Bassok and Novick, 2012 ). Likewise, problem solvers who misunderstand key conceptual pieces or cannot identify the deep, salient features of a problem will generate inadequate, incomplete, or faulty solutions ( Chi et al. , 1981 ; Nehm and Ridgway, 2011 ).

Our findings strengthen the conclusions of previous work in two important ways. First, we studied problems from a wider range of biology topics. Second, we studied a larger population of students, which allowed us to use both qualitative and quantitative methods.

Limitations of This Research

Think-aloud protocols typically take place in an interview setting in which students verbally articulate their thought processes while solving a problem. When students are silent, the interviewer is there to prompt them to continue thinking aloud. We modified this protocol and taught students how to write out their procedures. However, one limitation of this study and all think-aloud studies is that it is not possible to analyze what students may have been thinking but did not state. Despite this limitation, we were able to identify a range of problem-solving procedures and errors that inform teaching and learning.

Implications for Teaching and Learning

There is general consensus among biology faculty that students need to develop problem-solving skills ( NRC, 2003 ; AAAS, 2011 ). However, problem solving is not intuitive to students, and these skills typically are not explicitly taught in the classroom ( Nehm, 2010 ; Hoskinson et al. , 2013 ). One reason for this misalignment between faculty values and their teaching practice is that biology problem-solving procedures have not been clearly defined. Our research presents a categorization of problem-solving procedures that faculty can use in their teaching. Instructors can use these well-defined problem-solving procedures to help students manage their knowledge of biology; students can be taught when and how to apply knowledge and how to restructure it. This gives students the tools to become more independent problem solvers ( Nehm, 2010 ).

We envision at least three ways that faculty can encourage students to become independent problem solvers. First, faculty can model the use of problem-solving procedures described in this paper and have students write out their procedures, which makes them explicit to both the students and instructor. Second, models should focus on domain-specific procedures, because these steps improve performance. Explicit modeling of domain-specific procedures would be eye-opening for students, who tend to think that studying for recognition is sufficient, particularly for multiple-choice assessment. However, our data and those of other researchers ( Stanger-Hall, 2012 ) suggest that studying for and working through problems using strong domain-specific knowledge can improve performance, even on multiple-choice tests. Third, faculty should shift from the current predominant use of lower-order problems ( Momsen et al. , 2010 ) toward the use of more higher-order problems. Our data show that lower-order problems prompt for domain-general problem solving, while higher-order problems prompt for domain-specific problem solving.

We took what we learned from the investigation reported here and applied it to develop an online tutorial called SOLVEIT for undergraduate biology students ( Kim et al. , 2015 ). In SOLVEIT, students are presented with problems similar to the stickleback problem shown in Figure 1 . The problems focus on species concepts and ecological relationships. In brief, SOLVEIT asks students to provide an initial solution to each problem, and then it guides students through the problem in a step-by-step manner that encourages them to practice several of the problem-solving procedures reported here, such as Recalling, Checking, Analyzing Visual Representations, and Correcting. In the final stages of SOLVEIT, students are asked to revise their initial solutions and to reflect on an expert’s solution as well as their own problem-solving process ( Kim et al. , 2015 ). Our findings of improved student learning with SOLVEIT ( Kim et al. , 2015 ) are consistent with the research of others that shows scaffolding can improve student problem solving ( Lin and Lehman, 1999 ; Belland, 2010 ; Singh and Haileselassie, 2010 ). Thus, research to uncover the difficulties of students during problem solving can be directly applied to improve student learning.

ACKNOWLEDGMENTS

We thank the students who participated in this study and the biology faculty who served as experts by providing Bloom’s rankings for each problem. We also thank the Biology Education Research Group at UGA, who improved the quality of this work with critical feedback on the manuscript. Finally, we thank the reviewers, whose feedback greatly improved the manuscript. Resources for this research were provided by UGA and the UGA Office of STEM Education.

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Submitted: 17 December 2015 Revised: 10 June 2016 Accepted: 11 June 2016

© 2016 L. B. Prevost and P. P. Lemons. CBE—Life Sciences Education © 2016 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

  • 1.1 The Science of Biology
  • Introduction
  • 1.2 Themes and Concepts of Biology
  • Chapter Summary
  • Review Questions
  • Critical Thinking Questions
  • Test Prep for AP® Courses
  • 2.1 Atoms, Isotopes, Ions, and Molecules: The Building Blocks
  • Science Practice Challenge Questions
  • 3.1 Synthesis of Biological Macromolecules
  • 3.2 Carbohydrates
  • 3.4 Proteins
  • 3.5 Nucleic Acids
  • 4.1 Studying Cells
  • 4.2 Prokaryotic Cells
  • 4.3 Eukaryotic Cells
  • 4.4 The Endomembrane System and Proteins
  • 4.5 Cytoskeleton
  • 4.6 Connections between Cells and Cellular Activities
  • 5.1 Components and Structure
  • 5.2 Passive Transport
  • 5.3 Active Transport
  • 5.4 Bulk Transport
  • 6.1 Energy and Metabolism
  • 6.2 Potential, Kinetic, Free, and Activation Energy
  • 6.3 The Laws of Thermodynamics
  • 6.4 ATP: Adenosine Triphosphate
  • 6.5 Enzymes
  • 7.1 Energy in Living Systems
  • 7.2 Glycolysis
  • 7.3 Oxidation of Pyruvate and the Citric Acid Cycle
  • 7.4 Oxidative Phosphorylation
  • 7.5 Metabolism without Oxygen
  • 7.6 Connections of Carbohydrate, Protein, and Lipid Metabolic Pathways
  • 7.7 Regulation of Cellular Respiration
  • 8.1 Overview of Photosynthesis
  • 8.2 The Light-Dependent Reaction of Photosynthesis
  • 8.3 Using Light to Make Organic Molecules
  • 9.1 Signaling Molecules and Cellular Receptors
  • 9.2 Propagation of the Signal
  • 9.3 Response to the Signal
  • 9.4 Signaling in Single-Celled Organisms
  • 10.1 Cell Division
  • 10.2 The Cell Cycle
  • 10.3 Control of the Cell Cycle
  • 10.4 Cancer and the Cell Cycle
  • 10.5 Prokaryotic Cell Division
  • 11.1 The Process of Meiosis
  • 11.2 Sexual Reproduction
  • 12.1 Mendel’s Experiments and the Laws of Probability
  • 12.2 Characteristics and Traits
  • 12.3 Laws of Inheritance
  • 13.1 Chromosomal Theory and Genetic Linkages
  • 13.2 Chromosomal Basis of Inherited Disorders
  • 14.1 Historical Basis of Modern Understanding
  • 14.2 DNA Structure and Sequencing
  • 14.3 Basics of DNA Replication
  • 14.4 DNA Replication in Prokaryotes
  • 14.5 DNA Replication in Eukaryotes
  • 14.6 DNA Repair
  • 15.1 The Genetic Code
  • 15.2 Prokaryotic Transcription
  • 15.3 Eukaryotic Transcription
  • 15.4 RNA Processing in Eukaryotes
  • 15.5 Ribosomes and Protein Synthesis
  • 16.1 Regulation of Gene Expression
  • 16.2 Prokaryotic Gene Regulation
  • 16.3 Eukaryotic Epigenetic Gene Regulation
  • 16.4 Eukaryotic Transcriptional Gene Regulation
  • 16.5 Eukaryotic Post-transcriptional Gene Regulation
  • 16.6 Eukaryotic Translational and Post-translational Gene Regulation
  • 16.7 Cancer and Gene Regulation
  • 17.1 Biotechnology
  • 17.2 Mapping Genomes
  • 17.3 Whole-Genome Sequencing
  • 17.4 Applying Genomics
  • 17.5 Genomics and Proteomics
  • 18.1 Understanding Evolution
  • 18.2 Formation of New Species
  • 18.3 Reconnection and Rates of Speciation
  • 19.1 Population Evolution
  • 19.2 Population Genetics
  • 19.3 Adaptive Evolution
  • 20.1 Organizing Life on Earth
  • 20.2 Determining Evolutionary Relationships
  • 20.3 Perspectives on the Phylogenetic Tree
  • 21.1 Viral Evolution, Morphology, and Classification
  • 21.2 Virus Infection and Hosts
  • 21.3 Prevention and Treatment of Viral Infections
  • 21.4 Other Acellular Entities: Prions and Viroids
  • 22.1 Prokaryotic Diversity
  • 22.2 Structure of Prokaryotes
  • 22.3 Prokaryotic Metabolism
  • 22.4 Bacterial Diseases in Humans
  • 22.5 Beneficial Prokaryotes
  • 23.1 The Plant Body
  • 23.4 Leaves
  • 23.5 Transport of Water and Solutes in Plants
  • 23.6 Plant Sensory Systems and Responses
  • 24.1 Animal Form and Function
  • 24.2 Animal Primary Tissues
  • 24.3 Homeostasis
  • 25.1 Digestive Systems
  • 25.2 Nutrition and Energy Production
  • 25.3 Digestive System Processes
  • 25.4 Digestive System Regulation
  • 26.1 Neurons and Glial Cells
  • 26.2 How Neurons Communicate
  • 26.3 The Central Nervous System
  • 26.4 The Peripheral Nervous System
  • 26.5 Nervous System Disorders
  • 27.1 Sensory Processes
  • 27.2 Somatosensation
  • 27.3 Taste and Smell
  • 27.4 Hearing and Vestibular Sensation
  • 27.5 Vision
  • 28.1 Types of Hormones
  • 28.2 How Hormones Work
  • 28.3 Regulation of Body Processes
  • 28.4 Regulation of Hormone Production
  • 28.5 Endocrine Glands
  • 29.1 Types of Skeletal Systems
  • 29.3 Joints and Skeletal Movement
  • 29.4 Muscle Contraction and Locomotion
  • 30.1 Systems of Gas Exchange
  • 30.2 Gas Exchange across Respiratory Surfaces
  • 30.3 Breathing
  • 30.4 Transport of Gases in Human Bodily Fluids
  • 31.1 Overview of the Circulatory System
  • 31.2 Components of the Blood
  • 31.3 Mammalian Heart and Blood Vessels
  • 31.4 Blood Flow and Blood Pressure Regulation
  • 32.1 Osmoregulation and Osmotic Balance
  • 32.2 The Kidneys and Osmoregulatory Organs
  • 32.3 Excretion Systems
  • 32.4 Nitrogenous Wastes
  • 32.5 Hormonal Control of Osmoregulatory Functions
  • 33.1 Innate Immune Response
  • 33.2 Adaptive Immune Response
  • 33.3 Antibodies
  • 33.4 Disruptions in the Immune System
  • 34.1 Reproduction Methods
  • 34.2 Fertilization
  • 34.3 Human Reproductive Anatomy and Gametogenesis
  • 34.4 Hormonal Control of Human Reproduction
  • 34.5 Fertilization and Early Embryonic Development
  • 34.6 Organogenesis and Vertebrate Formation
  • 34.7 Human Pregnancy and Birth
  • 35.1 The Scope of Ecology
  • 35.2 Biogeography
  • 35.3 Terrestrial Biomes
  • 35.4 Aquatic Biomes
  • 35.5 Climate and the Effects of Global Climate Change
  • 36.1 Population Demography
  • 36.2 Life Histories and Natural Selection
  • 36.3 Environmental Limits to Population Growth
  • 36.4 Population Dynamics and Regulation
  • 36.5 Human Population Growth
  • 36.6 Community Ecology
  • 36.7 Behavioral Biology: Proximate and Ultimate Causes of Behavior
  • 37.1 Ecology for Ecosystems
  • 37.2 Energy Flow through Ecosystems
  • 37.3 Biogeochemical Cycles
  • 38.1 The Biodiversity Crisis
  • 38.2 The Importance of Biodiversity to Human Life
  • 38.3 Threats to Biodiversity
  • 38.4 Preserving Biodiversity
  • A | The Periodic Table of Elements
  • B | Geological Time
  • C | Measurements and the Metric System

Learning Objectives

In this section, you will explore the following questions:

  • What are the characteristics shared by the natural sciences?
  • What are the steps of the scientific method?

Connection for AP ® courses

Biology is the science that studies living organisms and their interactions with one another and with their environment. The process of science attempts to describe and understand the nature of the universe by rational means. Science has many fields; those fields related to the physical world, including biology, are considered natural sciences. All of the natural sciences follow the laws of chemistry and physics. For example, when studying biology, you must remember living organisms obey the laws of thermodynamics while using free energy and matter from the environment to carry out life processes that are explored in later chapters, such as metabolism and reproduction.

Two types of logical reasoning are used in science: inductive reasoning and deductive reasoning. Inductive reasoning uses particular results to produce general scientific principles. Deductive reasoning uses logical thinking to predict results by applying scientific principles or practices. The scientific method is a step-by-step process that consists of: making observations, defining a problem, posing hypotheses, testing these hypotheses by designing and conducting investigations, and drawing conclusions from data and results. Scientists then communicate their results to the scientific community. Scientific theories are subject to revision as new information is collected.

The content presented in this section supports the Learning Objectives outlined in Big Idea 2 of the AP ® Biology Curriculum Framework. The Learning Objectives merge Essential Knowledge content with one or more of the seven Science Practices. These objectives provide a transparent foundation for the AP ® Biology course, along with inquiry-based laboratory experiences, instructional activities, and AP ® Exam questions.

Teacher Support

Illustrate uses of the scientific method in class. Divide students in groups of four or five and ask them to design experiments to test the existence of connections they have wondered about. Help them decide if they have a working hypothesis that can be tested and falsified. Give examples of hypotheses that are not falsifiable because they are based on subjective assessments. They are neither observable nor measurable. For example, birds like classical music is based on a subjective assessment. Ask if this hypothesis can be modified to become a testable hypothesis. Stress the need for controls and provide examples such as the use of placebos in pharmacology.

Biology is not a collection of facts to be memorized. Biological systems follow the law of physics and chemistry. Give as an example gas laws in chemistry and respiration physiology. Many students come with a 19th century view of natural sciences; each discipline is in its own sphere. Give as an example, bioinformatics which uses organism biology, chemistry, and physics to label DNA with light emitting reporter molecules (Next Generation sequencing). These molecules can then be scanned by light-sensing machinery, allowing huge amounts of information to be gathered on their DNA. Bring to their attention the fact that the analysis of these data is an application of mathematics and computer science.

For more information about next generation sequencing, check out this informative review .

What is biology? In simple terms, biology is the study of life. This is a very broad definition because the scope of biology is vast. Biologists may study anything from the microscopic or submicroscopic view of a cell to ecosystems and the whole living planet ( Figure 1.2 ). Listening to the daily news, you will quickly realize how many aspects of biology are discussed every day. For example, recent news topics include Escherichia coli ( Figure 1.3 ) outbreaks in spinach and Salmonella contamination in peanut butter. On a global scale, many researchers are committed to finding ways to protect the planet, solve environmental issues, and reduce the effects of climate change. All of these diverse endeavors are related to different facets of the discipline of biology.

The Process of Science

Biology is a science, but what exactly is science? What does the study of biology share with other scientific disciplines? Science (from the Latin scientia , meaning “knowledge”) can be defined as knowledge that covers general truths or the operation of general laws, especially when acquired and tested by the scientific method. It becomes clear from this definition that the application of the scientific method plays a major role in science. The scientific method is a method of research with defined steps that include experiments and careful observation.

The steps of the scientific method will be examined in detail later, but one of the most important aspects of this method is the testing of hypotheses by means of repeatable experiments. A hypothesis is a suggested explanation for an event, which can be tested. Although using the scientific method is inherent to science, it is inadequate in determining what science is. This is because it is relatively easy to apply the scientific method to disciplines such as physics and chemistry, but when it comes to disciplines like archaeology, psychology, and geology, the scientific method becomes less applicable as it becomes more difficult to repeat experiments.

These areas of study are still sciences, however. Consider archaeology—even though one cannot perform repeatable experiments, hypotheses may still be supported. For instance, an archaeologist can hypothesize that an ancient culture existed based on finding a piece of pottery. Further hypotheses could be made about various characteristics of this culture, and these hypotheses may be found to be correct or false through continued support or contradictions from other findings. A hypothesis may become a verified theory. A theory is a tested and confirmed explanation for observations or phenomena. Science may be better defined as fields of study that attempt to comprehend the nature of the universe.

Natural Sciences

What would you expect to see in a museum of natural sciences? Frogs? Plants? Dinosaur skeletons? Exhibits about how the brain functions? A planetarium? Gems and minerals? Or, maybe all of the above? Science includes such diverse fields as astronomy, biology, computer sciences, geology, logic, physics, chemistry, and mathematics ( Figure 1.4 ). However, those fields of science related to the physical world and its phenomena and processes are considered natural sciences . Thus, a museum of natural sciences might contain any of the items listed above.

There is no complete agreement when it comes to defining what the natural sciences include, however. For some experts, the natural sciences are astronomy, biology, chemistry, earth science, and physics. Other scholars choose to divide natural sciences into life sciences , which study living things and include biology, and physical sciences , which study nonliving matter and include astronomy, geology, physics, and chemistry. Some disciplines such as biophysics and biochemistry build on both life and physical sciences and are interdisciplinary. Natural sciences are sometimes referred to as “hard science” because they rely on the use of quantitative data; social sciences that study society and human behavior are more likely to use qualitative assessments to drive investigations and findings.

Not surprisingly, the natural science of biology has many branches or subdisciplines. Cell biologists study cell structure and function, while biologists who study anatomy investigate the structure of an entire organism. Those biologists studying physiology, however, focus on the internal functioning of an organism. Some areas of biology focus on only particular types of living things. For example, botanists explore plants, while zoologists specialize in animals.

Scientific Reasoning

One thing is common to all forms of science: an ultimate goal “to know.” Curiosity and inquiry are the driving forces for the development of science. Scientists seek to understand the world and the way it operates. To do this, they use two methods of logical thinking: inductive reasoning and deductive reasoning.

Inductive reasoning is a form of logical thinking that uses related observations to arrive at a general conclusion. This type of reasoning is common in descriptive science. A life scientist such as a biologist makes observations and records them. These data can be qualitative or quantitative, and the raw data can be supplemented with drawings, pictures, photos, or videos. From many observations, the scientist can infer conclusions (inductions) based on evidence. Inductive reasoning involves formulating generalizations inferred from careful observation and the analysis of a large amount of data. Brain studies provide an example. In this type of research, many live brains are observed while people are doing a specific activity, such as viewing images of food. The part of the brain that “lights up” during this activity is then predicted to be the part controlling the response to the selected stimulus, in this case, images of food. The “lighting up” of the various areas of the brain is caused by excess absorption of radioactive sugar derivatives by active areas of the brain. The resultant increase in radioactivity is observed by a scanner. Then, researchers can stimulate that part of the brain to see if similar responses result.

Deductive reasoning or deduction is the type of logic used in hypothesis-based science. In deductive reason, the pattern of thinking moves in the opposite direction as compared to inductive reasoning. Deductive reasoning is a form of logical thinking that uses a general principle or law to predict specific results. From those general principles, a scientist can deduce and predict the specific results that would be valid as long as the general principles are valid. Studies in climate change can illustrate this type of reasoning. For example, scientists may predict that if the climate becomes warmer in a particular region, then the distribution of plants and animals should change. These predictions have been made and tested, and many such changes have been found, such as the modification of arable areas for agriculture, with change based on temperature averages.

Both types of logical thinking are related to the two main pathways of scientific study: descriptive science and hypothesis-based science. Descriptive (or discovery) science , which is usually inductive, aims to observe, explore, and discover, while hypothesis-based science , which is usually deductive, begins with a specific question or problem and a potential answer or solution that can be tested. The boundary between these two forms of study is often blurred, and most scientific endeavors combine both approaches. The fuzzy boundary becomes apparent when thinking about how easily observation can lead to specific questions. For example, a gentleman in the 1940s observed that the burr seeds that stuck to his clothes and his dog’s fur had a tiny hook structure. On closer inspection, he discovered that the burrs’ gripping device was more reliable than a zipper. He eventually developed a company and produced the hook-and-loop fastener often used on lace-less sneakers and athletic braces. Descriptive science and hypothesis-based science are in continuous dialogue.

The Scientific Method

Biologists study the living world by posing questions about it and seeking science-based responses. This approach is common to other sciences as well and is often referred to as the scientific method. The scientific method was used even in ancient times, but it was first documented by England’s Sir Francis Bacon (1561–1626) ( Figure 1.5 ), who set up inductive methods for scientific inquiry. The scientific method is not exclusively used by biologists but can be applied to almost all fields of study as a logical, rational problem-solving method.

The scientific process typically starts with an observation (often a problem to be solved) that leads to a question. Let’s think about a simple problem that starts with an observation and apply the scientific method to solve the problem. One Monday morning, a student arrives at class and quickly discovers that the classroom is too warm. That is an observation that also describes a problem: the classroom is too warm. The student then asks a question: “Why is the classroom so warm?”

Proposing a Hypothesis

Recall that a hypothesis is a suggested explanation that can be tested. To solve a problem, several hypotheses may be proposed. For example, one hypothesis might be, “The classroom is warm because no one turned on the air conditioning.” But there could be other responses to the question, and therefore other hypotheses may be proposed. A second hypothesis might be, “The classroom is warm because there is a power failure, and so the air conditioning doesn’t work.”

Once a hypothesis has been selected, the student can make a prediction. A prediction is similar to a hypothesis but it typically has the format “If . . . then . . . .” For example, the prediction for the first hypothesis might be, “ If the student turns on the air conditioning, then the classroom will no longer be too warm.”

Testing a Hypothesis

A valid hypothesis must be testable. It should also be falsifiable , meaning that it can be disproven by experimental results. Importantly, science does not claim to “prove” anything because scientific understandings are always subject to modification with further information. This step—openness to disproving ideas—is what distinguishes sciences from non-sciences. The presence of the supernatural, for instance, is neither testable nor falsifiable. To test a hypothesis, a researcher will conduct one or more experiments designed to eliminate one or more of the hypotheses. Each experiment will have one or more variables and one or more controls. A variable is any part of the experiment that can vary or change during the experiment. The control group contains every feature of the experimental group except it is not given the manipulation that is hypothesized about. Therefore, if the results of the experimental group differ from the control group, the difference must be due to the hypothesized manipulation, rather than some outside factor. Look for the variables and controls in the examples that follow. To test the first hypothesis, the student would find out if the air conditioning is on. If the air conditioning is turned on but does not work, there should be another reason, and this hypothesis should be rejected. To test the second hypothesis, the student could check if the lights in the classroom are functional. If so, there is no power failure and this hypothesis should be rejected. Each hypothesis should be tested by carrying out appropriate experiments. Be aware that rejecting one hypothesis does not determine whether or not the other hypotheses can be accepted; it simply eliminates one hypothesis that is not valid ( see this figure ). Using the scientific method, the hypotheses that are inconsistent with experimental data are rejected.

While this “warm classroom” example is based on observational results, other hypotheses and experiments might have clearer controls. For instance, a student might attend class on Monday and realize she had difficulty concentrating on the lecture. One observation to explain this occurrence might be, “When I eat breakfast before class, I am better able to pay attention.” The student could then design an experiment with a control to test this hypothesis.

In hypothesis-based science, specific results are predicted from a general premise. This type of reasoning is called deductive reasoning: deduction proceeds from the general to the particular. But the reverse of the process is also possible: sometimes, scientists reach a general conclusion from a number of specific observations. This type of reasoning is called inductive reasoning, and it proceeds from the particular to the general. Inductive and deductive reasoning are often used in tandem to advance scientific knowledge ( see this figure ). In recent years a new approach of testing hypotheses has developed as a result of an exponential growth of data deposited in various databases. Using computer algorithms and statistical analyses of data in databases, a new field of so-called "data research" (also referred to as "in silico" research) provides new methods of data analyses and their interpretation. This will increase the demand for specialists in both biology and computer science, a promising career opportunity.

Science Practice Connection for AP® Courses

Think about it.

Almost all plants use water, carbon dioxide, and energy from the sun to make sugars. Think about what would happen to plants that don’t have sunlight as an energy source or sufficient water. What would happen to organisms that depend on those plants for their own survival?

Make a prediction about what would happen to the organisms living in a rain forest if 50% of its trees were destroyed. How would you test your prediction?

Use this example as a model to make predictions. Emphasize there is no rigid scientific method scheme. Active science is a combination of observations and measurement. Offer the example of ecology where the conventional scientific method is not always applicable because researchers cannot always set experiments in a laboratory and control all the variables.

Possible answers:

Destruction of the rain forest affects the trees, the animals which feed on the vegetation, take shelter on the trees, and large predators which feed on smaller animals. Furthermore, because the trees positively affect rain through massive evaporation and condensation of water vapor, drought follows deforestation.

Tell students a similar experiment on a grand scale may have happened in the past and introduce the next activity “What killed the dinosaurs?”

Some predictions can be made and later observations can support or disprove the prediction.

Ask, “what killed the dinosaurs?” Explain many scientists point to a massive asteroid crashing in the Yucatan peninsula in Mexico. One of the effects was the creation of smoke clouds and debris that blocked the Sun, stamped out many plants and, consequently, brought mass extinction. As is common in the scientific community, many other researchers offer divergent explanations.

Go to this site for a good example of the complexity of scientific method and scientific debate.

Visual Connection

In the example below, the scientific method is used to solve an everyday problem. Order the scientific method steps (numbered items) with the process of solving the everyday problem (lettered items). Based on the results of the experiment, is the hypothesis correct? If it is incorrect, propose some alternative hypotheses.

  • The original hypothesis is correct. There is something wrong with the electrical outlet and therefore the toaster doesn’t work.
  • The original hypothesis is incorrect. Alternative hypothesis includes that toaster wasn’t turned on.
  • The original hypothesis is correct. The coffee maker and the toaster do not work when plugged into the outlet.
  • The original hypothesis is incorrect. Alternative hypotheses includes that both coffee maker and toaster were broken.
  • All flying birds and insects have wings. Birds and insects flap their wings as they move through the air. Therefore, wings enable flight.
  • Insects generally survive mild winters better than harsh ones. Therefore, insect pests will become more problematic if global temperatures increase.
  • Chromosomes, the carriers of DNA, are distributed evenly between the daughter cells during cell division. Therefore, each daughter cell will have the same chromosome set as the mother cell.
  • Animals as diverse as humans, insects, and wolves all exhibit social behavior. Therefore, social behavior must have an evolutionary advantage.
  • 1- Inductive, 2- Deductive, 3- Deductive, 4- Inductive
  • 1- Deductive, 2- Inductive, 3- Deductive, 4- Inductive
  • 1- Inductive, 2- Deductive, 3- Inductive, 4- Deductive
  • 1- Inductive, 2-Inductive, 3- Inductive, 4- Deductive

The scientific method may seem too rigid and structured. It is important to keep in mind that, although scientists often follow this sequence, there is flexibility. Sometimes an experiment leads to conclusions that favor a change in approach; often, an experiment brings entirely new scientific questions to the puzzle. Many times, science does not operate in a linear fashion; instead, scientists continually draw inferences and make generalizations, finding patterns as their research proceeds. Scientific reasoning is more complex than the scientific method alone suggests. Notice, too, that the scientific method can be applied to solving problems that aren’t necessarily scientific in nature.

Two Types of Science: Basic Science and Applied Science

The scientific community has been debating for the last few decades about the value of different types of science. Is it valuable to pursue science for the sake of simply gaining knowledge, or does scientific knowledge only have worth if we can apply it to solving a specific problem or to bettering our lives? This question focuses on the differences between two types of science: basic science and applied science.

Basic science or “pure” science seeks to expand knowledge regardless of the short-term application of that knowledge. It is not focused on developing a product or a service of immediate public or commercial value. The immediate goal of basic science is knowledge for knowledge’s sake, though this does not mean that, in the end, it may not result in a practical application.

In contrast, applied science or “technology,” aims to use science to solve real-world problems, making it possible, for example, to improve a crop yield, find a cure for a particular disease, or save animals threatened by a natural disaster ( Figure 1.8 ). In applied science, the problem is usually defined for the researcher.

Some individuals may perceive applied science as “useful” and basic science as “useless.” A question these people might pose to a scientist advocating knowledge acquisition would be, “What for?” A careful look at the history of science, however, reveals that basic knowledge has resulted in many remarkable applications of great value. Many scientists think that a basic understanding of science is necessary before an application is developed; therefore, applied science relies on the results generated through basic science. Other scientists think that it is time to move on from basic science and instead to find solutions to actual problems. Both approaches are valid. It is true that there are problems that demand immediate attention; however, few solutions would be found without the help of the wide knowledge foundation generated through basic science.

One example of how basic and applied science can work together to solve practical problems occurred after the discovery of DNA structure led to an understanding of the molecular mechanisms governing DNA replication. Strands of DNA, unique in every human, are found in our cells, where they provide the instructions necessary for life. During DNA replication, DNA makes new copies of itself, shortly before a cell divides. Understanding the mechanisms of DNA replication enabled scientists to develop laboratory techniques that are now used to identify genetic diseases. Without basic science, it is unlikely that applied science could exist.

Another example of the link between basic and applied research is the Human Genome Project, a study in which each human chromosome was analyzed and mapped to determine the precise sequence of DNA subunits and the exact location of each gene. (The gene is the basic unit of heredity represented by a specific DNA segment that codes for a functional molecule.) Other less complex organisms have also been studied as part of this project in order to gain a better understanding of human chromosomes. The Human Genome Project ( Figure 1.9 ) relied on basic research carried out with simple organisms and, later, with the human genome. An important end goal eventually became using the data for applied research, seeking cures and early diagnoses for genetically related diseases.

While research efforts in both basic science and applied science are usually carefully planned, it is important to note that some discoveries are made by serendipity , that is, by means of a fortunate accident or a lucky surprise. Penicillin was discovered when biologist Alexander Fleming accidentally left a petri dish of Staphylococcus bacteria open. An unwanted mold grew on the dish, killing the bacteria. The mold turned out to be Penicillium , and a new antibiotic was discovered. Even in the highly organized world of science, luck—when combined with an observant, curious mind—can lead to unexpected breakthroughs.

Reporting Scientific Work

Whether scientific research is basic science or applied science, scientists must share their findings in order for other researchers to expand and build upon their discoveries. Collaboration with other scientists—when planning, conducting, and analyzing results—is important for scientific research. For this reason, important aspects of a scientist’s work are communicating with peers and disseminating results to peers. Scientists can share results by presenting them at a scientific meeting or conference, but this approach can reach only the select few who are present. Instead, most scientists present their results in peer-reviewed manuscripts that are published in scientific journals. Peer-reviewed manuscripts are scientific papers that are reviewed by a scientist’s colleagues, or peers. These colleagues are qualified individuals, often experts in the same research area, who judge whether or not the scientist’s work is suitable for publication. The process of peer review helps to ensure that the research described in a scientific paper or grant proposal is original, significant, logical, and thorough. Grant proposals, which are requests for research funding, are also subject to peer review. Scientists publish their work so other scientists can reproduce their experiments under similar or different conditions to expand on the findings.

A scientific paper is very different from creative writing. Although creativity is required to design experiments, there are fixed guidelines when it comes to presenting scientific results. First, scientific writing must be brief, concise, and accurate. A scientific paper needs to be succinct but detailed enough to allow peers to reproduce the experiments.

The scientific paper consists of several specific sections—introduction, materials and methods, results, and discussion. This structure is sometimes called the “IMRaD” format. There are usually acknowledgment and reference sections as well as an abstract (a concise summary) at the beginning of the paper. There might be additional sections depending on the type of paper and the journal where it will be published; for example, some review papers require an outline.

The introduction starts with brief, but broad, background information about what is known in the field. A good introduction also gives the rationale of the work; it justifies the work carried out and also briefly mentions the end of the paper, where the hypothesis or research question driving the research will be presented. The introduction refers to the published scientific work of others and therefore requires citations following the style of the journal. Using the work or ideas of others without proper citation is considered plagiarism .

The materials and methods section includes a complete and accurate description of the substances used, and the method and techniques used by the researchers to gather data. The description should be thorough enough to allow another researcher to repeat the experiment and obtain similar results, but it does not have to be verbose. This section will also include information on how measurements were made and what types of calculations and statistical analyses were used to examine raw data. Although the materials and methods section gives an accurate description of the experiments, it does not discuss them.

Some journals require a results section followed by a discussion section, but it is more common to combine both. If the journal does not allow the combination of both sections, the results section simply narrates the findings without any further interpretation. The results are presented by means of tables or graphs, but no duplicate information should be presented. In the discussion section, the researcher will interpret the results, describe how variables may be related, and attempt to explain the observations. It is indispensable to conduct an extensive literature search to put the results in the context of previously published scientific research. Therefore, proper citations are included in this section as well.

Finally, the conclusion section summarizes the importance of the experimental findings. While the scientific paper almost certainly answered one or more scientific questions that were stated, any good research should lead to more questions. Therefore, a well-done scientific paper leaves doors open for the researcher and others to continue and expand on the findings.

Review articles do not follow the IMRAD format because they do not present original scientific findings, or primary literature; instead, they summarize and comment on findings that were published as primary literature and typically include extensive reference sections.

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Access for free at https://openstax.org/books/biology-ap-courses/pages/1-introduction
  • Authors: Julianne Zedalis, John Eggebrecht
  • Publisher/website: OpenStax
  • Book title: Biology for AP® Courses
  • Publication date: Mar 8, 2018
  • Location: Houston, Texas
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Synthetic Biology

Synthetic biology is a field of science that involves redesigning organisms for useful purposes by engineering them to have new abilities. Synthetic biology researchers and companies around the world are harnessing the power of nature to solve problems in medicine, manufacturing and agriculture.

What can synthetic biology do?

Redesigning organisms so that they produce a substance, such as a medicine or fuel, or gain a new ability, such as sensing something in the environment, are common goals of synthetic biology projects. Some examples of what scientists are producing with synthetic biology are:

  • Microorganisms harnessed for bioremediation  to clean pollutants from our water, soil and air.
  • Rice modified to produce beta-carotene , a nutrient usually associated with carrots, that prevents  vitamin A deficiency . Vitamin A deficiency causes blindness in 250,000 - 500,000 children every year and greatly increases a child's risk of death from infectious diseases.
  • Yeast engineered to produce rose oil  as an eco-friendly and sustainable substitute for real roses that perfumers use to make luxury scents.

What is the difference between synthetic biology and genome editing?

In some ways, synthetic biology is similar to another approach called " genome editing " because both involve changing an organism's genetic code; however, some people draw a distinction between these two approaches based on how that change is made. In synthetic biology, scientists typically stitch together long stretches of DNA and insert them into an organism's genome. These synthesized pieces of DNA could be genes that are found in other organisms or they could be entirely novel. In genome editing, scientists typically use tools to make smaller changes to the organism's own DNA. Genome editing tools can also be used to delete or add small stretches of DNA in the genome.

Synthetic biology

Can you synthesize an organism's entire genome?

Can researchers synthesize an organism's entire genome? The answer to this question is yes, and it has already been done. In 2002, scientists in the United States synthesized a viral genome for the first time. Viral genomes are much smaller compared to the genomes of most bacteria and microorganisms.  Scientists  showed that it was possible to create the polio virus from scratch and brought attention to the risk that synthetic biology could be used to develop biological weapons. While this group of researchers did not intend to cause harm with their research, their work understandably raised concerns that bad actors might use synthetic biology for malicious purposes. Please see the " What are the ethical and social implications ?" section of this resource to learn about the federal regulations in place to regulate so-called " dual use research of concern ", or research that could be directly misapplied to pose a significant threat to public health and safety, agricultural crops and other plants, animals, the environment, or national security.

The first synthetic bacterial genome was completed in 2008 with the  synthesis of the genome of  Mycoplasm genitalium , a bacterium that can cause urinary and genital tract infections in humans. In 2017, another group of scientists  partially synthesized the genome of  Saccharomyces cerevisiae , the yeast that is used to make bread and brew wine and beer.

Today, researchers are continuing to push the limits of existing DNA-synthesis technology to help understand how genomes work. One group of researchers, called the  "Genome Project-Write"  (GP-Write)", is seeking to synthesize, or "write" whole genomes from human cell lines and the genomes of other plants and animals important to agriculture and public health. The name of their project is a play on the  Human Genome Project  (HGP). In 2003, scientists working on the HGP  sequenced , or "read", the more than 3 billion DNA letters, or base pairs, that make up the human genome. One of the leading motivations for GP-Write is to stimulate innovation in DNA synthesis technologies through the proposed research. Importantly, the research in GP-Write involving human genomes will occur only in cells and no human embryos will be used in this research.

What are the ethical and social implications?

Projects that propose to synthesize entire genomes raise important ethical questions about potential harms and benefits to society. Many of the ethical questions relevant to synthetic biology are similar to  ethical discussions related to genome editing . Are humans crossing moral boundaries by redesigning organisms with synthetic biology techniques? If synthetic biology yields new treatments and cures for diseases, who in our society will have access to them? What are the environmental impacts of introducing modified organisms into the ecosystem? Such ethical questions have been the subject of  research  since the beginning of the HGP and will continue to be researched as technology evolves and changes. Most scientists, ethicists and policymakers agree that entire societies must discuss and weigh the potential harms and benefits of synthetic biology in order to answer these questions. Leading voices in bioethics, including the  Presidential Commission for the Study of Bioethical Issues  and the  National Academies of Sciences, Engineering and Medicine , have expressed the importance of public engagement and dialogue in the governance of emerging synthetic biology and genome editing technologies.

As the synthesis of the polio virus demonstrates, there are also biosecurity concerns related to synthetic biology. The US government's  Federal Select Agents Program  regulates the possession of high-risk infectious agents like polio for research and other purposes. Additionally, federally-funded research, such as research supported by the National Institutes of Health (NIH) that involves high-risk infectious agents, is subject to additional oversight and risk management as laid out by the  Dual Use Research of Concern (DURC) policy. For more information about the biosecurity policies that NIH has in place, please visit  this website . More broadly, the federal government has a policy in place, called the  Coordinated Framework for Regulation of Biotechnology , to oversee the introduction of synthetic biology products into the market.

For additional resources about the ethics, governance and societal implications of synthetic biology, please refer to the following websites and publications:

Resources Related to the Ethical and Social Implications of Synthetic Biology:

  • Biodefense in the Age of Synthetic Biology  (National Academies of Sciences, Engineering, and Medicine)
  • Human Genome Editing: Science, Ethics, and Governance  (National Academies of Sciences, Engineering, and Medicine)
  • New Directions: The Ethics of Synthetic Biology and Emerging Technologies  (Presidential Commission for the Study of Bioethical Issues)

Additional Resources

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Building with Biology

Synthetic Biology News

Last updated: August 14, 2019

problem 1. A question proposed for solution ; a matter stated for examination or proof; hence, a matter difficult of solution or settlement; a doubtful case; a question involving doubt. 2. (Science: mathematics) Anything which is required to be done; as, in geometry, to bisect a line, to draw a perpendicular; or, in algebra, to find an unknown quantity. Problem differs from theorem in this, that a problem is something to be done, as to bisect a triangle, to describe a circle, etc.; a theorem is something to be proved, as that all the angles of a triangle are equal to two right angles. (Science: geometry) plane problem, a problem requiring in its geometric solution the use of a conic section or higher curve. Origin: F. Probleme, L. Problema, fr. Gr. Anything thrown forward, a question proposed for solution, fr. To throw or lay before; before, forward – to throw. Cf. Parable.

Last updated on May 28th, 2023

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  • v.15(4); Winter 2016

Step by Step: Biology Undergraduates’ Problem-Solving Procedures during Multiple-Choice Assessment

Luanna b. prevost.

† Department of Integrative Biology, University of South Florida, Tampa, FL 33620

Paula P. Lemons

‡ Department of Biochemistry and Molecular Biology, University of Georgia, Athens, GA 30602

Associated Data

Findings from a mixed-methods investigation of undergraduate biology problem solving are reported. Students used a variety of problem-solving procedures that are domain general and domain specific. This study provides a model for research on alternative problem types and can be applied immediately in the biology classroom.

This study uses the theoretical framework of domain-specific problem solving to explore the procedures students use to solve multiple-choice problems about biology concepts. We designed several multiple-choice problems and administered them on four exams. We trained students to produce written descriptions of how they solved the problem, and this allowed us to systematically investigate their problem-solving procedures. We identified a range of procedures and organized them as domain general, domain specific, or hybrid. We also identified domain-general and domain-specific errors made by students during problem solving. We found that students use domain-general and hybrid procedures more frequently when solving lower-order problems than higher-order problems, while they use domain-specific procedures more frequently when solving higher-order problems. Additionally, the more domain-specific procedures students used, the higher the likelihood that they would answer the problem correctly, up to five procedures. However, if students used just one domain-general procedure, they were as likely to answer the problem correctly as if they had used two to five domain-general procedures. Our findings provide a categorization scheme and framework for additional research on biology problem solving and suggest several important implications for researchers and instructors.

INTRODUCTION

The call to reform undergraduate education involves shifting the emphasis in science classes away from rote memorization of facts toward learning core concepts and scientific practices ( National Research Council [NRC], 2003 ; American Association for the Advancement of Science [AAAS], 2011 ). To develop instruction that focuses on core concepts and scientific practices, we need more knowledge about the concepts that are challenging for students to learn. For example, biology education research has established that students struggle with the concepts of carbon cycling (e.g., Anderson et al. , 1990 ; Hartley et al ., 2011 ) and natural selection (e.g., Nehm and Reilly, 2007 ), but we know much less about students’ conceptual difficulties in ecology and physiology. Researchers and practitioners also need to discover how students develop the ability to use scientific practices. Although these efforts are underway (e.g., Anderson et al. , 2012 ; Gormally et al. , 2012 ; Dirks et al. , 2013 ; Brownell et al. , 2014 ), many research questions remain. As research accumulates, educators can create curricula and assessments that improve student learning for all. We investigate one key scientific practice that is understudied in biology education, problem solving ( AAAS, 2011 ; Singer et al. , 2012 ).

For the purposes of this article, we define problem solving as a decision-making process wherein a person is presented with a task, and the path to solving the task is uncertain. We define a problem as a task that presents a challenge that cannot be solved automatically ( Martinez, 1998 ). Problem-solving research began in the 1940s and 1950s and focused on problem-solving approaches that could be used to solve any problem regardless of the discipline ( Duncker and Lees, 1945 ; Polya, 1957 ; Newell and Simon, 1972 ; Jonassen, 2000 , 2012 ; Bassok and Novick, 2012 ). Despite the broad applicability of these domain-general problem-solving approaches, subsequent research has shown that the strongest problem-solving approaches derive from deep knowledge of a domain ( Newell and Simon, 1972 ; Chi et al. , 1981 ; Pressley et al. , 1987 ). Domain is a term that refers to a body of knowledge that can be broad, like biology, or narrow, like ecosystem structure and function. This body of literature has developed into a theoretical framework called domain-specific problem solving. We situate our research within this theoretical framework.

THE THEORETICAL FRAMEWORK OF DOMAIN-SPECIFIC PROBLEM SOLVING

Domain-specific problem solving has its origins in information-processing theory (IPT; Newell and Simon, 1972 ). IPT focuses on the cognitive processes used to reach a problem solution and emphasizes the general thinking processes people use when they attempt problem solving, such as brainstorming ( Runco and Chand, 1995 ; Halpern, 1997 ) and working backward by beginning with the problem goal and working in reverse toward the initial problem state ( Newell et al. , 1958 ; Chi and Glaser, 1985 ). Despite the empirical evidence for general thinking processes, one of IPT’s shortcomings as a comprehensive view of human cognition ( Dawson, 1998 ) is that the knowledge base of the problem solver is not considered.

Domain-specific problem solving expands IPT to recognize that experts in a particular domain have a relatively complete and well-organized knowledge base that enables them to solve the complex problems they face (e.g., Chase and Simon, 1973 ). One of the landmark studies showing the differences between the knowledge base of experts and nonexperts, or novices, was conducted in science, specifically in physics. Chi and colleagues (1981) compared the classification of physics problems by advanced physics PhD students (i.e., experts) and undergraduates who had just completed a semester of mechanics (i.e., novices), identifying fundamental differences. Chemistry researchers built on Chi’s work to identify differences in how experts and novices track their problem solving and use problem categorization and multiple representations ( Bunce et al ., 1991 ; Kohl and Finkelstein, 2008 ; Catrette and Bodner, 2010 ). Biology researchers built upon this work by conducting similar problem-solving studies among experts and novices in evolution and genetics ( Smith, 1992 ; Smith et al. , 2013 ; Nehm and Ridgway, 2011 ). Taken together, these studies established that experts tend to classify problems based on deep, conceptual features, while novices classify problems based on superficial features that are irrelevant to the solution.

Domain-specific problem-solving research within biology also has revealed important individual differences within groups of problem solvers. These studies show that wide variation in problem-solving performance exists. For example, some novices who solve problems about evolution classify problems and generate solutions that are expert-like, while others do not ( Nehm and Ridgway, 2011 ). This research points to the importance of studying variations in problem solving within novice populations.

Given the centrality of the knowledge base for domain-specific problem solving, it is necessary to describe the components of that knowledge base. Domain-specific problem-solving research recognizes three types of knowledge that contribute to expertise. Declarative knowledge consists of the facts and concepts about the domain. Procedural knowledge represents the how-to knowledge that is required to carry out domain-specific tasks. Conditional knowledge describes the understanding of when and where to use one’s declarative and procedural knowledge ( Alexander and Judy, 1988 ). Note that the field of metacognition also uses this three-type structure to describe metacognitive knowledge, or what you know about your own thinking ( Brown, 1978 ; Jacobs and Paris, 1987 ; Schraw and Moshman, 1995 ). However, for this paper, we use these terms to describe knowledge of biology, not metacognitive knowledge. More specifically, we focus on procedural knowledge.

Procedural knowledge consists of procedures. Procedures are tasks that are carried out automatically or intentionally during problem solving ( Alexander and Judy, 1988 ). Procedures exist on a continuum. They can be highly specific to the domain, such as analyzing the evolutionary relationships represented by a phylogenetic tree, or general and applicable to problems across many domains, such as paraphrasing a problem-solving prompt ( Pressley et al. , 1987 , 1989 ; Alexander and Judy, 1988 ).

APPLYING DOMAIN-SPECIFIC PROBLEM SOLVING TO MULTIPLE-CHOICE ASSESSMENT IN BIOLOGY

We used domain-specific problem solving to investigate the most common form of assessment in the college biology classroom, multiple-choice assessment ( Zheng et al ., 2008 ; Momsen et al ., 2013 ). College biology and science, technology, engineering, and mathematics (STEM) courses rely on multiple-choice assessment due to large enrollments, limited teaching assistant support, and ease of scoring. Outside the classroom, multiple-choice assessment is used on high-stakes exams that determine acceptance to professional schools, like the Medical College Admissions Test and Graduate Record Exam. To our knowledge, the framework of domain-specific problem solving has not been applied previously to investigate multiple-choice assessment in college biology.

It has become common practice within the biology education community to think about assessment, including multiple-choice assessment, by determining the Bloom’s taxonomy ranking of assessment items (e.g., Bissell and Lemons, 2006 ; Crowe et al. , 2008 ; Momsen et al. , 2010 , 2013 ). Bloom’s Taxonomy of Educational Objectives was built to facilitate the exchange of test items among faculty; it was not based primarily on the evaluation of student work ( Bloom, 1956 ; Anderson and Krathwohl, 2001 ). Bloom’s taxonomy helps educators think about the range of cognitive processes they could ask their students to perform and has served as an invaluable resource enabling educators to improve alignment between learning objectives, assessments, and classroom curricula (e.g., Crowe et al. , 2008 ). When applying Bloom’s taxonomy to assessment items, items are ranked as remembering, understanding, applying, analyzing, evaluating, and synthesizing. Items ranked as remembering and understanding are grouped as lower-order items; and items ranked as applying, analyzing, evaluating, and synthesizing are grouped as higher-order items ( Zoller, 1993 ; Crowe et al. , 2008 ). Despite the value of Bloom’s taxonomy for instructors, what is not known is the relationship between the procedural knowledge of domain-specific problem solving and the Bloom’s ranking of biology assessments. This is a critical gap in the literature, because efforts to improve student learning in college science classrooms may be stymied if critical insights about student work from domain-specific problem solving are not linked to our understanding of assessment and curricular design.

In the study reported here, we used the theoretical lens of domain-specific problem solving to describe the procedural knowledge of nonmajors in an introductory biology course. We addressed the following research questions:

  • What are the domain-general and domain-specific procedures students use to solve multiple-choice biology problems?
  • To what extent do students use domain-general and domain-specific procedures when solving lower-order versus higher-order problems?
  • To what extent does the use of domain-general or domain-specific procedures influence the probability of answering problems correctly?

Setting and Participants

We recruited participants from a nonmajors introductory biology course at a southeastern public research university in the Spring 2011 semester. One of the authors (P.P.L.) was the course instructor. The course covered four major areas in biology: evolution, ecology, physiology, and organismal diversity. The instructor delivered course content using lecture interspersed with clicker questions and additional opportunities for students to write and discuss. Students also completed five in-class case studies during the semester; students completed cases in self-selected small groups and turned in one completed case study per group for grading. In addition to group case studies, the instructor assessed student learning via individual exams. Students also received points toward their final grades based on clicker participation.

In the second week of the semester, the instructor announced this research study in class and via the course-management system, inviting all students to participate. Students who volunteered to participate by completing an informed consent form were asked to produce written think-alouds for problems on course exams throughout the semester. One hundred sixty-four students completed an informed consent form. Of the 164 consenting students, 140 students actually produced a written think-aloud for at least one of 13 problems; of the 140 students, 18 did written think-alouds for all 13 problems. The remainder of students did written think-alouds for one to 13 problems. On average, research participants provided written think-alouds for 7.76 problems.

The 164 consenting students represented 73.9% of the course enrollment ( n = 222). The 164 consenting students included 70.8% females and 29.2% males; 20.4% freshmen, 40.9% sophomores, 24.1% juniors, and 13.9% seniors. The 164 students were majoring in the following areas: 3.7% business, 1.5% education, 4.4% humanities, 11.0% life and physical sciences, 5.9% engineering, and 72.3% social sciences.

This research was conducted under exempt status at the University of Georgia (UGA; IRB project 201110340).

Data Collection

Problem development..

We wrote 16 multiple-choice problems to include in this study. All problems related to material dealt with during class and focused specifically on ecosystems, evolution, and structure–function relationships. On data analysis, three problems were excluded, because most students were confused by the wording or visual representations or were able to solve the problem correctly with a superficial strategy. Each problem was preceded by a prompt for students to provide their written think-aloud (see Written Think-Alouds section). Each problem was also labeled with a preliminary Bloom’s taxonomy categorization ( Anderson and Krathwohl, 2001 ). A summary of all problems, including a description, the preliminary Bloom’s ranking, and the faculty consensus Bloom’s ranking, is provided in Table 1 . As an example, one of the final 13 problems is shown in Figure 1 . All other problems are shown in Supplemental Figure S1.

An external file that holds a picture, illustration, etc.
Object name is ar71fig1.jpg

Sample problem from the domain of evolution used to probe students’ problem-solving procedures. The preliminary ranking that students saw for this question was Applying and Analyzing based on Bloom’s taxonomy. Experts ranked this problem as Analyzing. The correct answer is E. Images of benthic and limnetic males are courtesy of Elizabeth Carefoot, Simon Fraser University.

Summary of problems used for data collection

For each problem, a description is included along with the preliminary Bloom’s ranking, and the final consensus Bloom’s ranking. The actual problems are included in Supplemental Figure S1.

Ranking of Problems by Bloom’s Level.

We wanted to investigate the use of domain-general or domain-specific procedures in lower-order versus higher-order problems. We asked three biology faculty members who were not investigators in this study to rank the Bloom’s levels of the problems we developed. The biology faculty members were selected because they have extensive teaching experience in college biology and also have experience ranking assessment items using Bloom’s taxonomy. The faculty used a protocol similar to one described previously ( Momsen et al. , 2010 ). To assist with Bloom’s ranking, we provided them with class materials relevant to the problems, including lecture notes and background readings. This is necessary, because the ranking of a problem depends on the material that students have encountered in class previously. The faculty members independently ranked each problem. Interrater reliability of independent rankings was determined using an intraclass coefficient (0.82). The faculty members met to discuss their rankings and settled disagreements by consensus. The preliminary Bloom’s rankings and the faculty consensus Bloom’s rankings for problems are reported in Table 1 . For the remainder of the paper, we use the consensus Bloom’s rankings to describe problems as either lower order or higher order.

Administration of Problems to Students.

The 13 problems included in this study were administered to students on exams 1, 2, 3, and the final exam as follows: three on exam 1, three on exam 2 four on exam 3, and three on the final exam. Students’ multiple-choice responses were part of the actual exam score. They received 0.5 extra-credit points for providing satisfactory documentation of their thought processes. Students did not receive extra credit if we judged their documentation to be insufficient. Insufficient responses were those in which students made only one or two brief statements about their problem-solving process (e.g., “I chose C”). Students could answer the multiple-choice problem and opt not to provide documentation of their thinking for extra credit. Students could receive up to 6.5 points of extra credit for documentation of the problem set. The total points possible for the semester were 500, so extra credit for this research could account for up to 1.3% of a student’s grade.

Written Think-Alouds.

We developed a protocol to capture students’ written descriptions of their thought processes while solving problems on exams based on a think-aloud interview approach. In the think-aloud interview approach, research participants are given a problem to solve and are asked to say aloud everything they are thinking while solving the problem ( Ericsson and Simon, 1984 ; Keys, 2000 ). In the written think-aloud, students are asked to write, rather than say aloud, what they are thinking as they solve a problem. To train students to perform a written think-aloud, the course instructor modeled the think-aloud in class. She then assigned a homework problem that required students to answer a multiple-choice problem and construct written think-alouds recounting how they solved the problem. We then reviewed students’ homework and provided feedback. We selected examples of good documentation and poor documentation and published these anonymously on the online course-management system. After this training and feedback, we included four problems on every exam for which we asked students to provide a written think-aloud description. We collected 1087 written think-alouds from 140 students (63% of course enrollment, n = 222) for 13 problems. Figure 2 shows a typical example of a student written think-aloud.

An external file that holds a picture, illustration, etc.
Object name is ar71fig2.jpg

Written think-aloud from an introductory biology student who had been instructed to write down her procedures for solving a multiple-choice biology problem. This document describes the student’s procedures for solving the problem shown in Figure 1 .

Data Analysis

We analyzed students’ written think-alouds using a combination of qualitative and quantitative methods. We used qualitative content analysis ( Patton, 1990 ) to identify and categorize the primary patterns of student thinking during problem solving. We used quantitative analysis to determine the relationship between use of domain-general, hybrid, and domain-specific procedures and problem type and to investigate the impact of domain-general/hybrid and domain-specific procedure use on answering correctly.

Qualitative Analyses of Students’ Written Think-alouds.

The goal of our qualitative analysis was to identify the cognitive procedures students follow to solve multiple-choice biology problems during an exam. Our qualitative analysis took place in two phases.

Phase 1: Establishing Categories of Student Problem-Solving Procedures.

Independently, we read dozens of individual think-alouds for each problem. While we read, we made notes about the types of procedures we observed. One author (P.P.L.) noted, for example, that students recalled concepts, organized their thinking, read and ruled out multiple-choice options, explained their selections, and weighed the pros and cons of multiple-choice options. The other author (L.B.P.) noted that students recalled theories, interpreted a phylogenetic tree, identified incomplete information, and refuted incorrect information. After independently reviewing the written think-alouds, we met to discuss what we had found and to build an initial list of categories of problem-solving procedures. Based on our discussion, we built a master list of categories of procedures (Supplemental Table S1).

Next, we compared our list with Bloom’s Taxonomy of Educational Objectives ( Anderson and Krathwohl, 2001 ) and the Blooming Biology Tool ( Crowe et al. , 2008 ). We sought to determine whether the cognitive processes described in these sources corresponded to the cognitive processes we observed in our initial review of students’ written think-alouds. Where there was overlap, we renamed our categories to use the language of Bloom’s taxonomy. For the categories that did not overlap, we kept our original names.

Phase 2: Assigning Student Problem-Solving Procedures to Categories.

Using the list of categories developed in phase 1, we categorized every problem-solving procedure articulated by students in the written think-alouds. We analyzed 1087 documents for 13 problems. For each of the 13 problems, we followed the same categorization process. In a one-on-one meeting, we discussed a few written think-alouds. While still in the same room, we categorized several written think-alouds independently. We then compared our categorizations and discussed any disagreements. We then repeated these steps for additional think-alouds while still together. Once we reached agreement on all categories for a single problem, we independently categorized a common subset of written think-alouds to determine interrater reliability. When interrater reliability was below a level we considered acceptable (0.8 Cronbach’s alpha), we went through the process again. Then one author (either L.B.P. or P.P.L.) categorized the remainder of the written think-alouds for that problem.

At the end of phase 2, after we had categorized all 1087 written think-alouds, we refined our category list, removing categories with extremely low frequencies and grouping closely related categories. For example, we combined the category Executing with Implementing into a category called Analyzing Visual Representations.

Phase 3: Aligning Categories with Our Theoretical Framework.

Having assigned student problem-solving procedures to categories, we determined whether the category aligned best with domain-general or domain-specific problem solving. To make this determination, we considered the extent to which the problem-solving procedures in a category depended on knowledge of biology. Categories of procedures aligned with domain-general problem solving were carried out without drawing on content knowledge (e.g., Clarifying). Categories aligned with domain-specific problem solving were carried out using content knowledge (e.g., Checking). We also identified two categories of problem solving that we labeled hybrids of domain-general and domain-specific problem solving, because students used content knowledge in these steps, but they did so superficially (e.g., Recognizing).

Supplemental Table S1 shows the categories that resulted from our analytical process, including phase 1 notes, phase 2 categories, and phase 3 final category names as presented in this paper. Categories are organized into the themes of domain-general, hybrid, and domain-specific problem solving (Supplemental Table S1).

Quantitative Analyses of Students’ Written Think-Alouds.

To determine whether students used domain-general/hybrid or domain-specific problem solving preferentially when solving problems ranked by faculty as lower order or higher order, we used generalized linear mixed models (GLMM). GLMM are similar to ordinary linear regressions but take into account nonnormal distributions. GLMM can also be applied to unbalanced repeated measures ( Fitzmaurice et al. , 2011 ). In our data set, an individual student could provide documentation to one or more problems (up to 13 problems). Thus, in some but not all cases, we have repeated measures for individuals. To account for these repeated measures, we used “student” as our random factor. We used the problem type (lower order or higher order) as our fixed factor. Because our independent variables, number of domain-general/hybrid procedures and number of domain-specific procedures, are counts, we used a negative binomial regression. For this analysis and subsequent quantitative analyses, we grouped domain-general and hybrid procedures. Even though hybrid procedures involve some use of content knowledge, the content knowledge is used superficially; we specifically wanted to investigate the impact of weak content-knowledge use compared with strong content-knowledge use. Additionally, the number of hybrid procedures in our data set is relatively low compared with domain-general and domain-specific.

To determine whether students who used more domain-general/hybrid procedures or domain-specific procedures were more likely to have correct answers to the problems, we also used GLMM. We used the number of domain-general/hybrid procedures and the number of domain-specific procedures as our fixed factors and student as our random factor. In this analysis, our dependent variable (correct or incorrect response) was dichotomous, so we used a logistic regression ( Fitzmaurice et al. , 2011 ). We also explored the correlations between the average number of domain-general/hybrid and domain-specific procedures used by students and their final percentage of points for the course.

In this section, we present the results of our analyses of students’ procedures while solving 13 multiple-choice, biology problems ( Figure 1 and Supplemental Figure S1). We used the written think-aloud protocol to discover students’ problem-solving procedures for all 13 problems.

Students Use Domain-General and Domain-Specific Procedures to Solve Multiple-Choice Biology Problems

We identified several categories of procedures practiced by students during problem solving, and we organized these categories based on the extent to which they drew upon knowledge of biology. Domain-general procedures do not depend on biology content knowledge. These procedures also could be used in other domains. Hybrid procedures show students assessing multiple-choice options with limited and superficial references to biology content knowledge. Domain-specific procedures depend on biology content knowledge and reveal students’ retrieval and processing of correct ideas about biology.

Domain-General Procedures.

We identified five domain-general problem-solving procedures that students practiced ( Table 2 ). Three of these have been described in Bloom’s taxonomy ( Anderson and Krathwohl, 2001 ). These include Analyzing Domain-General Visual Representations, Clarifying, and Comparing Language of Options. In addition, we discovered two other procedures, Correcting and Delaying, that we also categorized as domain general ( Table 2 ).

Students’ problem-solving procedures while solving multiple-choice biology problems

The procedures are categorized as domain-general, hybrid, and domain-specific. Superscripts indicate whether the problem-solving procedure aligns with previously published conceptions of student thinking or was newly identified in this study: a , Anderson and Krathwohl (2001) ; b identified in this study; c , Crowe et al . (2008) .

During Correcting, students practiced metacognition. Broadly defined, metacognition occurs when someone knows, is aware of, or monitors his or her own learning ( White, 1998 ). When students corrected, they identified incorrect thinking they had displayed earlier in their written think-aloud and mentioned the correct way of thinking about the problem.

When students Delayed, they described their decision to postpone full consideration of one multiple-choice option until they considered other multiple-choice options. We interpreted these decisions as students either not remembering how the option connected with the question or not being able to connect that option to the question well enough to decide whether it could be the right answer.

Hybrid Procedures.

We identified two problem-solving procedures that we categorized as hybrid, Comparing Correctness of Options and Recognizing. Students who compared correctness of options stated that one choice appeared more correct than the other without giving content-supported reasoning for their choice. Similarly, students who recognized an option as correct did not support this conclusion with a content-based rationale.

Domain-Specific Procedures.

In our data set, we identified six domain-specific problem-solving procedures practiced by students ( Table 2 ). Four of these have been previously described. Specifically, Analyzing Domain-Specific Visual Representations, Checking, and Recalling were described in Bloom’s taxonomy ( Anderson and Krathwohl, 2001 ). Predicting was described by Crowe and colleagues (2008) . We identified two additional categories of domain-specific problem-solving procedures practiced by students who completed our problem set, Adding Information and Asking a Question.

Adding Information occurred when students recalled material that was pertinent to one of the multiple-choice options and incorporated that information into their explanations of why a particular option was wrong or right.

Asking a Question provides another illustration of students practicing metacognition. When students asked a question, they pointed out that they needed to know some specific piece of content that they did not know yet. Typically, students who asked a question did so repeatedly in a single written think-aloud.

Students Make Errors While Solving Multiple-Choice Biology Problems

In addition to identifying domain-general, hybrid, and domain-general procedures that supported students’ problem-solving, we identified errors in students’ problem solving. We observed six categories of errors, including four that we categorized as domain general and two categorized as domain specific ( Table 3 ).

Students’ errors while solving multiple-choice biology problems

The errors are presented in alphabetical order, described, and illustrated with example quotes from different students’ documentation of their solutions to the problem shown in Figure 1 (except for Misreading, which is from problem 13 in Supplemental Figure S1).

The domain-general errors include Contradicting, Disregarding Evidence, Misreading, and Opinion-Based Judgment. In some cases, students made statements that they later contradicted; we called this Contradicting. Disregarding Evidence occurred when students’ failed to indicate use of evidence. Several problems included data in the question prompt or in visual representations. These data could be used to help students select the best multiple-choice option, yet many students gave no indication that they considered these data. When students’ words led us to believe that they did not examine the data, we assigned the category Disregarding Evidence.

Students also misread the prompt or the multiple-choice options, and we termed this Misreading. For example, Table 3 shows the student Misreading; the student states that Atlantic eels are in the presence of krait toxins, whereas the question prompt stated there are no krait in the Atlantic Ocean. In other cases, students stated that they arrived at a decision based on a feeling or because that option just seemed right. For example, in selecting option C for the stickleback problem ( Figure 1 ), one student said, “E may be right, but I feel confident with C. I chose Answer C.” These procedures were coded as Opinion-Based Judgment.

We identified two additional errors that we classified as domain specific, Making Incorrect Assumptions and Misunderstanding Content. Making Incorrect Assumptions was identified when students made faulty assumptions about the information provided in the prompt. In these cases, students demonstrated in one part of their written think-aloud that they understood the conditions for or components of a concept. However, in another part of the written think-aloud, students assumed the presence or absence of these conditions or components without carefully examining whether they held for the given problem. In the example shown in Table 3 , the student assumed additional information on fertility that was not provided in the problem.

We classified errors that showed a poor understanding of the biology content as Misunderstanding Content. Misunderstanding Content was exhibited when students stated incorrect facts from their long-term memory, made false connections between the material presented and biology concepts, or showed gaps in their understanding of a concept. In the Misunderstanding Content example shown in Table 3 , the student did not understand that the biological species concept requires two conditions, that is, the offspring must be viable and fertile. The student selected the biological species concept based only on evidence of viability, demonstrating misunderstanding.

To illustrate the problem-solving procedures described above, we present three student written think-alouds ( Table 4, A–C ). All three think-alouds were generated in response to the stickleback problem; pseudonyms are used to protect students’ identities ( Figure 1 ). Emily correctly solved the stickleback problem using a combination of domain-general and domain-specific procedures ( Table 4A ). She started by thinking about the type of answer she was looking for (Predicting). Then she analyzed the stickleback drawings and population table (Analyzing Domain-General Visual Representations) and explained why options were incorrect or correct based on her knowledge of species concepts (Checking). Brian ( Table 4B ) took an approach that included domain-general and hybrid procedures. He also made some domain-general and domain-specific errors, which resulted in an incorrect answer; Brian analyzed some of the domain-general visual representations presented in the problem but disregarded others. He misunderstood the content, incorrectly accepting the biological species concept. He also demonstrated Recognizing when he correctly eliminated choice B without giving a rationale for this step. In our third example ( Table 4C ), Jessica used domain-general, hybrid, and domain-specific procedures, along with a domain-specific error, and arrived at an incorrect answer.

Students’ written think-alouds describing their processes for solving the stickleback problem

Different types of problem-solving processes are indicated with different font types: Domain-general problem-solving steps: blue lowercase font; domain-specific problem-solving steps: blue uppercase font, hybrid problem-solving steps: blue italics; domain-general errors: orange lowercase font; domain-specific errors: orange uppercase font. The written think-alouds are presented in the exact words of the students. A, Emily, all domain-general and domain-specific steps; correct answer: E; B, Brian, domain-general and hybrid steps, domain-general and domain-specific errors; incorrect answer: C; C, Jessica, domain-general, hybrid, and domain-specific steps; domain-specific errors; incorrect answer: C.

Domain-Specific Procedures Are Used More Frequently for Higher-Order Problems Than Lower-Order Problems

To determine the extent to which students use domain-general and domain-specific procedures when solving lower-order versus higher-order problems, we determined the frequency of domain-general and hybrid procedures and domain-specific procedures for problems categorized by experts as lower order or higher order. We grouped domain-general and hybrid procedures, because we specifically wanted to examine the difference between weak and strong content usage. As Table 5, A and B , shows, students frequently used both domain-general/hybrid and domain-specific procedures to solve all problems. For domain-general/hybrid procedures, by far the most frequently used procedure for lower-order problems was Recognizing ( n = 413); the two most frequently used procedures for higher-order problems were Analyzing Domain-General Representations ( n = 153) and Recognizing ( n = 105; Table 5A ). For domain-specific procedures, the use of Checking dominated both lower-order ( n = 903) and higher-order problems ( n = 779). Recalling also was used relatively frequently for lower-order problems ( n = 207), as were Analyzing Domain-Specific Visual Representations, Predicting, and Recalling for higher-order problems ( n = 120, n = 106, and n = 107, respectively). Overall, students used more domain-general and hybrid procedures when solving lower-order problems (1.43 ± 1.348 per problem) than when solving higher-order problems (0.74 ± 1.024 per problem; binomial regression B = 0.566, SE = 0.079, p < 0.005). Students used more domain-specific procedures when solving higher-order problems (2.57 ± 1.786 per problem) than when solving lower-order problems (2.38 ± 2.2127 per problem; binomial regression B = 0.112, SE = 0.056, p < 0.001).

Frequency of each problem-solving procedure for lower-order and higher-order problems

Procedures are presented from left to right in alphabetical order. A color scale is used to represent the frequency of each procedure, with the lowest-frequency procedures shown in dark blue, moderate-frequency procedures shown in white, and high-frequency procedures shown in dark red.

Most Problem-Solving Errors Made by Students Involve Misunderstanding Content

We also considered the frequency of problem-solving errors made by students solving lower-order and higher-order problems. As Table 6 shows, most errors were categorized with the domain-specific category Misunderstanding Content, and this occurred with about equal frequency in lower-order and higher-order problems. The other categories of errors were less frequent. Interestingly, the domain-general errors Contradicting and Opinion-Based Judgment both occurred more frequently with lower-order problems. In contrast, the domain-specific error Making Incorrect Assumptions occurred more frequently with higher-order problems.

Frequency of errors for lower-order and higher-order problems

Categories of errors are presented from left to right in alphabetical order. A color scale is used to represent the frequency of each type of error, with the lowest-frequency errors shown in dark blue, moderate-frequency errors shown in white, and high-frequency errors shown in dark red.

Using Multiple Domain-Specific Procedures Increases the Likelihood of Answering a Problem Correctly

To examine the extent to which the use of domain-general or domain-specific procedures influences the probability of answering problems correctly, we performed a logistic regression. Predicted probabilities of answering correctly are shown in Figure 3 for domain-general and hybrid procedures and Figure 4 for domain-specific procedures. Coefficients of the logistic regression analyses are presented in Supplemental Tables S2 and S3. As Figure 3 shows, using zero domain-general or hybrid procedures was associated with a 0.53 predicted probability of being correct. Using one domain-general or hybrid procedure instead of zero increased the predicted probability of correctly answering a problem to 0.79. However, students who used two or more domain-general or hybrid procedures instead of one did not increase the predicted probability of answering a problem correctly. In contrast, as Figure 4 shows, using zero domain-specific procedures was associated with only a 0.34 predicted probability of answering the problem correctly, and students who used one domain-specific procedure had a 0.54 predicted probability of success. Strikingly, the more domain-specific procedures used by students, the more likely they were to answer a problem correctly up to five procedures; students who used five domain-specific procedures had a 0.97 probability of answering correctly. Predicted probabilities for students using seven and nine domain-specific codes show large confidence intervals around the predictions due to the low sample size ( n = 8 and 4, respectively). Also, we examined the extent to which the use of domain-general or domain-specific procedures correlates with course performance. We observed a weak positive correlation between the average number of domain-specific procedures used by students for a problem and their final percentage of points in the course (Spearman’s rho = 0.306; p < 0.001). There was no correlation between the average number of domain-general/hybrid procedures used by students for a problem and their final percentage of points in the course (Spearman’s rho = 0.015; p = 0.857).

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Predicted probability of a correct answer based on the number of domain-general and hybrid procedures.

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Predicted probability of a correct answer based on the number of domain-specific procedures.

We have used the theoretical framework of domain-specific problem solving to investigate student cognition during problem solving of multiple-choice biology problems about ecology, evolution, and systems biology. Previously, research exploring undergraduate cognition during problem solving has focused on problem categorization or students’ solutions to open-response problems ( Smith and Good, 1984 ; Smith, 1988 ; Lavoie, 1993 ; Nehm and Ridgway, 2011 ; Smith et al. 2013 ). Our goal was to describe students’ procedural knowledge, including the errors they made in their procedures. Below we draw several important conclusions from our findings and consider the implications of this research for teaching and learning.

Domain-Specific Problem Solving Should Be Used for Innovative Investigations of Biology Problem Solving

Students in our study used a variety of procedures to solve multiple-choice biology problems, but only a few procedures were used at high frequency, such as Recognizing and Checking. Other procedures that biology educators might most want students to employ were used relatively infrequently, including Correcting and Predicting. Still other procedures that we expected to find in our data set were all but absent, such as Stating Assumptions. Our research uncovers the range of procedures promoted by multiple-choice assessment in biology. Our research also provides evidence for the notion that multiple-choice assessments are limited in their ability to prompt some of the critical types of thinking used by biologists.

We propose that our categorization scheme and the theoretical framework of domain-specific problem solving should be applied for further study of biology problem solving. Future studies could be done to understand whether different ways of asking students to solve a problem at the same Bloom’s level could stimulate students to use different procedures. For example, if the stickleback problem ( Figure 1 ) were instead presented to students as a two-tier multiple-choice problem, as multiple true–false statements, or as a constructed-response problem, how would students’ procedures differ? Additionally, it would be useful to investigate whether the more highly desired, but less often observed procedures of Correcting and Predicting are used more frequently in upper-level biology courses and among more advanced biology students.

We also propose research to study the interaction between procedure and content. With our focus on procedural knowledge, we intentionally avoided an analysis of students’ declarative knowledge. However, our process of analysis led us to the conclusion that our framework can be expanded for even more fruitful research. For example, one could look within the procedural category Checking to identify the declarative knowledge being accessed. Of all the relevant declarative knowledge for a particular problem, which pieces do students typically access and which pieces are typically overlooked? The answer to this question may tell us that, while students are using an important domain-specific procedure, they struggle to apply a particular piece of declarative knowledge. As another example, one could look within the procedural category Analyzing Visual Representations to identify aspects of the visual representation that confuse or elude students. Findings from this type of research would show us how to modify visual representations for clarity or how to scaffold instruction for improved learning. We are suggesting that future concurrent studies of declarative and procedural knowledge will reveal aspects of student cognition that will stay hidden if these two types of knowledge are studied separately. Indeed, problem-solving researchers have investigated these types of interactions in the area of comprehension of science textbooks ( Alexander and Kulikowich, 1991 , 1994 ).

Lower-Order Problems May Not Require Content Knowledge, While Higher-Order Problems Promote Strong Content Usage

Because of the pervasive use among biology educators of Bloom’s taxonomy to write and evaluate multiple-choice assessments, we decided it was valuable to examine the relationship between domain-general and domain-specific procedures and lower-order versus higher-order problems.

For both lower-order and higher-order problems, domain-specific procedures were used much more frequently than domain-general procedures ( Table 5, A and B ). This is comforting and unsurprising. We administered problems about ecosystems, evolution, and structure–function relationships, so we expected and hoped students would use their knowledge of biology to solve these problems. However, two other results strike us as particularly important. First, domain-general procedures are highly prevalent ( Table 5A , n = 1108 across all problems). The use of domain-general procedures is expected. There are certain procedures that are good practice in problem solving regardless of content, such as Analyzing Domain-General Visual Representations and Clarifying. However, students’ extensive use of other domain-general/hybrid categories, namely Recognizing, is disturbing. Here we see students doing what all biology educators who use multiple-choice assessment fear, scanning the options for one that looks right based on limited knowledge. It is even more concerning that students’ use of Recognizing is nearly four times more prevalent in lower-order problems than higher-order problems and that overall domain-general procedures are more prevalent in lower-order problems ( Table 5A ). As researchers have discovered, lower-order problems, not higher-order problems, are the type most often found in college biology courses ( Momsen et al ., 2010 ). That means biology instructors’ overreliance on lower-order assessment is likely contributing to students’ overreliance on procedures that do not require biology content knowledge.

Second, it is striking that domain-specific procedures are more prevalent among higher-order problems than lower-order problems. These data suggest that higher-order problems promote strong content usage by students. As others have argued, higher-order problems should be used in class and on exams more frequently ( Crowe et al. , 2008 ; Momsen et al. , 2010 ).

Using Domain-Specific Procedures May Improve Student Performance

Although it is interesting in and of itself to learn the procedures used by students during multiple-choice assessment, the description of these categories of procedures begs the question: does the type of procedure used by students make any difference in their ability to choose a correct answer? As explained in the Introduction , the strongest problem-solving approaches stem from a relatively complete and well-organized knowledge base within a domain ( Chase and Simon, 1973 ; Chi et al. , 1981 ; Pressley et al. , 1987 ; Alexander and Judy, 1998). Thus, we hypothesized that use of domain-specific procedures would be associated with solving problems correctly, but use of domain-general procedures would not. Indeed, our data support this hypothesis. While limited use of domain-general procedures was associated with improved probability of success in solving multiple-choice problems, students who practiced extensive domain-specific procedures almost guaranteed themselves success in multiple-choice problem solving. In addition, as students used more domain-specific procedures, there was a weak but positive increase in the course performance, while use of domain-general procedures showed no correlation to performance. These data reiterate the conclusions of prior research that successful problem solvers connect information provided within the problem to their relatively strong domain-specific knowledge ( Smith and Good, 1984 ; Pressley et al. , 1987 ). In contrast, unsuccessful problem solvers heavily depend on relatively weak domain-specific knowledge ( Smith and Good, 1984 ; Smith, 1988 ). General problem-solving procedures can be used to make some progress in reaching a solution to domain-specific problems, but a problem solver can get only so far with this type of thinking. In solving domain-specific problems, at some point, the solver has to understand the particulars of a domain to reach a legitimate solution (reviewed in Pressley et al. , 1987 ; Bassok and Novick, 2012 ). Likewise, problem solvers who misunderstand key conceptual pieces or cannot identify the deep, salient features of a problem will generate inadequate, incomplete, or faulty solutions ( Chi et al. , 1981 ; Nehm and Ridgway, 2011 ).

Our findings strengthen the conclusions of previous work in two important ways. First, we studied problems from a wider range of biology topics. Second, we studied a larger population of students, which allowed us to use both qualitative and quantitative methods.

Limitations of This Research

Think-aloud protocols typically take place in an interview setting in which students verbally articulate their thought processes while solving a problem. When students are silent, the interviewer is there to prompt them to continue thinking aloud. We modified this protocol and taught students how to write out their procedures. However, one limitation of this study and all think-aloud studies is that it is not possible to analyze what students may have been thinking but did not state. Despite this limitation, we were able to identify a range of problem-solving procedures and errors that inform teaching and learning.

Implications for Teaching and Learning

There is general consensus among biology faculty that students need to develop problem-solving skills ( NRC, 2003 ; AAAS, 2011 ). However, problem solving is not intuitive to students, and these skills typically are not explicitly taught in the classroom ( Nehm, 2010 ; Hoskinson et al. , 2013 ). One reason for this misalignment between faculty values and their teaching practice is that biology problem-solving procedures have not been clearly defined. Our research presents a categorization of problem-solving procedures that faculty can use in their teaching. Instructors can use these well-defined problem-solving procedures to help students manage their knowledge of biology; students can be taught when and how to apply knowledge and how to restructure it. This gives students the tools to become more independent problem solvers ( Nehm, 2010 ).

We envision at least three ways that faculty can encourage students to become independent problem solvers. First, faculty can model the use of problem-solving procedures described in this paper and have students write out their procedures, which makes them explicit to both the students and instructor. Second, models should focus on domain-specific procedures, because these steps improve performance. Explicit modeling of domain-specific procedures would be eye-opening for students, who tend to think that studying for recognition is sufficient, particularly for multiple-choice assessment. However, our data and those of other researchers ( Stanger-Hall, 2012 ) suggest that studying for and working through problems using strong domain-specific knowledge can improve performance, even on multiple-choice tests. Third, faculty should shift from the current predominant use of lower-order problems ( Momsen et al. , 2010 ) toward the use of more higher-order problems. Our data show that lower-order problems prompt for domain-general problem solving, while higher-order problems prompt for domain-specific problem solving.

We took what we learned from the investigation reported here and applied it to develop an online tutorial called SOLVEIT for undergraduate biology students ( Kim et al. , 2015 ). In SOLVEIT, students are presented with problems similar to the stickleback problem shown in Figure 1 . The problems focus on species concepts and ecological relationships. In brief, SOLVEIT asks students to provide an initial solution to each problem, and then it guides students through the problem in a step-by-step manner that encourages them to practice several of the problem-solving procedures reported here, such as Recalling, Checking, Analyzing Visual Representations, and Correcting. In the final stages of SOLVEIT, students are asked to revise their initial solutions and to reflect on an expert’s solution as well as their own problem-solving process ( Kim et al. , 2015 ). Our findings of improved student learning with SOLVEIT ( Kim et al. , 2015 ) are consistent with the research of others that shows scaffolding can improve student problem solving ( Lin and Lehman, 1999 ; Belland, 2010 ; Singh and Haileselassie, 2010 ). Thus, research to uncover the difficulties of students during problem solving can be directly applied to improve student learning.

Supplementary Material

Acknowledgments.

We thank the students who participated in this study and the biology faculty who served as experts by providing Bloom’s rankings for each problem. We also thank the Biology Education Research Group at UGA, who improved the quality of this work with critical feedback on the manuscript. Finally, we thank the reviewers, whose feedback greatly improved the manuscript. Resources for this research were provided by UGA and the UGA Office of STEM Education.

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1.7: Probabilities in genetics

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Introduction

The Punnett square is a valuable tool, but it's not ideal for every genetics problem. For instance, suppose you were asked to calculate the frequency of the recessive class not for an Aa x Aa cross, not for an AaBb x AaBb cross, but for an AaBbCcDdEe x AaBbCcDdEe cross. If you wanted to solve that question using a Punnett square, you could do it – but you'd need to complete a Punnett square with 1024 boxes. Probably not what you want to draw during an exam, or any other time, if you can help it!

The five-gene problem above becomes less intimidating once you realize that a Punnett square is just a visual way of representing probability calculations. Although it’s a great tool when you’re working with one or two genes, it can become slow and cumbersome as the number goes up. At some point, it becomes quicker (and less error-prone) to simply do the probability calculations by themselves, without the visual representation of a clunky Punnett square. In all cases, the calculations and the square provide the same information, but by having both tools in your belt, you can be prepared to handle a wider range of problems in a more efficient way.

In this article, we’ll review some probability basics, including how to calculate the probability of two independent events both occurring (event X and event Y) or the probability of either of two mutually exclusive events occurring (event X or event Y). We’ll then see how these calculations can be applied to genetics problems, and, in particular, how they can help you solve problems involving relatively large numbers of genes.

In this problem, we’re supposed to find the frequency of the recessive class among the offspring of an AaBbCcDdEe x AaBbCcDdEe cross – that is, the frequency of aabbccddee individuals. How do we get an aabbccddee individual? There’s only one way for that to happen: both parents must contribute an abcde gamete.

What, then, is the probability that one of the parents will make an abcde gamete? Both parents are heterozygous for all five genes, so there’s a 1/2 chance of getting the recessive (lowercase) allele for any one gene. To get our desired gamete, we need all five genes in recessive form ( a and b and c and d and e ). This is a case where we can apply the product rule , which states that the probability of event X and event Y happening is the product of their individual probabilities (probability of X times probability of Y), assuming that X and Y are independent events. Thus, the overall probability of one parent producing an abcde gamete is:

Probability of abcde gamete = (probability of a ) x (probability of b ) x (probability of c ) x (probability of d ) x (probability of e )

\(P(abcde)=P(a)\cdot P(b)\cdot P(c)\cdot P(d)\cdot P(e)\)

\(P(abcde)=(1/2)\cdot (1/2)\cdot (1/2)\cdot (1/2)\cdot (1/2)=(1/2)^5=1/32\)

If that’s the probability of one parent making an abcde gamete, what’s the likelihood of both parents doing so? Again, we can apply the "and" rule (product rule), since we need both parent 1 and parent 2 to make an abcde gamete in order to get our target recessive homozygote. Thus, the overall probability is:

Probability of aabbccddee individual = (probability of parent 1 making an abcde gamete) x (probability of parent 2 making an abcde gamete)

\(P(aabbccddee)=P(abcde_\text{parent A})\cdot P(abcde_\text{parent B})\)

\(P(aabbccddee)=(1/32)\cdot (1/32)=1/1024\)

That’s our overall probability for a recessive homozygote for all five genes.

The 1/1024 probability corresponds to 1 box out of the 1024 boxes of the Punnett square you’d have to draw to represent this cross. The probability calculation is the same calculation we’d implicitly do by drawing the Punnett square, just faster and with fewer chances for mistakes.

Probability basics

Probabilities are mathematical measures of likelihood. In other words, they’re a way of quantifying (giving a specific, numerical value to) how likely something is to happen. A probability of 1 for an event means that it is guaranteed to happen, while a probability of 0 for an event means that it is guaranteed not to happen. A simple example of probability is having a 1/2 chance of getting heads when you flip a coin, as Sal explains in this intro to probability video.

Probabilities can be either empirical, meaning that they are calculated from real-life observations, or theoretical, meaning that they are predicted using a set of rules or assumptions.

  • The empirical probability of an event is calculated by counting the number of times that event occurs and dividing it by the total number of times that event could have occurred. For instance, if the event you were looking for was a wrinkled pea seed, and you saw it 1,850 times out of the 7,324 total seeds you examined, the empirical probability of getting a wrinkled seed would be 1,850/7,324 = 0.253, or very close to 1 in 4 seeds.
  • The theoretical probability of an event is calculated based on information about the rules and circumstances that produce the event. It reflects the number of times an event is expected to occur relative to the number of times it could possibly occur. For instance, if you had a pea plant heterozygous for a seed shape gene ( Rr ) and let it self-fertilize, you could use the rules of probability and your knowledge of genetics to predict that 1 out of every 4 offspring would get two recessive alleles ( rr ) and appear wrinkled, corresponding to a 0.25 (1/4) probability. We’ll talk more below about how to apply the rules of probability in this case.

In general, the larger the number of data points that are used to calculate an empirical probability, such as shapes of individual pea seeds, the more closely it will approach the theoretical probability.

The product rule

One probability rule that's very useful in genetics is the product rule , which states that the probability of two (or more) independent events occurring together can be calculated by multiplying the individual probabilities of the events. For example, if you roll a six-sided die once, you have a 1/6 chance of getting a six. If you roll two dice at once, your chance of getting two sixes is: (probability of a six on die 1) x (probability of a six on die 2) = (1/6) ⋅ (1/6) = 1/36.

In general, you can think of the product rule as the “and” rule: if both event X and event Y must happen in order for a certain outcome to occur, and if X and Y are independent of each other (don’t affect each other’s likelihood), then you can use the product rule to calculate the probability of the outcome by multiplying the probabilities of X and Y.

We can use the product rule to predict frequencies of fertilization events. For instance, consider a cross between two heterozygous ( Aa ) individuals. What are the odds of getting an aa individual in the next generation? The only way to get an aa individual is if the mother contributes an a gamete and the father contributes an a gamete. Each parent has a 1/2 chance of making an a gamete. Thus, the chance of an aa offspring is: (probability of mother contributing a ) x (probability of father contributing a ) = (1/2) ⋅ (1/2) = 1/4.

Illustration of how a Punnett square can represent the product rule. Punnett square:||A|a-|-|-|-A||AA|**Aa**a||_Aa_|***aa*** There's a 1/2 chance of getting an a allele from the male parent, corresponding to the rightmost column of the Punnett square. Similarly, there's a 1/2 chance of getting an a allele from the maternal parent, corresponding to the bottommost row of the Punnett square. The intersect of these the row and column, corresponding to the bottom right box of the table, represents the probability of getting an a allele from the maternal parent and the paternal parent (1 out of 4 boxes in the Punnett square, or a 1/4 chance).

This is the same result you’d get with a Punnett square, and actually the same logical process as well—something that took me years to realize! The only difference is that, in the Punnett square, we'd do the calculation visually: we'd represent the 1/2 probability of an a gamete from each parent as one out of two columns (for the father) and one out of two rows (for the mother). The 1-square intersect of the column and row (out of the 4 total squares of the table) represents the 1/4 chance of getting an a from both parents.

The sum rule of probability

In some genetics problems, you may need to calculate the probability that any one of several events will occur. In this case, you’ll need to apply another rule of probability, the sum rule. According to the sum rule , the probability that any of several mutually exclusive events will occur is equal to the sum of the events’ individual probabilities.

For example, if you roll a six-sided die, you have a 1/6 chance of getting any given number, but you can only get one number per roll. You could never get both a one and a six at the same time; these outcomes are mutually exclusive. Thus, the chances of getting either a one or a six are: (probability of getting a 1) + (probability of getting a 6) = (1/6) + (1/6) = 1/3.

You can think of the sum rule as the “or” rule: if an outcome requires that either event X or event Y occur, and if X and Y are mutually exclusive (if only one or the other can occur in a given case), then the probability of the outcome can be calculated by adding the probabilities of X and Y.

As an example, let's use the sum rule to predict the fraction of offspring from an Aa x Aa cross that will have the dominant phenotype ( AA or Aa genotype). In this cross, there are three events that can lead to a dominant phenotype:

  • Two A gametes meet (giving AA genotype), or
  • A gamete from Mom meets a gamete from Dad (giving Aa genotype), or
  • a gamete from Mom meets A gamete from Dad (giving Aa genotype)

In any one fertilization event, only one of these three possibilities can occur (they are mutually exclusive).

Since this is an “or” situation where the events are mutually exclusive, we can apply the sum rule. Using the product rule as we did above, we can find that each individual event has a probability of 1/4. So, the probability of offspring with a dominant phenotype is: (probability of A from Mom and A from Dad) + (probability of A from Mom and a from Dad) + (probability of a from Mom and A from Dad) = (1/4) + (1/4) + (1/4) = 3/4.

Illustration of how a Punnett square can represent the sum rule. Punnett square:||A|a-|-|-|-A||**AA**|**Aa**a||**Aa**|aa The **bolded** boxes represent events that result in a dominant phenotype (AA or Aa genotype). In one, an A sperm combines with an A egg. In another, an A sperm combines with an a egg, and in a third, an a sperm combines with an A egg. Each event has a 1/4 chance of happening (1 out of 4 boxes in the Punnett square). The chance that any of these three events will occur is 1/4+1/4+1/4 = 3/4.

Once again, this is the same result we’d get with a Punnett square. One out of the four boxes of the Punnett square holds the dominant homozygote, AA . Two more boxes represent heterozygotes, one with a maternal A and a paternal a , the other with the opposite combination. Each box is 1 out of the 4 boxes in the whole Punnett square, and since the boxes don't overlap (they’re mutually exclusive), we can add them up (1/4 + 1/4 + 1/4 = 3/4) to get the probability of offspring with the dominant phenotype.

The product rule and the sum rule

Applying probability rules to dihybrid crosses.

Direct calculation of probabilities doesn’t have much advantage over Punnett squares for single-gene inheritance scenarios. (In fact, if you prefer to learn visually, you may find direct calculation trickier rather than easier.) Where probabilities shine, though, is when you’re looking at the behavior of two, or even more, genes.

For instance, let’s imagine that we breed two dogs with the genotype BbCc , where dominant allele B specifies black coat color (versus b , yellow coat color) and dominant allele C specifies straight fur (versus c , curly fur). Assuming that the two genes assort independently and are not sex-linked, how can we predict the number of BbCc puppies among the offspring?

One approach is to draw a 16-square Punnett square. For a cross involving two genes, a Punnett square is still a good strategy. Alternatively, we can use a shortcut technique involving four-square Punnett squares and a little application of the product rule. In this technique, we break the overall question down into two smaller questions, each relating to a different genetic event:

  • What’s the probability of getting a Bb genotype?
  • What’s the probability of getting an Cc genotype?

In order for a puppy to have a BbCc genotype, both of these events must take place: the puppy must receive Bb alleles, and it must receive Cc alleles. The two events are independent because the genes assort independently (don't affect one another's inheritance). So, once we calculate the probability of each genetic event, we can multiply these probabilities using the product rule to get the probability of the genotype of interest ( BbCc ).

Diagram illustrating how 2X2 Punnett squares can be used in conjunction with the product rule to determine the probability of a particular genotype in a dihybrid cross. Upper panel: Question: when two BbCc dogs are crossed, what is the likelihood of getting a BbCc offspring individual? Lower panel: Solution: probability of BbCc = (probability of Bb) x (probability of Cc). Punnett square for fur color:||B|b-|-|-|-B||BB|**Bb**b||**Bb**|bb Probability of Bb genotype: 1/2. Punnett square for fur texture:||C|c-|-|-|-C||CC|**Cc**c||**Cc**|cc Probability of Cc genotype: 1/2. Probability of BbCc = (probability of Bb) x (probability of Cc). Probability of BbCc = (1/2) x (1/2) = 1/4

To calculate the probability of getting a Bb genotype, we can draw a 4-square Punnett square using the parents' alleles for the coat color gene only, as shown above. Using the Punnett square, you can see that the probability of the Bb genotype is 1/2. (Alternatively, we could have calculated the probability of Bb using the product rule for gamete contributions from the two parents and the sum rule for the two gamete combinations that give Bb .) Using a similar Punnett square for the parents' fur texture alleles, the probability of getting an Cc genotype is also 1/2. To get the overall probability of the BbCc genotype, we can simply multiply the two probabilities, giving an overall probability of 1/4.

16-square Punnett square illustrating the same solution reached using the probability method. ||BC|Bc|bC|bc-|-|-|-|-|-BC||BBCC|BBCc|BbCC|**BbCc**Bc||BBCc|BBcc|**BbCc**|BbccbC||BbCC|**BbCc**|bbCC|bbCcbc||**BbCc**|Bbcc|bbCc|bbcc Fraction of progeny of **BbCc** genotype: 4/16 = 1/4

You can also use this technique to predict phenotype frequencies. Give it a try in the practice question below!

Check your understanding

Query \(\PageIndex{1}\)

We can break the question down into two smaller questions:

  • What fraction of offspring will have black coat color?
  • What fraction of offspring will have straight fur?

Since black coat color and straight fur are dominant traits, all BB and Bb puppies will have black coats, and all CC and Cc puppies will have straight fur, corresponding to 3/4 of puppies in each case. (You can draw out the individual Punnett squares for the color and texture genes to confirm these frequencies.)

To get the probability of a puppy having both black coat color and straight fur, you can multiply the probabilities of these two independent events: \((3/4)\cdot(3/4)=9/16\).

9/16 of the puppies will have black coats and straight fur.

Beyond dihybrid crosses

The probability method is most powerful (and helpful) in cases involving a large number of genes.

For instance, imagine a cross between two individuals with various alleles of four unlinked genes: AaBbCCdd x AabbCcDd . Suppose you wanted to figure out the probability of getting offspring with the dominant phenotype for all four traits. Fortunately, you can apply the exact same logic as in the case of the dihybrid crosses above. To have the dominant phenotype for all four traits, and organism must have: one or more copies of the dominant allele A and one or more copies of dominant allele B and one or more copies of the dominant allele C and one or more copies of the dominant allele D .

Since the genes are unlinked, these are four independent events, so we can calculate a probability for each and then multiply the probabilities to get the probability of the overall outcome.

  • The probability of getting one or more copies of the dominant A allele is 3/4. (Draw a Punnett square for Aa x Aa to confirm for yourself that 3 out of the 4 squares are either AA or Aa .)
  • The probability of getting one or more copies of the dominant B allele is 1/2. (Draw a Punnett square for Bb x bb : you’ll find that half the offspring are Bb , and the other half bb .)
  • The probability of getting one or more copies of the dominant C allele is 1. (If one of the parents is homozygous CC , there’s no way to get offspring without a C allele!)
  • The probability of getting one or more copies of the dominant D allele is 1/2, as for B . (Half the offspring will be Dd , and the other half will be dd .)

To get the overall probability of offspring with the dominant phenotype for all four genes, we can multiply the probabilities of the four independent events: \((3/4)\cdot(1/2)\cdot(1)\cdot(1/2)=3/16\).

Query \(\PageIndex{2}\)

It’s not possible to get a quadruple homozygous recessive individual out of this cross. That’s because the probability of getting two recessive c alleles is zero. The first parent has only dominant alleles for this gene, ensuring that each of the offspring will receive at least one dominant C allele (and thus cannot display the recessive phenotype).

How does the zero probability of a cc genotype figure in mathematically? To get the overall probability of the aabbccdd genotype, we'd have to multiply the probabilities of the desired genotypes for the other three genes ( aa , 1/4; bb , 1/2; and dd , 1/2) by the zero corresponding to the cc genotype, giving an overall probability of zero.

\(P(aabbccdd)=P(aa) \cdot P(bb) \cdot P(cc) \cdot P(dd)\)

\(P(aabbccdd)=(1/4)\cdot(1/2)\cdot(0)\cdot(1/2)=0\)

The probability of getting an individual with a recessive phenotype for all four genes is 0.

Contributors and Attributions

Khan Academy (CC BY-NC-SA 3.0; All Khan Academy content is available for free at www.khanacademy.org )

Attribution:

This article is a modified derivative of the following articles:

  • “ Mendel’s experiments and the laws of probability ,” by OpenStax College, Biology ( CC BY 3.0 ). Download the original article for free at http://cnx.org/contents/[email protected] .
  • “ Laws of inheritance ,” by OpenStax College, Biology ( CC BY 3.0 ). Download the original article for free at http://cnx.org/contents/[email protected] .

The modified article is licensed under a CC BY-NC-SA 4.0 license.

Additional references:

Griffiths, A. J. F., Miller, J. H., Suzuki, D. T., Lewontin, R. C., and Gelbart, W. M. (2000). Using genetic ratios. In An introduction to genetic analysis (7th ed.). New York, NY: W. H. Freeman. Retrieved from http://www.ncbi.nlm.nih.gov/books/NBK21812/ .

Purves, W. K., Sadava, D., Orians, G. H., and Heller, H. C. (2003). Punnett squares or probability calculations: A choice of methods. In Life: The science of biology (7th ed., pp. 195-196). Sunderland, MA: Sinauer Associates.

Reece, J. B., Urry, L. A., Cain, M. L., Wasserman, S. A., Minorsky, P. V., and Jackson, R. B. (2011). Mendel and the gene idea. In Campbell Biology (10th ed., pp. 267-291). San Francisco, CA: Pearson.

Raven, P. H., Johnson, G. B., Mason, K. A., Losos, J. B., and Singer, S. R. (2014). Patterns of inheritance. In Biology (10th ed., AP ed., pp. 221-238). New York, NY: McGraw-Hill.

Staroscik, A. (2015). Punnett square calculator. In SciencePrimer.com . Retrieved from http://scienceprimer.com/punnett-square-calculator .

The Adapa Project. (2014, August 13). What are the laws of segregation and independent assortment and why are they so important? In BioBook . Retrieved from https://adapaproject.org/bbk_temp/tiki-index.php?page=Leaf%3A+What+are+the+laws+of+segregation+and+independent+assortment+and+why+are+they+so+important%3F .

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Test And Quizzes for Biology, Pre-AP, Or AP Biology For Teachers And Students

Dimensional Analysis: Definition, Examples, And Practice

dimensional analysis

If you’ve heard the term “dimensional analysis,” you might find it a bit overwhelming. While there’s a lot to “unpack” when learning about dimensional analysis, it’s a lot easier than you might think. Learn more about the basics and a few examples of how to utilize the unique method of conversion.

Dimensional Analysis: Definition, Examples, and Practice

solving problems biology definition

As we mentioned, you may hear dimensional analysis referred to as unit analysis; it is often also known as factor-label method or the unit factor method. A formal definition of dimensional analysis refers to a method of analysis “in which physical quantities are expressed in terms of their fundamental dimensions that is often used.”

Most people might agree that this definition needs to be broken down a bit and simplified. It might be easier to understand this method of analysis if we look at it as a method of solving problems by looking converting one thing to another.

While dimensional analysis may seem like just another equation, one of the unique (and important) parts of the equation is that the unit of measurement always plays a role in the equation (not just the numbers).

We use conversions in everyday life (such as when following a recipe) and in math class or in a biology course. When we think about dimensional analysis, we’re looking at units of measurement, and this could be anything from miles per gallon or pieces of pie per person.

Many people may “freeze up” when they see a dimensional analysis worksheet or hear about it in class, but if you’re struggling with some of the concepts, just remember that it’s about units of measurements and conversion. Dimensional analysis is used in a variety of applications and is frequently used by chemists and other scientists.

The Conversion Factor in Dimensional Analysis

solving problems biology definition

One important thing to consider when using dimensional analysis is the conversion factor. A conversion factor , which is always equal to 1, is a fraction or numerical ratio that can help you express the measurement from one unit to the next.

When using a conversion factor, the values must represent the same quantity. For example, one yard is the same as three feet or seven days is the same as one week. Let’s do a quick example of a conversion factor.

Imagine you have 20 ink pens and you multiply that by 1; you still have the same amount of pens. You might want to find out how many packages of pens that 20 pens equal and to figure this out, you need your conversion factor.

solving problems biology definition

Now, imagine that you found the packaging for a set of ink pens and the label says that there are 10 pens to each package. Your conversion factor ends up being your conversion factor. The equation might look something like this:

20 ink pens x 1 package of pens/10 pens = 2 packages of ink pens. We’ve canceled out the pens (as a unit) and ended up with the package of pens.

​ While this is a basic scenario, and you probably wouldn’t need to use a conversion factor to figure out how many pens you have, it gives you an idea of what it does and how it works. As you can see, conversion factors work a lot like fractions (working with numerators and denominators)

Even though you’re more likely to work with more complex units of measurement while in chemistry, physics, or other science and math courses, you should have a better understanding of using the conversion factor in relation to the units of measurement.

Steps For Working Through A Problem Using Dimensional Analysis

solving problems biology definition

Like many things, practice makes perfect and dimensional analysis is no exception. Before you tackle a dimensional analysis that your instructor hands to you, here are some tips to consider before you get started.

  • Read the problem carefully and take your time
  • Find out what unit should be your answer
  • Write down your problem in a way that you can understand
  • Consider a simple math equation and don’t forget the conversion factors
  • Remember, some of the units should cancel out, resulting in the unit you want
  • Double-check and retry if you have to
  • The answer you come up with should make sense to you

To help you understand the basic steps we are using an easy problem that you could probably figure out fairly quickly. The question is: How many seconds are in a day?

solving problems biology definition

First, you need to read the question and determine the unit you want to end up with; in this case, you want to figure out “seconds in a day.” To turn this word problem into a math equation, you might decide to put seconds/day or sec/day.

The next step is to figure out what you already know. You know that there are 60 seconds to one minute and you also know that there are 24 hours in one day; all of these units work together, and you should be able to come up with your final unit of measurement. Again, it’s best to write down everything you know into an equation.

After you’ve done a little math, your starting factor might end up being 60 seconds/1 minute. Next, you will need to work your way into figuring out how many seconds per hour. This equation will be 60 seconds/1 minute x 60 minutes/1 hour. The minutes cancel themselves out, and you have seconds per hour.

Remember, you want to find out seconds per day so you’ll need to add another factor that will cancel out the hours. The equation should be 60 seconds/1 minute x 60 minutes/1 hour x 24 hours/1 day. All units but seconds per day should cancel out and if you’ve done your math correctly 86,400 seconds/1 day.

When doing a dimensional analysis problem, it’s more important to pay attention to the units and make sure you are canceling out the right ones to get the final product. Doing your math correctly important, but it’s easier to double-check than trying to backtrack and figure out how you ended up with the wrong unit.

Our example is relatively simple, and you probably had no problem getting the right answer or using the right units. As you work through your science courses, you will be faced with more difficult units to understand. While dimensional analysis will undoubtedly be more challenging, just keep your eye on the units, and you should be able to get through a problem just fine.

Why Use Dimensional Analysis?

solving problems biology definition

As we’ve demonstrated, dimensional analysis can help you figure out problems that you may encounter in your everyday. While you’re likely to explore dimensional analysis a bit more as you take science courses, it can be particularly helpful for Biology students to learn more.

Some believe that dimensional analysis can help students in Biology have a “better feel for numbers” and help them transition more easily into courses like Organic Chemistry or even Physics (if you haven’t taken those courses yet).

Can you figure out a math equation or a word problem without dimensional analysis? Of course, and many people have their own ways of working through a problem. If you do it correctly, dimensional analysis can actually help you answer a problem more efficiently and accurately.

Ready To Test Your Dimensional Analysis Skills?

If you want to practice dimensional analysis, there are dozens of online dimensional analysis worksheets. While many of them are pretty basic or geared towards specific fields of study like Chemistry, we found a worksheet that has an interesting variety. Test out what we’ve talked about and check your answers when you’re done.

  • How many minutes are in 1 year?
  • Traveling at 65 miles/hour, how many minutes will it take to drive 125 miles to San Diego?
  • Convert 4.65 km to meters
  • Convert 9,474 mm to centimeters
  • Traveling at 65 miles/hour, how many feet can you travel in 22 minutes? (1 mile = 5280 feet)

Ready to check out your answers and see more questions? Click here .

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    Forming a Hypothesis. The next step in a scientific investigation is forming a hypothesis.A hypothesis is a possible answer to a scientific question, but it isn't just any answer. A hypothesis must be based on scientific knowledge, and it must be logical. A hypothesis also must be falsifiable. In other words, it must be possible to make observations that would disprove the hypothesis if it ...

  7. 1.3: The Science of Biology

    The scientific method can be applied to almost all fields of study as a logical, rational, problem-solving method. Figure 1.3.1 1.3. 1: Sir Francis Bacon: Sir Francis Bacon (1561-1626) is credited with being the first to define the scientific method. The scientific process typically starts with an observation (often a problem to be solved ...

  8. Step by Step: Biology Undergraduates' Problem-Solving Procedures during

    For the purposes of this article, we define problem solving as a decision-making process wherein a person is presented with a task, and the path to solving the task is uncertain. We define a problem as a task that presents a challenge that cannot be solved automatically ( Martinez, 1998 ).

  9. 1.1 The Science of Biology

    Biology is the science that studies living organisms and their interactions with one another and with their environment. The process of science attempts to describe and understand the nature of the universe by rational means. Science has many fields; those fields related to the physical world, including biology, are considered natural sciences.

  10. Insight learning Definition and Examples

    Definition noun A type of learning that uses reason, especially to form conclusions, inferences, or judgments, to solve a problem. Supplement Unlike learning by trial-and-error, insight learning is solving problems not based on actual experience

  11. Probabilities in genetics (article)

    , or very close to 1 in 4 seeds. The theoretical probability of an event is calculated based on information about the rules and circumstances that produce the event. It reflects the number of times an event is expected to occur relative to the number of times it could possibly occur.

  12. Synthetic Biology

    Synthetic biology is a field of science that involves redesigning organisms for useful purposes by engineering them to have new abilities. Synthetic biology researchers and companies around the world are harnessing the power of nature to solve problems in medicine, manufacturing and agriculture.

  13. Problem Definition and Examples

    1. A question proposed for solution; a matter stated for examination or proof; hence, a matter difficult of solution or settlement; a doubtful case; a question involving doubt. 2. (Science: mathematics) Anything which is required to be done; as, in geometry, to bisect a line, to draw a perpendicular; or, in algebra, to find an unknown quantity.

  14. Unsolved problems in biology—The state of current thinking

    We are still many years away from solving this problem, and it lies at the heart of understanding developmental biology, cancer pathogenesis. ... "The origin of life and its evolution is clearly the central problem in Biology. ... The Oxford English Dictionary definition of plasticity, when applied to biology is, "The adaptability of an ...

  15. How Does Cell Division Solve the Problem of Increasing Size

    When an organism grows, it's because its cells are dividing not getting bigger. Cells divide for several reasons including to keep them from getting too big.

  16. Scientific Method

    Definition The scientific method is a series of processes that people can use to gather knowledge about the world around them, improve that knowledge, and attempt to explain why and/or how things occur. This method involves making observations, forming questions, making hypotheses, doing an experiment, analyzing the data, and forming a conclusion.

  17. List of unsolved problems in biology

    Category v t e This article lists notable unsolved problems in biology . General biology Evolution and origins of life Origin of life. Exactly how, where, and when did life on Earth originate? Which, if any, of the many hypotheses is correct? What were the metabolic pathways used by the earliest life forms? How did genetic code originate?

  18. Executive Function: Definition, Examples, Signs of Dysfunction

    solving a problem, such as finding fixes for a mysterious leak; interacting socially, such as expressing empathy, maintaining control during debates, and adjusting your behaviors based on the ...

  19. Art of Problem Solving

    Sciences known collectively as "biology" include botany, the study of plants; ornithology, the study of birds; zoology, the study of animals; ecology, the study of the ecosystem; entomology, the study of insects; and other sciences.

  20. Step by Step: Biology Undergraduates' Problem-Solving Procedures during

    However, problem solving is not intuitive to students, and these skills typically are not explicitly taught in the classroom (Nehm, 2010; Hoskinson et al., 2013). One reason for this misalignment between faculty values and their teaching practice is that biology problem-solving procedures have not been clearly defined.

  21. 1.7: Probabilities in genetics

    The product rule. One probability rule that's very useful in genetics is the product rule, which states that the probability of two (or more) independent events occurring together can be calculated by multiplying the individual probabilities of the events. For example, if you roll a six-sided die once, you have a 1/6 chance of getting a six.

  22. The Biology Project: BioMath

    Then test your knowledge. Linear Functions Learn the definition of linear function, how to calculate the slope of a line, how to solve a linear equation, and how linear models are used in biology. Then practice what you have learned. Quadratic Functions Learn the definition of a quadratic function, what the graph of quadratic function looks ...

  23. Dimensional Analysis: Definition, Examples, and Practice

    As we mentioned, you may hear dimensional analysis referred to as unit analysis; it is often also known as factor-label method or the unit factor method. A formal definition of dimensional analysis refers to a method of analysis "in which physical quantities are expressed in terms of their fundamental dimensions that is often used.".