Logo for FHSU Digital Press

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

5 Teaching Mathematics Through Problem Solving

Janet Stramel

Problem Solving

In his book “How to Solve It,” George Pólya (1945) said, “One of the most important tasks of the teacher is to help his students. This task is not quite easy; it demands time, practice, devotion, and sound principles. The student should acquire as much experience of independent work as possible. But if he is left alone with his problem without any help, he may make no progress at all. If the teacher helps too much, nothing is left to the student. The teacher should help, but not too much and not too little, so that the student shall have a reasonable share of the work.” (page 1)

What is a problem  in mathematics? A problem is “any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method” (Hiebert, et. al., 1997). Problem solving in mathematics is one of the most important topics to teach; learning to problem solve helps students develop a sense of solving real-life problems and apply mathematics to real world situations. It is also used for a deeper understanding of mathematical concepts. Learning “math facts” is not enough; students must also learn how to use these facts to develop their thinking skills.

According to NCTM (2010), the term “problem solving” refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. When you first hear “problem solving,” what do you think about? Story problems or word problems? Story problems may be limited to and not “problematic” enough. For example, you may ask students to find the area of a rectangle, given the length and width. This type of problem is an exercise in computation and can be completed mindlessly without understanding the concept of area. Worthwhile problems  includes problems that are truly problematic and have the potential to provide contexts for students’ mathematical development.

There are three ways to solve problems: teaching for problem solving, teaching about problem solving, and teaching through problem solving.

Teaching for problem solving begins with learning a skill. For example, students are learning how to multiply a two-digit number by a one-digit number, and the story problems you select are multiplication problems. Be sure when you are teaching for problem solving, you select or develop tasks that can promote the development of mathematical understanding.

Teaching about problem solving begins with suggested strategies to solve a problem. For example, “draw a picture,” “make a table,” etc. You may see posters in teachers’ classrooms of the “Problem Solving Method” such as: 1) Read the problem, 2) Devise a plan, 3) Solve the problem, and 4) Check your work. There is little or no evidence that students’ problem-solving abilities are improved when teaching about problem solving. Students will see a word problem as a separate endeavor and focus on the steps to follow rather than the mathematics. In addition, students will tend to use trial and error instead of focusing on sense making.

Teaching through problem solving  focuses students’ attention on ideas and sense making and develops mathematical practices. Teaching through problem solving also develops a student’s confidence and builds on their strengths. It allows for collaboration among students and engages students in their own learning.

Consider the following worthwhile-problem criteria developed by Lappan and Phillips (1998):

  • The problem has important, useful mathematics embedded in it.
  • The problem requires high-level thinking and problem solving.
  • The problem contributes to the conceptual development of students.
  • The problem creates an opportunity for the teacher to assess what his or her students are learning and where they are experiencing difficulty.
  • The problem can be approached by students in multiple ways using different solution strategies.
  • The problem has various solutions or allows different decisions or positions to be taken and defended.
  • The problem encourages student engagement and discourse.
  • The problem connects to other important mathematical ideas.
  • The problem promotes the skillful use of mathematics.
  • The problem provides an opportunity to practice important skills.

Of course, not every problem will include all of the above. Sometimes, you will choose a problem because your students need an opportunity to practice a certain skill.

Key features of a good mathematics problem includes:

  • It must begin where the students are mathematically.
  • The feature of the problem must be the mathematics that students are to learn.
  • It must require justifications and explanations for both answers and methods of solving.

Needlepoint of cats

Problem solving is not a  neat and orderly process. Think about needlework. On the front side, it is neat and perfect and pretty.

Back of a needlepoint

But look at the b ack.

It is messy and full of knots and loops. Problem solving in mathematics is also like this and we need to help our students be “messy” with problem solving; they need to go through those knots and loops and learn how to solve problems with the teacher’s guidance.

When you teach through problem solving , your students are focused on ideas and sense-making and they develop confidence in mathematics!

Mathematics Tasks and Activities that Promote Teaching through Problem Solving

Teacher teaching a math lesson

Choosing the Right Task

Selecting activities and/or tasks is the most significant decision teachers make that will affect students’ learning. Consider the following questions:

  • Teachers must do the activity first. What is problematic about the activity? What will you need to do BEFORE the activity and AFTER the activity? Additionally, think how your students would do the activity.
  • What mathematical ideas will the activity develop? Are there connections to other related mathematics topics, or other content areas?
  • Can the activity accomplish your learning objective/goals?

problem solving method of teaching mathematics ppt

Low Floor High Ceiling Tasks

By definition, a “ low floor/high ceiling task ” is a mathematical activity where everyone in the group can begin and then work on at their own level of engagement. Low Floor High Ceiling Tasks are activities that everyone can begin and work on based on their own level, and have many possibilities for students to do more challenging mathematics. One gauge of knowing whether an activity is a Low Floor High Ceiling Task is when the work on the problems becomes more important than the answer itself, and leads to rich mathematical discourse [Hover: ways of representing, thinking, talking, agreeing, and disagreeing; the way ideas are exchanged and what the ideas entail; and as being shaped by the tasks in which students engage as well as by the nature of the learning environment].

The strengths of using Low Floor High Ceiling Tasks:

  • Allows students to show what they can do, not what they can’t.
  • Provides differentiation to all students.
  • Promotes a positive classroom environment.
  • Advances a growth mindset in students
  • Aligns with the Standards for Mathematical Practice

Examples of some Low Floor High Ceiling Tasks can be found at the following sites:

  • YouCubed – under grades choose Low Floor High Ceiling
  • NRICH Creating a Low Threshold High Ceiling Classroom
  • Inside Mathematics Problems of the Month

Math in 3-Acts

Math in 3-Acts was developed by Dan Meyer to spark an interest in and engage students in thought-provoking mathematical inquiry. Math in 3-Acts is a whole-group mathematics task consisting of three distinct parts:

Act One is about noticing and wondering. The teacher shares with students an image, video, or other situation that is engaging and perplexing. Students then generate questions about the situation.

In Act Two , the teacher offers some information for the students to use as they find the solutions to the problem.

Act Three is the “reveal.” Students share their thinking as well as their solutions.

“Math in 3 Acts” is a fun way to engage your students, there is a low entry point that gives students confidence, there are multiple paths to a solution, and it encourages students to work in groups to solve the problem. Some examples of Math in 3-Acts can be found at the following websites:

  • Dan Meyer’s Three-Act Math Tasks
  • Graham Fletcher3-Act Tasks ]
  • Math in 3-Acts: Real World Math Problems to Make Math Contextual, Visual and Concrete

Number Talks

Number talks are brief, 5-15 minute discussions that focus on student solutions for a mental math computation problem. Students share their different mental math processes aloud while the teacher records their thinking visually on a chart or board. In addition, students learn from each other’s strategies as they question, critique, or build on the strategies that are shared.. To use a “number talk,” you would include the following steps:

  • The teacher presents a problem for students to solve mentally.
  • Provide adequate “ wait time .”
  • The teacher calls on a students and asks, “What were you thinking?” and “Explain your thinking.”
  • For each student who volunteers to share their strategy, write their thinking on the board. Make sure to accurately record their thinking; do not correct their responses.
  • Invite students to question each other about their strategies, compare and contrast the strategies, and ask for clarification about strategies that are confusing.

“Number Talks” can be used as an introduction, a warm up to a lesson, or an extension. Some examples of Number Talks can be found at the following websites:

  • Inside Mathematics Number Talks
  • Number Talks Build Numerical Reasoning

Light bulb

Saying “This is Easy”

“This is easy.” Three little words that can have a big impact on students. What may be “easy” for one person, may be more “difficult” for someone else. And saying “this is easy” defeats the purpose of a growth mindset classroom, where students are comfortable making mistakes.

When the teacher says, “this is easy,” students may think,

  • “Everyone else understands and I don’t. I can’t do this!”
  • Students may just give up and surrender the mathematics to their classmates.
  • Students may shut down.

Instead, you and your students could say the following:

  • “I think I can do this.”
  • “I have an idea I want to try.”
  • “I’ve seen this kind of problem before.”

Tracy Zager wrote a short article, “This is easy”: The Little Phrase That Causes Big Problems” that can give you more information. Read Tracy Zager’s article here.

Using “Worksheets”

Do you want your students to memorize concepts, or do you want them to understand and apply the mathematics for different situations?

What is a “worksheet” in mathematics? It is a paper and pencil assignment when no other materials are used. A worksheet does not allow your students to use hands-on materials/manipulatives [Hover: physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics]; and worksheets are many times “naked number” with no context. And a worksheet should not be used to enhance a hands-on activity.

Students need time to explore and manipulate materials in order to learn the mathematics concept. Worksheets are just a test of rote memory. Students need to develop those higher-order thinking skills, and worksheets will not allow them to do that.

One productive belief from the NCTM publication, Principles to Action (2014), states, “Students at all grade levels can benefit from the use of physical and virtual manipulative materials to provide visual models of a range of mathematical ideas.”

You may need an “activity sheet,” a “graphic organizer,” etc. as you plan your mathematics activities/lessons, but be sure to include hands-on manipulatives. Using manipulatives can

  • Provide your students a bridge between the concrete and abstract
  • Serve as models that support students’ thinking
  • Provide another representation
  • Support student engagement
  • Give students ownership of their own learning.

Adapted from “ The Top 5 Reasons for Using Manipulatives in the Classroom ”.

any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method

should be intriguing and contain a level of challenge that invites speculation and hard work, and directs students to investigate important mathematical ideas and ways of thinking toward the learning

involves teaching a skill so that a student can later solve a story problem

when we teach students how to problem solve

teaching mathematics content through real contexts, problems, situations, and models

a mathematical activity where everyone in the group can begin and then work on at their own level of engagement

20 seconds to 2 minutes for students to make sense of questions

Mathematics Methods for Early Childhood Copyright © 2021 by Janet Stramel is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

Share This Book

Library homepage

  • school Campus Bookshelves
  • menu_book Bookshelves
  • perm_media Learning Objects
  • login Login
  • how_to_reg Request Instructor Account
  • hub Instructor Commons
  • Download Page (PDF)
  • Download Full Book (PDF)
  • Periodic Table
  • Physics Constants
  • Scientific Calculator
  • Reference & Cite
  • Tools expand_more
  • Readability

selected template will load here

This action is not available.

Mathematics LibreTexts

Module 1: Problem Solving Strategies

  • Last updated
  • Save as PDF
  • Page ID 10352

Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. As you solve more problems (and learn how other people solved them), you learn strategies and techniques that can be useful. But no single strategy works every time.

Pólya’s How to Solve It

George Pólya was a great champion in the field of teaching effective problem solving skills. He was born in Hungary in 1887, received his Ph.D. at the University of Budapest, and was a professor at Stanford University (among other universities). He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985.1

1. Image of Pólya by Thane Plambeck from Palo Alto, California (Flickr) [CC BY

Screen Shot 2018-08-30 at 4.43.05 PM.png

In 1945, Pólya published the short book How to Solve It , which gave a four-step method for solving mathematical problems:

First, you have to understand the problem.

After understanding, then make a plan.

Carry out the plan.

Look back on your work. How could it be better?

This is all well and good, but how do you actually do these steps?!?! Steps 1. and 2. are particularly mysterious! How do you “make a plan?” That is where you need some tools in your toolbox, and some experience to draw upon.

Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor (and where it becomes so much fun). We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems!

Problem Solving Strategy 1 (Guess and Test)

Make a guess and test to see if it satisfies the demands of the problem. If it doesn't, alter the guess appropriately and check again. Keep doing this until you find a solution.

Mr. Jones has a total of 25 chickens and cows on his farm. How many of each does he have if all together there are 76 feet?

Step 1: Understanding the problem

We are given in the problem that there are 25 chickens and cows.

All together there are 76 feet.

Chickens have 2 feet and cows have 4 feet.

We are trying to determine how many cows and how many chickens Mr. Jones has on his farm.

Step 2: Devise a plan

Going to use Guess and test along with making a tab

Many times the strategy below is used with guess and test.

Make a table and look for a pattern:

Procedure: Make a table reflecting the data in the problem. If done in an orderly way, such a table will often reveal patterns and relationships that suggest how the problem can be solved.

Step 3: Carry out the plan:

Notice we are going in the wrong direction! The total number of feet is decreasing!

Better! The total number of feet are increasing!

Step 4: Looking back:

Check: 12 + 13 = 25 heads

24 + 52 = 76 feet.

We have found the solution to this problem. I could use this strategy when there are a limited number of possible answers and when two items are the same but they have one characteristic that is different.

Videos to watch:

1. Click on this link to see an example of “Guess and Test”

http://www.mathstories.com/strategies.htm

2. Click on this link to see another example of Guess and Test.

http://www.mathinaction.org/problem-solving-strategies.html

Check in question 1:

clipboard_e6298bbd7c7f66d9eb9affcd33892ef0d.png

Place the digits 8, 10, 11, 12, and 13 in the circles to make the sums across and vertically equal 31. (5 points)

Check in question 2:

Old McDonald has 250 chickens and goats in the barnyard. Altogether there are 760 feet . How many of each animal does he have? Make sure you use Polya’s 4 problem solving steps. (12 points)

Problem Solving Strategy 2 (Draw a Picture). Some problems are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric thinking visually can help!

Videos to watch demonstrating how to use "Draw a Picture".

1. Click on this link to see an example of “Draw a Picture”

2. Click on this link to see another example of Draw a Picture.

Problem Solving Strategy 3 ( Using a variable to find the sum of a sequence.)

Gauss's strategy for sequences.

last term = fixed number ( n -1) + first term

The fix number is the the amount each term is increasing or decreasing by. "n" is the number of terms you have. You can use this formula to find the last term in the sequence or the number of terms you have in a sequence.

Ex: 2, 5, 8, ... Find the 200th term.

Last term = 3(200-1) +2

Last term is 599.

To find the sum of a sequence: sum = [(first term + last term) (number of terms)]/ 2

Sum = (2 + 599) (200) then divide by 2

Sum = 60,100

Check in question 3: (10 points)

Find the 320 th term of 7, 10, 13, 16 …

Then find the sum of the first 320 terms.

Problem Solving Strategy 4 (Working Backwards)

This is considered a strategy in many schools. If you are given an answer, and the steps that were taken to arrive at that answer, you should be able to determine the starting point.

Videos to watch demonstrating of “Working Backwards”

https://www.youtube.com/watch?v=5FFWTsMEeJw

Karen is thinking of a number. If you double it, and subtract 7, you obtain 11. What is Karen’s number?

1. We start with 11 and work backwards.

2. The opposite of subtraction is addition. We will add 7 to 11. We are now at 18.

3. The opposite of doubling something is dividing by 2. 18/2 = 9

4. This should be our answer. Looking back:

9 x 2 = 18 -7 = 11

5. We have the right answer.

Check in question 4:

Christina is thinking of a number.

If you multiply her number by 93, add 6, and divide by 3, you obtain 436. What is her number? Solve this problem by working backwards. (5 points)

Problem Solving Strategy 5 (Looking for a Pattern)

Definition: A sequence is a pattern involving an ordered arrangement of numbers.

We first need to find a pattern.

Ask yourself as you search for a pattern – are the numbers growing steadily larger? Steadily smaller? How is each number related?

Example 1: 1, 4, 7, 10, 13…

Find the next 2 numbers. The pattern is each number is increasing by 3. The next two numbers would be 16 and 19.

Example 2: 1, 4, 9, 16 … find the next 2 numbers. It looks like each successive number is increase by the next odd number. 1 + 3 = 4.

So the next number would be

25 + 11 = 36

Example 3: 10, 7, 4, 1, -2… find the next 2 numbers.

In this sequence, the numbers are decreasing by 3. So the next 2 numbers would be -2 -3 = -5

-5 – 3 = -8

Example 4: 1, 2, 4, 8 … find the next two numbers.

This example is a little bit harder. The numbers are increasing but not by a constant. Maybe a factor?

So each number is being multiplied by 2.

16 x 2 = 32

1. Click on this link to see an example of “Looking for a Pattern”

2. Click on this link to see another example of Looking for a Pattern.

Problem Solving Strategy 6 (Make a List)

Example 1 : Can perfect squares end in a 2 or a 3?

List all the squares of the numbers 1 to 20.

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400.

Now look at the number in the ones digits. Notice they are 0, 1, 4, 5, 6, or 9. Notice none of the perfect squares end in 2, 3, 7, or 8. This list suggests that perfect squares cannot end in a 2, 3, 7 or 8.

How many different amounts of money can you have in your pocket if you have only three coins including only dimes and quarters?

Quarter’s dimes

0 3 30 cents

1 2 45 cents

2 1 60 cents

3 0 75 cents

Videos demonstrating "Make a List"

Check in question 5:

How many ways can you make change for 23 cents using only pennies, nickels, and dimes? (10 points)

Problem Solving Strategy 7 (Solve a Simpler Problem)

Geometric Sequences:

How would we find the nth term?

Solve a simpler problem:

1, 3, 9, 27.

1. To get from 1 to 3 what did we do?

2. To get from 3 to 9 what did we do?

Let’s set up a table:

Term Number what did we do

problem solving method of teaching mathematics ppt

Looking back: How would you find the nth term?

problem solving method of teaching mathematics ppt

Find the 10 th term of the above sequence.

Let L = the tenth term

problem solving method of teaching mathematics ppt

Problem Solving Strategy 8 (Process of Elimination)

This strategy can be used when there is only one possible solution.

I’m thinking of a number.

The number is odd.

It is more than 1 but less than 100.

It is greater than 20.

It is less than 5 times 7.

The sum of the digits is 7.

It is evenly divisible by 5.

a. We know it is an odd number between 1 and 100.

b. It is greater than 20 but less than 35

21, 23, 25, 27, 29, 31, 33, 35. These are the possibilities.

c. The sum of the digits is 7

21 (2+1=3) No 23 (2+3 = 5) No 25 (2 + 5= 7) Yes Using the same process we see there are no other numbers that meet this criteria. Also we notice 25 is divisible by 5. By using the strategy elimination, we have found our answer.

Check in question 6: (8 points)

Jose is thinking of a number.

The number is not odd.

The sum of the digits is divisible by 2.

The number is a multiple of 11.

It is greater than 5 times 4.

It is a multiple of 6

It is less than 7 times 8 +23

What is the number?

Click on this link for a quick review of the problem solving strategies.

https://garyhall.org.uk/maths-problem-solving-strategies.html

SlidePlayer

  • My presentations

Auth with social network:

Download presentation

We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!

Presentation is loading. Please wait.

Problem Solving Strategies

Published by Tyler Perkins Modified over 8 years ago

Similar presentations

Presentation on theme: "Problem Solving Strategies"— Presentation transcript:

Problem Solving Strategies

An introduction to Problem Solving Math 110 Iris Yang.

problem solving method of teaching mathematics ppt

M ATHEMATICAL P ROBLEM S OLVING What is it? Why encourage it? How is teaching like a problem-solving endeavor?

problem solving method of teaching mathematics ppt

Chapter 1 The Art of Problem Solving © 2008 Pearson Addison-Wesley. All rights reserved.

problem solving method of teaching mathematics ppt

Kevin Cummins The maths toolbox is a set of strategies that students can put into place to solve mathematical problems. The purpose.

problem solving method of teaching mathematics ppt

Polya’s Four Step Problem Solving Process

problem solving method of teaching mathematics ppt

Welcome to MATH 302A Please find the index card with your name on it and sit there. On the other side of the index card, write: Name as you wish to be.

problem solving method of teaching mathematics ppt

MAKING PROBLEM SOLVING LESS PROBLEMATIC

problem solving method of teaching mathematics ppt

Exploration 1.1 With 24 people in class, including yourself, if each person shakes hands with every person, how many handshakes will there be?

problem solving method of teaching mathematics ppt

Problem Solving The process of applying previously acquired knowledge to new and unfamiliar situations.

problem solving method of teaching mathematics ppt

Correlating Go Math & Standards for Mathematical Practices

problem solving method of teaching mathematics ppt

SASE Contextualised group work – teaching a broader mathematics curriculum to first year science students: Case study – Problem solving Jo-ann Larkins.

problem solving method of teaching mathematics ppt

Problem Solving Tool: KFC.

problem solving method of teaching mathematics ppt

Test Preparation Strategies

problem solving method of teaching mathematics ppt

Survey of Mathematical Ideas Math 100 Chapter 1 John Rosson Tuesday January 23, 2007.

problem solving method of teaching mathematics ppt

M ATH C OMMITTEE Mathematical Shifts Mathematical Practices.

problem solving method of teaching mathematics ppt

PROBLEM SOLVING in Math What you need to know. OVERVIEW: Define “Problem” Where do I start… How can I solve problems… Trying strategies –Patterns –Tables.

problem solving method of teaching mathematics ppt

Problem solving Math 123. Why problem solving? Essential for mathematics According to NCTM, one of the processes through which mathematics should be.

problem solving method of teaching mathematics ppt

Helping Children with Problem Solving CHAPTER 6 Tina Rye Sloan To accompany Helping Children Learn Math9e, Reys et al. ©2009 John Wiley & Sons.

problem solving method of teaching mathematics ppt

Helping Children with Problem Solving CHAPTER 6 Tina Rye Sloan To accompany Helping Children Learn Math10e, Reys et al. ©2012John Wiley & Sons.

problem solving method of teaching mathematics ppt

Buckland CE Primary School

About project

© 2024 SlidePlayer.com Inc. All rights reserved.

slide1

Teaching Mathematics through Problem Solving

Jul 23, 2013

330 likes | 541 Views

Teaching Mathematics through Problem Solving. Sonja Karsh and Joyce Tonner Student Achievement Officers, Literacy and Numeracy Secretariat. Teaching Through Problem Solving.

Share Presentation

  • math lesson design
  • sonja karsh
  • metric unit
  • problem solving
  • numeracy secretariat

karif

Presentation Transcript

Teaching Mathematics through Problem Solving Sonja Karsh and Joyce Tonner Student Achievement Officers, Literacy and Numeracy Secretariat

Teaching Through Problem Solving “ It’s the questions that drive mathematics. Solving problems and making up new ones is the essence of mathematical life.” Fosnot and Dolk, 2001 Instructional Strategies: Quotations and Think-Pair-Share

Learning Goals During this session, numeracy coaches will: • develop an understanding of the difference between learning through problem solving andlearning about problem solving • solve problems to deepen their understanding of the big ideas of measurement • study, practise, and reflect on the critical aspects of content-focused coaching Instructional Strategies: Identify learning goals

Job-embedded structures we will use today: • Co-teaching • Teacher inquiry / study • Coaching

The meaning of “3” Discuss with your elbow partner instances in your professional life where “3” has significance. Instructional Strategies: Accessing Prior Knowledge through Connections

Building the Who’s Whoof Teaching through Problem Solving In your group, reflect on the characteristics we can list on our Who’s Who of “Teaching Through Problem Solving.” Instructional Strategies: Creating an anticipation chart

1: The “before” … from front matter of Coaching binder (Coaching Institute 2006), www.curriculum.org The pre-lesson conference • The teacher clarifies lesson goals and objectives • The coach becomes familiar with the teacher’s thinking, beliefs, and knowledge • The coach and the teacher agree to be accountable for effective student learning • The coach and teacher collaboratively design the lesson • The coach and teacher develop a shared view of understandings, strategies, concepts and skills on which students are working Instructional Strategies: Conferencing

The “before” continued • The coach and teacher determine what will be the evidence of student achievement • The coach and teacher identify resources, materials and procedures to be used in a lesson • The coach and teacher anticipate students’ responses • The coach and teacher describe the lesson’s relationship to the curriculum

2: The “during” … from front matter of Coaching binder (Coaching Institute 2006), www.curriculum.org Lesson • The coach’s role is collaborative • The coach is partner with the teacher in working towards shared goals, not a critic of the teacher’s practice • The teacher and coach co-create conditions to make the lesson one in which students learn Instructional Strategies: Co-Teaching

The “during” continued • The teacher and coach negotiate how they collaborate; (e.g., the teacher and coach collaboratively respond to emergent and dynamic student thinking and adjust instruction as they gather evidence of learning)

3: The “after” … from front matter of Coaching binder (Coaching Institute 2006), www.curriculum.org The post-lesson conference • The teacher and coach talk about how the lesson plan was implemented • The teacher and coach talk about the degree of success of the lesson • The teacher and coach discuss problems that arose and whether or not the students learned what they were supposed to learn • The teacher and coach analyse the students’ work and use the evidence as feedback for planning the next lesson

Measurement Strand: Attributes, Units, and Measurement Sense Grade 1 Identify and describe common two dimensional shapes Grade 2 Estimate, measure, and record the distance around the objects, using non standard units Grade 3 Estimate, measure, and record the perimeter of two-dimensional shapes, through investigation using standard units Grade 5 Estimate and the perimeter and area of regular and irregular polygons, using a variety of tools Grade 6 Select and justify the appropriate metric unit to measure length or distance in a given real-life situation Grade 4 Estimate, measure, using a variety of tools and strategies, and record the perimeter and area of polygons Big Idea: The closer a shape approaches a square, the smaller the perimeter Connections from other strands: Number Sense and Numeration - Ratio

The Three Part Lesson: 1 2 3 The “Warm Up” A candy box holds 4 chocolates. What are the dimensions of the box that creates the longest perimeter? Instructional Strategies: Activating Prior Knowledge

The Three Part Lesson: 1 2 3 The “Problem” Ms. T. promised her class that she would give them one minute of play time for every unit of a perimeter they could create.  If they create a shape 60 cm long, they will receive an extra hour to play any game of their choice!  What is the greatest perimeter the students can create inside a 10 cm by 10 cm grid? Coach’s Corner - Pre-lesson conference What questions would you ask? Content-focused coaching: The teacher explains the goals of the lesson and how she/he plans to teach it. Concept:Measuring perimeter Approach: Teaching through Problem Solving Instructional Strategies: Problem Solving and Metacognitive Reflections

Extensions If you received one minute for each segment of .75cm, how much time would you have now? Build the net of the polyhedron that has the greatest perimeter.

Math Congress Please post your work so we can share the thinking. Coach’s Corner - The lesson: Co-teaching • Joyce and Sonja confer to select the work to be shared. The purpose is to show a range of approaches and strategies, and highlight the big idea(s) of the lesson. • The relationship is collaborative and focused on student learning, not on the teacher’s performance. • The discussion focused on the representations that support their use. Co-teachers set the criteria. In this case, help in making generalizations. Instructional Strategies: Math congress

Math Congress Other criteria for selecting student work to be shared. • comparing solutions of others – same / different • giving feedback that can be used to edit solution presentation • different strategies • different representations • conceptual models • emerging math concepts and/or properties • error analysis Instructional Strategies: Math congress

Your results The Three Part Lesson: 1 23 • What strategies did you use to increase the perimeter of your shape? • How do you know you have found the greatest perimeter possible? • What is the relationship between the perimeter and the number of sides of a shape? • What is the relationship between the perimeter and the number of corners in a shape? Instructional Strategies: Analysing Data to Reveal the Math

Possible student solutions • Able to count units • Able to recognize we are counting small lengths, not dots or vertices • Able to use squares and rectangles • Able to recognize counting corners results in two units • Able to write their thinking in a number sentence • Able to connect the ratio of the lengths to the amount of time they win

Coach’s Corner - Lesson • The coach’s role is collaborative • The coach is a partner with the teacher in working towards shared goals, not a critic of the teacher’s practice • The teacher and coach co-create conditions to make the lesson one in which students learn • What questions would you ask? • What observations would you make? • What suggestions would you add to the lesson?

Adding to the Who’s Who In your group, reflect on what we have done to date. List any additional characteristics we could add to our Who’s Who of “Teaching Through Problem Solving.” Each group will be asked to report on one characteristic. Instructional Strategies: Re-visiting anticipation chart

The post-lesson conference • The teacher and the coach talk about how the lesson plan was implemented, and with what level of success. • They discuss what problems arose and whether or not the students learned what they were supposed to learn • This process involves looking at students’ work • The feedback gathered here often contributes to data used for planning the next lesson. Instructional Strategies: Pose Questions and/or Problems

Coach’s Corner - Post-lesson conference With a partner, role play the post-lesson conference. • What observations would you make? • What questions would you ask? • How would you determine next steps with the teacher? Remember to keep the discussion focused on students’ learning.

Content-focused Coaching • Pre-lesson conference • The lesson • Post-lesson conference Instructional Strategies: Reviewing key terms and structures

Core Issues in Math Lesson Design • Lesson goals • Lesson plan and design • Students’ relevant prior knowledge • Relationship between the nature of the task and the activity on one hand and the lesson goals on the other hand • Strategies for students to make public their thinking and understanding • Evidence of students’ understanding and learning • Students’ difficulties, confusions, and misconceptions • Ways to encourage collaboration in an atmosphere of mutual respect • Strategies to foster relevant student discussions

Thank you for sharing your thoughts, ideas, and expertise today. Enjoy the rest of the LNS Coaching Institute.

  • More by User

Teaching and Learning Mathematics through Problem Solving

Teaching and Learning Mathematics through Problem Solving

Teaching and Learning Mathematics through Problem Solving. Facilitator’s Handbook A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 (with reference to Volume Two). The Literacy and Numeracy Secretariat Professional Learning Series.

1.12k views • 65 slides

Problem Solving Through Search

Problem Solving Through Search

Problem Solving Through Search. Problems and Search. Problem formulation: an essential step in building an intelligent agent Search: a fundamental and very common solution technique Chapter 3: “Goal”-oriented problems, and basic search strategies Chapter 4: “Informed” search strategies .

339 views • 17 slides

Teaching (and Learning) Through Problem Solving

Teaching (and Learning) Through Problem Solving

Teaching (and Learning) Through Problem Solving. Perspectives. TTPS: Teaching ABOUT Problem Solving. For the last 25-30 years, “ Problem Solving ” has become an increasing focus of mathematics education, including elementary level mathematics.

143 views • 11 slides

Teaching Through Problem Solving

Teaching Through Problem Solving

Teaching Through Problem Solving. EDN 322. NCTM process standards. Problem solving Reasoning and proof Communication Connections Representation. What is a problem? (Van De Walle, 2004). A problem is any task or exploration for which the solution has not been explained…

232 views • 9 slides

Building Math in the classroom - Teaching Through Problem-Solving -

Building Math in the classroom - Teaching Through Problem-Solving -

Building Math in the classroom - Teaching Through Problem-Solving -. Day 6. What we can learn from all your posters. Three triangles are similar triangles (table 1,3,4,5,6,7,10,12) Area changes (table 2, 8, 9,eM) Fold, symmetry, slope (table 11). Three triangles are similar.

363 views • 19 slides

Teaching Problem Solving

Teaching Problem Solving

Teaching Problem Solving. Marie Norman, PhD. Associate Director and Coordinator of Graduate Student Programs Eberly Center for Teaching Excellence [email protected]. Mathematical problem solving: 4 steps. Posing the right question Translating a real-world problem into math Computation

667 views • 33 slides

Teaching Mathematics Through Problem Solving

Teaching Mathematics Through Problem Solving

Teaching Mathematics Through Problem Solving. MNPS Numeracy Coaches Ernestine Saville Brock Mathematics Coordinator. MNPS Vision.

771 views • 53 slides

Generalization through problem solving

Generalization through problem solving

Generalization through problem solving. Part II. The Wallace-Bolyai-Gerwien theorem Cut a quadrilateral into 2 halves. Gergely Wintsche Mathematics Teaching and Didactic Center Faculty of Science Eötvös Loránd University, Budapest.

328 views • 17 slides

TEACHING  LOGIC  AND   PROBLEM-SOLVING  THROUGH   COMPUTER  SCIENCE

TEACHING  LOGIC  AND   PROBLEM-SOLVING  THROUGH   COMPUTER  SCIENCE

TEACHING  LOGIC  AND   PROBLEM-SOLVING  THROUGH   COMPUTER  SCIENCE. Chris Bolognese ( [email protected] ) Upper Arlington High School. What Computer Science Is NOT. Computer Science is not technical support. What Computer Science Is NOT.

435 views • 25 slides

Generalization through problem solving

Generalization through problem solving. Part III .-IV . Probability through statistics. Gergely Wintsche Mathematics Teaching and Didactic Center Faculty of Science Eötvös Loránd University, Budapest.

305 views • 22 slides

Problem Solving in Mathematics

Problem Solving in Mathematics

Problem Solving in Mathematics. Presented by Dot Shea 2013. Problem Solving. Newman’s error analysis states that a s tudent wishing to solve a written mathematics problem typically has to work through five basic steps: 1. Reading the problem 2. Comprehend what is read

1.65k views • 11 slides

Teaching Mathematics through Problem Solving Sonja Karsh & Joyce Tonner August 22, 2006

Teaching Mathematics through Problem Solving Sonja Karsh & Joyce Tonner August 22, 2006

Teaching Mathematics through Problem Solving Sonja Karsh & Joyce Tonner August 22, 2006. Teaching Mathematics through Problem Solving. presented by Sonja Karsh and Joyce Tonner Student Achievement Officers, Literacy and Numeracy Secretariat. Teaching Through Problem Solving.

479 views • 28 slides

Mathematics Upper Primary Problem Solving

Mathematics Upper Primary Problem Solving

Mathematics Upper Primary Problem Solving. Objectives. To share on some common problem solving methods To highlight some problematic areas/common misconceptions in pupils. Ratio. 3. difference. Unchanged data. Ratio.

306 views • 16 slides

Teaching Mathematics via Cooperative Problem Solving

Teaching Mathematics via Cooperative Problem Solving

Teaching Mathematics via Cooperative Problem Solving. Dr. Patrick M. Kimani Assistant Professor Department of Mathematics McCarthy Hall 154 California State University, Fullerton [email protected]. Overview. Background Standards Activity! Discussion Reflection. Background.

404 views • 19 slides

Teaching Mathematics through Problem Solving Emma Ames Jim Fey Mary Jo Messenger Hal Schoen

Teaching Mathematics through Problem Solving Emma Ames Jim Fey Mary Jo Messenger Hal Schoen

Teaching Mathematics through Problem Solving Emma Ames Jim Fey Mary Jo Messenger Hal Schoen. 1. Problem Solving.

666 views • 59 slides

Problem Solving Through Play

Problem Solving Through Play

Problem Solving Through Play. Problem Solving Through Play. Any narrow conceptualisation of play fails to do justice to the powerful contribution play makes, and ensures that play continues to be 'probably one of the least understood aspects of an early educator's work'.

433 views • 23 slides

Teaching and Learning Mathematics through Problem Solving

Teaching and Learning Mathematics through Problem Solving. Facilitator ’ s Handbook A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 (with reference to Volume Two). The Literacy and Numeracy Secretariat Professional Learning Series.

1.06k views • 65 slides

Building Math in the classroom - Teaching Through Problem-Solving -

Building Math in the classroom - Teaching Through Problem-Solving -. Day 7. Kyozai Kenkyu. Tuesday: Kyozai Kenkyu & Goal of the lesson (Problem situation & Curriculum) Wednesday: Questioning, Anticipating students’ responses, and beyond show and tell Thursday: Designing a poster.

224 views • 9 slides

Building Math in the classroom - Teaching Through Problem-Solving -

Building Math in the classroom - Teaching Through Problem-Solving -. Day 4. Directions for Reflections on Practice Posters. Complete and hang your poster in the third of the classroom where your table group is located, by 12 noon on Thursday, July 12 at the latest.

165 views • 4 slides

Teaching Problem Solving Skills

Teaching Problem Solving Skills

Teaching Problem Solving Skills. Doris Young Professor of General Practice University of Melbourne. What are the ingredients of a 5 star doctor?. Astute Diagnostician Up to date knowledge Good communicator Preventive health Appropriate use of health resources. Diagnostician.

232 views • 16 slides

CHAPTER 3 Teaching Through Problem Solving

CHAPTER 3 Teaching Through Problem Solving

CHAPTER 3 Teaching Through Problem Solving. Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition Van de Walle, Karp and Bay-Williams Developed by E. Todd Brown /Professor Emeritus University of Louisville. Problem Solving. Teaching for problem solving

218 views • 17 slides

Teaching and Learning Mathematics through Problem Solving

657 views • 65 slides

Got any suggestions?

We want to hear from you! Send us a message and help improve Slidesgo

Top searches

Trending searches

problem solving method of teaching mathematics ppt

66 templates

problem solving method of teaching mathematics ppt

9 templates

problem solving method of teaching mathematics ppt

spring flowers

88 templates

problem solving method of teaching mathematics ppt

st patricks day

12 templates

problem solving method of teaching mathematics ppt

world war 1

45 templates

problem solving method of teaching mathematics ppt

calendar 2024

35 templates

Celebrate Slidesgo’s big 5! Five years of great presentations, faster

Problem Solving and Mathematical Reasoning

Problem solving and mathematical reasoning presentation, free google slides theme and powerpoint template.

Let's make math learning more fun, especially at early levels of education. This new template has some cute illustrations and lots of elements related to math, including backgrounds that look like blackboards. This is a great choice for teachers who want to turn their classes into a more entertaining experience for their students. Customize the slides to add your own activities or explanations!

Features of this template

  • 100% editable and easy to modify
  • 36 different slides to impress your audience
  • Contains easy-to-edit graphics such as graphs, maps, tables, timelines and mockups
  • Includes 500+ icons and Flaticon’s extension for customizing your slides
  • Designed to be used in Google Slides and Microsoft PowerPoint
  • 16:9 widescreen format suitable for all types of screens
  • Includes information about fonts, colors, and credits of the free resources used

How can I use the template?

Am I free to use the templates?

How to attribute?

Combines with:

This template can be combined with this other one to create the perfect presentation:

Problem Solving and Mathematical Reasoning Infographics

Attribution required

Related posts on our blog.

How to Add, Duplicate, Move, Delete or Hide Slides in Google Slides | Quick Tips & Tutorial for your presentations

How to Add, Duplicate, Move, Delete or Hide Slides in Google Slides

How to Change Layouts in PowerPoint | Quick Tips & Tutorial for your presentations

How to Change Layouts in PowerPoint

How to Change the Slide Size in Google Slides | Quick Tips & Tutorial for your presentations

How to Change the Slide Size in Google Slides

Related presentations.

Problem Solving and Mathematical Reasoning Infographics presentation template

Premium template

Unlock this template and gain unlimited access

Math Lesson presentation template

Click through the PLOS taxonomy to find articles in your field.

For more information about PLOS Subject Areas, click here .

Loading metrics

Open Access

Peer-reviewed

Research Article

Assessing the attitude and problem-based learning in mathematics through PLS-SEM modeling

Roles Conceptualization, Data curation, Formal analysis, Methodology, Validation, Writing – original draft

Affiliation School of Education, Shaanxi Normal University, Xi’an, P.R. China

ORCID logo

Roles Funding acquisition, Investigation, Project administration, Resources, Supervision, Writing – review & editing

* E-mail: [email protected]

Roles Project administration, Supervision, Writing – review & editing

Roles Data curation, Software, Writing – original draft

  • Samina Zamir, 
  • Zhang Yang, 
  • Hao Wenwu, 
  • Uzma Sarwar

PLOS

  • Published: May 19, 2022
  • https://doi.org/10.1371/journal.pone.0266363
  • Reader Comments

20 Jan 2023: The PLOS ONE Staff (2023) Correction: Assessing the attitude and problem-based learning in mathematics through PLS-SEM modeling. PLOS ONE 18(1): e0280909. https://doi.org/10.1371/journal.pone.0280909 View correction

Table 1

Mathematics plays a leading part in day-to-day life and has enhanced a necessary component for human accomplishments. Students from many countries do not reach the expected level in mathematics. Therefore, it is essential to pay close consideration to the causes related to ability in mathematics. Mathematics attitude is considered as one of the critical variables in the process of mathematics learning. This study aimed to determine students’ attitudes and achievements through problem-based learning in mathematics. The selected study group contained 600 students and 35 teachers from rural public secondary schools in District Rawalpindi, Pakistan. The data collection was done using questionnaires from students and teachers and collected data analyzed by SPSS 23 and Amos 23. This study’s result was carried out using Partial Least square structural equation Model (PLS-SEM), descriptive analysis, and hypotheses testing. The outcomes in this study indicated that the mean fluctuated between 1 to 4.5, 3.71 to 4.20, and Std. Deviation fluctuated between 0.6 to 2.0 and 0.75 to 1.55 in the students and teacher models, respectively. The results of the PLS-SEM students’ model show a negative attitude towards mathematics. The teachers’ PLS-SEM model showed the Effects of using problem-based learning (PBL) on students’ achievements. According to the hypotheses testing, the acceptance of hypotheses by stating that the Confidence in Learning Mathematics Scale (C), Value of Mathematics Scale (V), and Student Mathematics Motivation Scale (M) are significant effects for the Students’ Attitude Toward Problem-Based Learning (ATPBL). But the Attitude Toward Enjoyment in Mathematics Scale (AE) was rejected, and it did not significantly affect the ATPBL. As well as, the Problem-solving learning and students’ achievement (PLA), Advantages of problem-solving learning (APL) and Difficulties in using problem-solving learning (DPL) have a significant positive effect on the ATPBL. Finally, this study suggested that teachers also adopt new teaching methods corresponding to mathematics, and there is a need to explore particular mathematics skills to enhance students’ learning abilities.

Citation: Zamir S, Yang Z, Wenwu H, Sarwar U (2022) Assessing the attitude and problem-based learning in mathematics through PLS-SEM modeling. PLoS ONE 17(5): e0266363. https://doi.org/10.1371/journal.pone.0266363

Editor: Prabhat Mittal, Satyawati College (Eve.), University of Delhi, INDIA

Received: October 15, 2021; Accepted: March 18, 2022; Published: May 19, 2022

Copyright: © 2022 Zamir et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the manuscript and its Supporting Information files.

Funding: ZY received the grant for the Social Science Fund Project of Shaanxi Province "Legitimacy Analysis of Education and Training Market" (2019Q005). This study was also supported by the National Social Science Foundation of China Project (BAA170014).

Competing interests: The authors have declared that no competing interests exist.

1. Introduction

The most imperative things about societies are their learning ability, and learning is a necessary behaviour in life through genetic intelligence and the environment. There has been a lot of advances in educational technology in the last few decades [ 1 ]. Learning ability constantly impact the human lifestyle. As well as it is, in both developed and developing economies, entrepreneurship is considered vibrant to the nation’s competitive ability and a high-powered resource for decreasing regional inequities thereby allowing the development of the country [ 2 , 3 ]. According to that, the knowledge capabilities of an individual affect the student’s way of life continually [ 4 ]. Scribbling, painting and drawing perform ana significant part in the growing up of children [ 5 , 6 ] and it is helping to build their knowledge, personality like that. Consequently, human societies attempt to increase the method of learning in education unceasingly. As well, the ability is the core dimension of personality between learning preferences and cognitive forms. It can be defined as the preferred personal method to collect and process information, decisions, interests, ideas, and attitudes [ 3 ].

Mathematics plays a dominant role in human lives, and it is broadly applied as an essential element in personal achievements and economics [ 7 , 8 ]. In the 21st century, mathematics plays a significant skill in individual satisfaction and involvement in society, school, and the labour market. It appears to be a key academic filter for students’ educational trajectories [ 9 ]. Mathematics plays an essential role in supporting people to grow to reason, problem-solving skills, and thinking, and the importance of mathematics in the education system has gradually increased. Not only that, the impact of students’ mathematics achievements, including students’ ability, family socioeconomic status (SES), curriculum, many factors, peer influence, parental participation, school environment, and teachers’ quality [ 10 , 11 ]. By taking a positive attitude towards mathematics, students will think that mathematics is fundamental, so they try to enhance their performance in mathematics [ 7 ]. However, learning mathematics has grown into a challenge for most students today. Lack of learning despair motivates many students to say, "I am not good at mathematics", even before trying to solve mathematical problems [ 11 ]. Hence, teachers have a significant part in enhancing students’ mathematics achievement [ 10 ]. Emotional understanding, belief, and attitude are three major categories in the effective field of mathematics education [ 12 ].

However, recent worldwide determinations showed that students from many countries do not accomplish as anticipated in mathematics [ 13 ]. Therefore, one must pay close attention to the factors related to mastering mathematics and attitudes are one of the variables that can play a crucial role in learning mathematics [ 7 ].

The recent regeneration of mathematics education has brought new requirements. These provide students with meaningful activities that allow them to share their information in society. Various learning approaches focus on actions are used mainly in primary schools. One method is "problem-based learning" (PBL), which is a skill-based learning technique used to investigate and solve complicated real-life difficulties [ 14 ]. Most of the newest studies on PBL accentuate that it is a technique to enable students to enthusiastically play the part of learners. Most of the studies on PBL focus on teaching in different fields of education. These studies focus on mathematics education, science, engineering, and medicine [ 15 ]. Kaptan [ 16 ] documented that the PBL method is very important for students to improve the skills and knowledge learned in mathematics class to their daily issues and daily life. Theoretically, PBL is based on constructivism, and its instructional design method is based on problem-solving and "contextual learning" [ 14 ]. In general, PBL is considered to contribute to increasing and maintaining academic success [ 17 ] increase performance abilities [ 18 ] have a confident impact on attitudes towards classes [ 15 ], self-learning abilities and improve communication, as well as independent working abilities and motivation, and produce more reasonable explanations to problems [ 19 ]. Therefore, students’ attitudes toward mathematics have been researching worldwide for several decades [ 20 ].

2. Theoretical reviews

Attitude is "a learned inclination on the part of an individual to respond positively or negatively to the concept, situation, some object, or another person" [ 21 ]. Thus, the attitude towards mathematics can be an aggregation of mathematical emotions and beliefs. Allport [ 22 ] defines an attitude as "a mental or neural state of readiness, prepared over practice, applying a directive or dynamic effect upon the individuals’ feedback to all objects and circumstances with which it is associated". Adediwura [ 23 ] describes attitude as a persons’ positive, neutral or negative thinking about mathematics. A positive attitude is very instructive because research shows that there is a link between student performance and their attitude toward mathematics [ 24 ]. Students who have a positive attitude toward mathematics have better problem-solving abilities and are better able to resolve unusual difficulties [ 25 ]. They capitalize more energy in solved problems and give up when the problem cannot be solved. Attitude is also be interchanged with personality and is recognized as a multidimensional structure, including self-confidence or anxiety, such as enjoyment or not, commitment or avoidance, beliefs about whether mathematics is difficult or easy, unimportant or important, uninteresting, interesting, and useless [ 12 ]. Köğce [ 26 ] showed that the mathematics attitude is subjective in some factors, and it can be considered as several groups: firstly, reasons connected with the student, secondly, reasons associated to the teacher and school, and finally reasons related to the society and environment. Reasons related to the students’ mathematical results, their past practices [ 27 ], and social image of the mathematics. Not only that, but the reasons also related with the teachers and their content of knowledge, resources used in the classroom, the teaching methods, personality, teaching topics with real-life enriched examples [ 28 ], and the teachers’ attitude towards mathematics. Therefore, their teachers’ attitudes influence students’ attitudes [ 29 ]; teachers’ wrong beliefs about mathematics powerfully affect their teaching practices [ 30 ]. As well as it is vital to improving a positive attitude towards mathematics between students and teachers.

There have been a lot of improvements in educational technology in the last few decades [ 1 ] like online education. Students can use this technology any subject areas (especially mathematics) to improve their knowledge. But empirical studies have found that students feel that they learn better in physical classrooms than through online education [ 31 ]. Hence, Educational technology is affecting the students and teachers’ attitude toward problem-based learning mathematics.

In recent times, many researchers have pointed out the student attitude and teachers’ attitude towards problem-based learning in mathematics in several cities /countries around the world. The attitude towards mathematics has been considered for past years and shows a high relationship between attitude (including motivation, enjoyment, and self-confidence) and mathematical performance. Mezirow [ 32 ] defines learning as a cycle that starts from experience, continues to reflect, and leads to action, which becomes the experience of reflection. Valkenburg [ 33 ] found that children give their attention very rapidly to media content that was only moderately various from their existing capabilities and knowledge and teachers should give their attention for that [ 34 ]. Attitude towards mathematics is the students’ and teachers’ prepared preference to behave, perceive, feel, and think towards mathematics. Many studies have been established to assess the effect in mathematics [ 35 ].

Yılmaz [ 28 ] presented a positive and vital association between students’ attitudes towards mathematics use and mathematics accomplishment. Secondly [ 36 ], proposed a progressive connection between mathematics accomplishment and mathematics attitudes. They revealed that scholars improve attitudes, ideas, and feelings about school subjects from different sources. Thirdly, Colomeischi [ 37 ] analyzed a correlation between learning style and gender, attitude towards mathematics, and mathematical achievement. Thus, Bayaga [ 38 ] explained the students’ attitudes toward mathematics achievement using a variety of factors (attitude, mathematics self-concept, school condition, family background, teaching, and parent’s educational level) and approaches. We’ve looked into the relationship between math attitude and mathematics performance. A positive relationship between attitudes toward mathematics and academic achievement has been established in the majority of studies conducted across a range of age groups. According to some of the findings, having a negative attitude toward mathematics is associated with minor academic consequences in college students [ 39 , 40 ] and children [ 7 ]. However, in addition to doing so, Zsoldos-Marchis [ 24 ] investigated the problem-solving potential of various primary preschool teachers’ attitudes toward mathematics.

Moreover, Russo [ 41 ] documented the association between math teachers’ enjoyment and attitudes toward student struggle and the number of times teachers spent teaching math. There are more methods developed around the world to analyze attitudes towards mathematics. Among them, one of the most well-known analysis methods is the Partial Least Structural Equation Model (PLS-SEM), and it is a flexible modeling method without data distribution assumptions. It is also essential and suitable for various education analyses. The main aim of this study was to estimate the student attitude and teachers’ attitudes towards problem-based learning in mathematics.

3. Methodology

3.1. participants and data collection.

The study population comprised 3,300 secondary mathematics students and 35 mathematics teachers in District Rawalpindi’s 35 rural public secondary schools. The population is the mathematics students and teachers in North Punjab District Rawalpindi Government Areas as of the 2020/2021 academic session. This study selected the North Punjab district because the schools and education system are better than other areas. Moreover, belonging to the Rawalpindi district so it will be convenient to access the schools. This study selected rural schools because, in mathematics, 10 th class students score low compared to urban schools.

First, purposive sampling will be used in identifying and selecting schools that meet the following criteria:

  • Evidence of continuous presentation of candidates for external examination in mathematics.
  • Availability of qualified mathematics teachers who used the problem-based learning method in their class.
  • Availability of teacher’s students and schools who agree to this study. Due to religious, cultural, regional, and local barriers.

The current study was approved by the Educational Research Ethics committee from the School of Education, Shaanxi Normal University. All procedures performed in the study involving human participants were in accordance with the ethical standards of the institutional research committee and consent was obtained from each respondent. Additional information regarding the ethical, cultural, and scientific considerations specific to inclusivity in global research is included in the Supporting Information ( S1 Appendix ).

By the above criteria, 35 schools will be purposively selected. In these schools, 600 mathematics (female, male) students and 35 mathematics teachers applied problem-based learning methods in their classes. The general overview of the students in the study is given in Tables 1 and 2 showed that the number of teachers in gender-wise and their qualifications.

thumbnail

  • PPT PowerPoint slide
  • PNG larger image
  • TIFF original image

https://doi.org/10.1371/journal.pone.0266363.t001

thumbnail

https://doi.org/10.1371/journal.pone.0266363.t002

3.2. Data analysis

A structured questionnaire with a Likert scale was used to investigate the mathematics attitudes toward students (see S2 Appendix ) and teachers (see S3 Appendix ). Descriptive statistics, hypothesis testing is used for analysis. Analysis was performed by examining the correlations, covariance patterns between the observed measures and hypotheses testing were used for this study. There are seven (7) proposed hypotheses (H 1 to H 7 ) used for analysis (see Fig 1 ).

thumbnail

https://doi.org/10.1371/journal.pone.0266363.g001

  • H 1 : Confidence in Learning Mathematics Scale is positively influenced to Student’s Attitude Toward Problem-Based Learning.
  • H 2 : Value of Mathematics Scale is positively influence by Student’s Attitude Toward Problem-Based Learning.
  • H 3 : Attitude Toward Enjoyment in Mathematics Scale is positively influence to Student’s Attitude Toward Problem-Based Learning.
  • H 4 : Student Mathematics Motivation Scale is positively influencing to Student’s Attitude Toward Problem-Based Learning.
  • H 5 : Problem-solving learning and students’ achievements positively influence Student’s Attitude Toward Problem-Based Learning.
  • H 6 : Difficulties in using problem-solving learning is positively influenced Student’s Attitude Toward Problem-Based Learning.
  • H 7 : Advantages of problem-solving learning is positively influenced to Student’s Attitude Toward Problem-Based Learning.

Descriptive statistics are shown that provide a general overview of the data of the respondents. The collected data was analyzed by SPSS 23 version and Amos 23. For data analysis, Partial Least square structural equation Model (PLS-SEM) was used, interpreted in two stages. The first was to evaluate the student model, and the second was to assess the teachers’ model. The first (Student’s Attitude Toward Problem-Based Learning -ATPBL) model consisted of four constructs with 46 indicators—Confidence in Learning Mathematics Scale (C) = 12 indicators; Value of Mathematics Scale (V) = 12 indicators; Attitude Toward Enjoyment in Mathematics Scale (AE) = 10 indicators; and Student Mathematics Motivation Scale (M) = 12 indicators. The second model consisted of three constructs with 22 indicators—Problem-solving learning and students’ achievement (PLA) = 8 indicators, Advantages of problem-solving learning (APL) = 7 indicators, and Difficulties in using problem-solving learning (DPL) = 7 indicators can be seen in S4 Appendix .

4. Results and discussion

4.1. student attitude towards problem-based learning in mathematics.

According to Table 3 , the mean fluctuated between 1 to 4.5 and Std. Deviation fluctuated between 0.6 to 2.0 and highly Std. Deviation reported from C4 ( I am always confused in my mathematics class .) in the Confidence in Learning Mathematics Scale group. But the low value of Std. Deviation value reported from AE5 ( I really like mathematics ) in attitude toward enjoyment in mathematics scale group. Table 3 shows the results of descriptive statistics in the SEM model’s exogenous variables.

thumbnail

https://doi.org/10.1371/journal.pone.0266363.t003

According to Fig 2 , the Confidence in Learning Mathematics Scale group had a high regression weight from C11 (In terms of my adult life, it is not important for me to do well in mathematics in high school). It recorded 0.664. But in the C1 (I have a lot of self-confidence when it comes to mathematics) showed that a low regression weight. It is recorded -22. As well as Confidence in Learning Mathematics Scale and Student’s Attitude toward Problem-Based Learning presented the 0.11 Standardized Regression Weight. Value of Mathematics Scale (V) showed the high regression weight with V10 (Taking mathematics is a waste of time.), and it recorded 1.01. But in the V1 (Mathematics is a very worthwhile and necessary subject) showed a low regression weight. It is recorded -.11. As well as Value of Mathematics Scale and Student’s Attitude toward Problem-Based Learning presented the 0.12 of Standardized Regression Weight. Hence, the Attitude toward Enjoyment in Mathematics Scale (AE) had a high regression weight from AE7 (Winning a prize in mathematics would make me feel unpleasantly conspicuous), and it recorded 0.88. Hence in the AE4 (I really like mathematics.) showed a low regression weight. It is recorded -.12.

thumbnail

https://doi.org/10.1371/journal.pone.0266363.g002

As well as Attitude toward Enjoyment in Mathematics Scale and Student’s Attitude toward Problem-Based Learning presented the 0.005 of Standardized Regression Weight. Furthermore, Student Mathematics Motivation Scale (M) had a high regression weight from M8 (The challenge of math problems does not appeal to me), and it recorded 0.90. Hence in the AE4 (I really like mathematics.) showed a low regression weight. It is recorded -.014. As well as Student Mathematics Motivation Scale and Student’s Attitude toward Problem-Based Learning presented 0.086 of Standardized Regression Weight. According to the SEM, the standardized estimation can be identified the most student have a negative attitude about mathematics. As well as Fig 2 showed that the squared multiple correlations (R 2 ). A strong positive correlation was reported in V10 (Taking mathematics is a waste of time) with a 1.0 value. V2 (I want to develop my mathematical skills), V12 (I expect to have little use for mathematics when I get out of school), M1 (I like math puzzles), M2 (Mathematics is enjoyable and stimulating to me), M4 (Once I start trying to work on a math puzzle, I find it hard to stop), M12 (I do as a little work in math as possible), C5 (I learn mathematics easily.), C12 (When I hear the word mathematics, I have a feeling of dislike.), AE1 (I have usually enjoyed studying mathematics in school.) showed that, the no correlation. Not only that, but there was also no negative correlation reported in this model.

4.2. Hypotheses testing for Student attitude towards problem-based learning in mathematics

The proposed hypotheses of this study were tested through the standardized coefficient values and p-values in AMOS 23.0. The students’ model’s dependent variable was the Student’s Attitude Toward Problem-Based Learning (ATPBL). The Confidence in Learning Mathematics Scale (C), Value of Mathematics Scale (V), Attitude Toward Enjoyment in Mathematics Scale (AE), and Student Mathematics Motivation Scale (M) were independent variables.

Table 4 showed the acceptance of hypothesizes states that the Confidence in Learning Mathematics Scale (C), Value of Mathematics Scale (V), and Student Mathematics Motivation Scale (M) and these states are significant effects on the Student’s Attitude Toward Problem-Based Learning. But hypotheses state that the Attitude Toward Enjoyment in Mathematics Scale (AE) was rejected, and it did not significantly impact the Student’s Attitude Toward Problem-Based Learning (ATPBL).

thumbnail

https://doi.org/10.1371/journal.pone.0266363.t004

4.3. Effects of using Problem-based Learning (PBL) on student’s achievements

According to Table 5 , the mean fluctuated between 3.71 to 4.20 and Std. Deviation fluctuated between 0.75 to 1.55 and high std. Deviation reported from PLA3 ( When I use this method , student achievement is high .) in Problem solving learning and students’ achievement group. But the low value of std. Deviation value reported from APL7 ( Problem-solving reduces the need to revise prior to examinations .) in Advantages of the problem-solving learning group.

thumbnail

https://doi.org/10.1371/journal.pone.0266363.t005

According to Fig 3 , the problem-solving learning and students’ achievement group had the high regression weight from PLA6 ( The mathematics curriculum is designed to use the problem-solving method frequently .), and it recorded 0.97. However, the PLA1 ( You always get a good response from students who are motivated actively to solve the problems by themselves . ) showed a low regression weight. It is recorded -.269. As well as problem-solving learning and students’ achievement (PLA) and Student’s Attitude toward Problem-Based Learning presented the 0.106 Standardized Regression Weight. Advantages of problem-solving learning (APL) showed the high regression weight with APL7 ( Textbooks are structured to support problem-solving strategies ) and recorded 0.314. But in the APL1 ( Problem-solving helps students to use mathematics in their daily life .) showed a low regression weight. It is recorded -.0.974. As well as Advantages of problem-solving learning (APL) and Student’s Attitude toward Problem-Based Learning presented the 0.031 of Standardized Regression Weight. Hence, Difficulties in using problem-solving learning (DPL) had a high regression weight from DPL2 ( This method is not suitable when the time span is short for teaching . ) , and it recorded 0.94. Moreover, the DPL4 (You need enough space, resources, and feasible environment in the class.) showed the low regression weight. It is recorded -.153. As well as Difficulties in using problem-solving learning (DPL) and Student’s Attitude toward Problem-Based Learning presented the 0.11 of Standardized Regression Weight.

thumbnail

https://doi.org/10.1371/journal.pone.0266363.g003

As well as Fig 3 showed the squared multiple correlations (R 2 ) and strong positive correlation reported in APL1 ( You always get a good response from students are motivated actively to solve the problems by themselves .), DPL2 ( This method is not suitable when time span is short for teaching .), APL2 ( You find the problem-solving method supportive for learners of all abilities in the class .), DPL6 ( It is more difficult to satisfy slow and weak learners through problem solving .), APL4 ( Students learn to draw diagram and pictures themselves to solve problems .), with .949, .883, .883, .859, .844 .824, respectively. ATPBL ( Student’s Attitude toward Problem-Based Learning ), APL3 ( When I use this method , student achievement is high .) PLA5 ( Problem-solving is helpful to make a learner more skilled and confident . ) DPL1 ( This method is difficult when students are larger in number in the classroom .) showed the very week but positive correlation. Not only that, but there was also no negative correlation reported in this model.

4.4. Hypotheses testing for effects of using Problem-based Learning (PBL) on student’s achievements

The proposed hypotheses of this study were tested through the standardized coefficient values, and p-values in AMOS 23.0 for the teachers’ model. In the teachers’ model dependent variable was the Student’s Attitude Toward Problem-Based Learning (ATPBL). The Problem-solving learning and students’ achievement (PLA) Advantages of problem-solving learning (APL) and Difficulties in using problem-solving learning (DPL) were independent variables in this study.

Table 6 showed the acceptance of hypothesizes by stating that the Problem-solving learning and students’ achievement (PLA), Advantages of problem-solving learning (APL), and Difficulties in using problem-solving learning (DPL). These states have a significant positive impact on the Student’s Attitude Toward Problem-Based Learning (ATPBL).

thumbnail

https://doi.org/10.1371/journal.pone.0266363.t006

5. Conclusion

Information about students’ attitudes towards problem-based learning in mathematics is influential to both the students and the teachers [ 30 ]. The current study Partial Least Structural Equation Model (PLS-SEM) approach investigates the student attitude and teachers’ attitude towards problem-based learning in mathematics. The demographic data of this study have also exposed those 600 students and 36 teachers are competent in handling mathematics.

In firstly, this study estimated the student attitude towards problem-based learning in mathematics. The PLS-SEM model showed that the mean fluctuated between 1 to 4.5 and Std. Deviation fluctuated between 0.6 to 2.0. Among the 46 indicators, the C4 (I am always confused in my mathematics class) showed a high Std. Deviation and, but the low value of Std. Deviation value reported from AE5 (I really like mathematics) indicator.

According to the regression weight, in the students’ model, the high weight record in C11 (In terms of my adult life it is not important for me to do well in mathematics in high school.) and it recorded 0.664, V10 (Taking mathematics is a waste of time.). It recorded 1.01, AE7 (Winning a prize in mathematics would make me feel unpleasantly conspicuous) and it recorded 0.88, M8 (The challenge of math problems does not appeal to me), and it recorded 0.90.

According to the regression weight, in the teachers’ model, the high weight record PLA6 (The mathematics curriculum is designed to use the problem-solving method frequently) and is recorded 0.97. APL7 (Textbooks are structured to support problem-solving strategies.), and it recorded 0.314. DPL2 (This method is not suitable when time span is short for teaching.), and it recorded 0.94.

According to the hypothesizes testing, the acceptance of hypothesizes by stating that the Confidence in Learning Mathematics Scale (C), Value of Mathematics Scale (V), and Student Mathematics Motivation Scale (M) and these states are significant effects on the Students’ Attitude Toward Problem-Based Learning. But it hypothesizes by stating that the Attitude Toward Enjoyment in Mathematics Scale (AE) was rejected, and it did not significantly affect the Students’ Attitude Toward Problem-Based Learning (ATPBL). As well as the acceptance of hypothesizes by stating that the Problem-solving learning and students’ achievement (PLA), Advantages of problem-solving learning (APL) and Difficulties in using problem-solving learning (DPL) has a significant positive impact on the Students’ Attitude Toward Problem-Based Learning (ATPBL).

This study significantly revealed students’ attitudes towards mathematics and the attitudes of teachers who use it to teach mathematics. Finally, this study suggested that teachers should also adopt new teaching methods corresponding to mathematics. There is a need to explore particular mathematics skills to enhance students’ learning abilities.

Supporting information

S1 appendix. this appendix contains inclusivity in global research..

https://doi.org/10.1371/journal.pone.0266363.s001

S2 Appendix. This appendix contains students’ questionnaire.

https://doi.org/10.1371/journal.pone.0266363.s002

S3 Appendix. This appendix contains teachers’ questionnaire.

https://doi.org/10.1371/journal.pone.0266363.s003

S4 Appendix. This appendix contains variables.

https://doi.org/10.1371/journal.pone.0266363.s004

S1 Dataset.

https://doi.org/10.1371/journal.pone.0266363.s005

Acknowledgments

The first author would like to thank his parents who support him in this work. We thank those anonymous reviewers whose comments/suggestions helped to improve and clarify this manuscript.

Institutional review board statement

This study is approved by the Educational Research Ethics committee from the School of Education, Shaanxi Normal University. All procedures performed in the study involving human participants were in accordance with the ethical standards of the institutional research committee.

Informed consent statement

Informed consent was obtained from all subjects involved in the study.

  • View Article
  • Google Scholar
  • 10. Hattie J. Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge; 2008.
  • PubMed/NCBI
  • 19. Diggs LL. Student attitude toward and achievement in science in a problem-based learning educational experience. University of Missouri-Columbia; 1997.
  • 22. Allport G W. Attitudes. In Murchison C. (Ed.), A handbook of social psychology. Worcester, MA: Clark University Press. 1995. https://doi.org/10.2466/pms.1995.80.3c.1187 pmid:7478876

Problem-Solving Method in Teaching

The problem-solving method is a highly effective teaching strategy that is designed to help students develop critical thinking skills and problem-solving abilities . It involves providing students with real-world problems and challenges that require them to apply their knowledge, skills, and creativity to find solutions. This method encourages active learning, promotes collaboration, and allows students to take ownership of their learning.

Table of Contents

Definition of problem-solving method.

Problem-solving is a process of identifying, analyzing, and resolving problems. The problem-solving method in teaching involves providing students with real-world problems that they must solve through collaboration and critical thinking. This method encourages students to apply their knowledge and creativity to develop solutions that are effective and practical.

Meaning of Problem-Solving Method

The meaning and Definition of problem-solving are given by different Scholars. These are-

Woodworth and Marquis(1948) : Problem-solving behavior occurs in novel or difficult situations in which a solution is not obtainable by the habitual methods of applying concepts and principles derived from past experience in very similar situations.

Skinner (1968): Problem-solving is a process of overcoming difficulties that appear to interfere with the attainment of a goal. It is the procedure of making adjustments in spite of interference

Benefits of Problem-Solving Method

The problem-solving method has several benefits for both students and teachers. These benefits include:

  • Encourages active learning: The problem-solving method encourages students to actively participate in their own learning by engaging them in real-world problems that require critical thinking and collaboration
  • Promotes collaboration: Problem-solving requires students to work together to find solutions. This promotes teamwork, communication, and cooperation.
  • Builds critical thinking skills: The problem-solving method helps students develop critical thinking skills by providing them with opportunities to analyze and evaluate problems
  • Increases motivation: When students are engaged in solving real-world problems, they are more motivated to learn and apply their knowledge.
  • Enhances creativity: The problem-solving method encourages students to be creative in finding solutions to problems.

Steps in Problem-Solving Method

The problem-solving method involves several steps that teachers can use to guide their students. These steps include

  • Identifying the problem: The first step in problem-solving is identifying the problem that needs to be solved. Teachers can present students with a real-world problem or challenge that requires critical thinking and collaboration.
  • Analyzing the problem: Once the problem is identified, students should analyze it to determine its scope and underlying causes.
  • Generating solutions: After analyzing the problem, students should generate possible solutions. This step requires creativity and critical thinking.
  • Evaluating solutions: The next step is to evaluate each solution based on its effectiveness and practicality
  • Selecting the best solution: The final step is to select the best solution and implement it.

Verification of the concluded solution or Hypothesis

The solution arrived at or the conclusion drawn must be further verified by utilizing it in solving various other likewise problems. In case, the derived solution helps in solving these problems, then and only then if one is free to agree with his finding regarding the solution. The verified solution may then become a useful product of his problem-solving behavior that can be utilized in solving further problems. The above steps can be utilized in solving various problems thereby fostering creative thinking ability in an individual.

The problem-solving method is an effective teaching strategy that promotes critical thinking, creativity, and collaboration. It provides students with real-world problems that require them to apply their knowledge and skills to find solutions. By using the problem-solving method, teachers can help their students develop the skills they need to succeed in school and in life.

  • Jonassen, D. (2011). Learning to solve problems: A handbook for designing problem-solving learning environments. Routledge.
  • Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235-266.
  • Mergendoller, J. R., Maxwell, N. L., & Bellisimo, Y. (2006). The effectiveness of problem-based instruction: A comparative study of instructional methods and student characteristics. Interdisciplinary Journal of Problem-based Learning, 1(2), 49-69.
  • Richey, R. C., Klein, J. D., & Tracey, M. W. (2011). The instructional design knowledge base: Theory, research, and practice. Routledge.
  • Savery, J. R., & Duffy, T. M. (2001). Problem-based learning: An instructional model and its constructivist framework. CRLT Technical Report No. 16-01, University of Michigan. Wojcikowski, J. (2013). Solving real-world problems through problem-based learning. College Teaching, 61(4), 153-156

Micro Teaching Skills

IMAGES

  1. Teaching About Problem-Solving PowerPoint

    problem solving method of teaching mathematics ppt

  2. PPT

    problem solving method of teaching mathematics ppt

  3. problem solving as a teaching method

    problem solving method of teaching mathematics ppt

  4. 7 Steps Of Problem Solving Goolge Slides and PPT Templates

    problem solving method of teaching mathematics ppt

  5. Problem solving method

    problem solving method of teaching mathematics ppt

  6. Teaching through Problem Solving

    problem solving method of teaching mathematics ppt

VIDEO

  1. Differentiate tan^-1(3x-x^3/1-3x^2) |Differentiaton|Calculas|Class 12|11th|Engineering|nda|Maths

  2. Problem solving Method in Science

  3. Teaching Methods

  4. Easy math problem

  5. Maths

  6. Solving a math problem Algebra I

COMMENTS

  1. Problem solving method

    INTRODUCTION • Problem solving is an instructional method or technique where by the teacher and pupils attempt in a conscious, planned and purposeful effort to arrive of some explanation or solution to some educationally significant difficulty for the purpose of finding a solution. Problem solving01/08/17 2. 3.

  2. Teaching Mathematics Through Problem Solving

    Teaching about problem solving begins with suggested strategies to solve a problem. For example, "draw a picture," "make a table," etc. You may see posters in teachers' classrooms of the "Problem Solving Method" such as: 1) Read the problem, 2) Devise a plan, 3) Solve the problem, and 4) Check your work. There is little or no ...

  3. Problem Solving In Mathematics

    Problem Solving In Mathematics Feb 27, 2022 • 0 likes • 856 views LorenKnights Follow Education Problem solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing , selecting alternatives for a solution; and implementing a solution. 1 of 17 Download Now Recommended

  4. Problem solving in mathematics

    1. Problem Solving in Mathematics Colleen Young Mathematics, Learning & Technology. 2. Definitions Just what is problem solving? 1 Problem Solving Ask the students 2 Teaching Ideas 3 Questions 4 Making it stick The importance of recall5 Further Resources 6.

  5. PDF Teaching Through Problem Solving

    The Problem of Teaching. (Teaching as Problem Solving) Can/should tell. Conventions [order of operation, etc.] Symbolism and representations [tables, graphs, etc.] Present and re‐present at times of need. Can/should present alternative methods to resolve.

  6. TEACHING MATHEMATICS Through Problem Solving

    The K - 12 Mathematics Curriculum. 11 What is critical thinking? It is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by observation, experience, reflection, reasoning, or communication, as guide to belief and action.

  7. Module 1: Problem Solving Strategies

    Step 2: Devise a plan. Going to use Guess and test along with making a tab. Many times the strategy below is used with guess and test. Make a table and look for a pattern: Procedure: Make a table reflecting the data in the problem.

  8. Teaching About Problem-Solving PowerPoint

    By using rich and engaging illustrations to show off the problem-solving strategies, this PowerPoint is also using the CPA (concrete, pictorial, abstract) method of learning. Soon, they'll be ready to tackle abstract mathematical problems without hesitation by using the strategies in this resource. To get started, simply press the green ...

  9. Teaching mathematics in the classroom with PowerPoint software

    TEACHING MATHEMATICS IN THE CLASSROOM WITH POWERPOINT SOFTWARE A Project Presented to the Faculty of California State University, San Bernardino by Robert Ward Kopp June 2012 Approved by: Dr. Corey Dunn, Mathematics Date Dr. Peter Williams, Chair Department of Mathematics Dr. Davida Fischman, Graduate Coordinator Department of Mathematics: MAT

  10. TEACHING PROBLEM-SOLVING STRATEGIES IN MATHEMATICS

    Abstract This study uses the methodology of design-based research in search of ways to teach problem-solving strategies in mathematics in an upper secondary school. Educational activities are designed and tested in a class for four weeks. The design of the activities is governed by three design principles, which are based on variation theory.

  11. Maths Problem Solving Strategies PowerPoint (Teacher-Made)

    You can use this lovely PowerPoint presentation to introduce or revise different strategies that can support solving mathematical calculations involving all four operations. Perfect for helping children to have a range of techniques to use independently in their work.To practise the techniques listed in this PowerPoint, you may be interested in our blether stations on solving maths problems ...

  12. Problem Solving Strategies

    Polya's Four-Step Model George Polya has had an important influence on problem solving in mathematics education. He noted that good problem solvers tend to forget the details and focus on the structure of the problem, while poor problem solvers do the opposite. Four-Step Process: 1. Understand the problem (See) 2. Devise a plan (Plan) 3. Carry out the plan (Do) 4. Look back (Check)

  13. PPT

    Teaching Through Problem Solving " It's the questions that drive mathematics. Solving problems and making up new ones is the essence of mathematical life.". Fosnot and Dolk, 2001 Instructional Strategies: Quotations and Think-Pair-Share. Learning Goals During this session, numeracy coaches will: • develop an understanding of the ...

  14. PPTX Mathematics, Learning and Technology

    PK !e1Í~X „2 [Content_Types].xml ¢ ( Ä[ÉnÛ0 ½ è? º ¶¬Õi '‡.§. š~+ÑŽZ-„Ȥõß—',# ‡Œ=}— ²£áó›™Ç™¡|yý·*g ¼•ES¯½`± ...

  15. Methods of teaching mathematics

    Maths,teaching,methods Techniques and Strategies in Teaching Math Different approaches and methods Approaches in teaching mathematics Heuristic method Principles of Teaching:Different Methods and Approaches Approaches in teaching and learning mathematics Strategies in teaching mathematics General Methods And Techniques Of Teaching

  16. PPT Making Mathematics Meaningful for Students with Learning Problems

    Strategy Examples Mnemonic Strategies DRAW for Algebra SPIES Example: Chart to Help Students Generate Problem-Solving Strategies Example: Helping Students Think About/Monitor Their Use of Different Strategies PPT # 5: Cue Important Features of a Mathematics Concept/Skill Using Multisensory Methods Examples of Visual Cuing Example: Cue Sheet to ...

  17. Problem Solving & Mathematical Reasoning

    Problem Solving and Mathematical Reasoning Presentation Free Google Slides theme and PowerPoint template Let's make math learning more fun, especially at early levels of education. This new template has some cute illustrations and lots of elements related to math, including backgrounds that look like blackboards.

  18. Maths Problem Solving Strategies PowerPoint (teacher made)

    You can use this lovely PowerPoint presentation to introduce or revise different strategies that can support solving mathematical calculations involving all four operations. Perfect for helping children to have a range of techniques to use independently in their work. Show more Related Searches

  19. Assessing the attitude and problem-based learning in mathematics ...

    Mathematics plays a leading part in day-to-day life and has enhanced a necessary component for human accomplishments. Students from many countries do not reach the expected level in mathematics. Therefore, it is essential to pay close consideration to the causes related to ability in mathematics. Mathematics attitude is considered as one of the critical variables in the process of mathematics ...

  20. Problem-Solving Method In Teaching

    The problem-solving method is an effective teaching strategy that promotes critical thinking, creativity, and collaboration. It provides students with real-world problems that require them to apply their knowledge and skills to find solutions. By using the problem-solving method, teachers can help their students develop the skills they need to ...

  21. Teaching problem solving

    Problem solving methods in maths Problem solving skills Math workshop for primary teachers Making Math Meaningful lesson plan Problem Solving

  22. Open-Ended Math Problem Solving PowerPoint

    A PowerPoint with 20 open-ended problem solving questions covering a range of mathematical concepts. This open-ended problem solving PowerPoint will promote deep, thoughtful, and creative responses from your students. More than one answer is acceptable; exploring possibilities is encouraged. The problems cover a range of mathematical concepts ...

  23. Problem solving method

    Similar to Problem solving method (20) method and approaches of teaching. Inquiry Approach and Problem Solving Method.pptx. Teaching Science. Inquiry training model. Scientific Method Assignment. Guided/exploratory approach. ENGAGE MOOC problem solving. ENGAGE problem-solving with convesation.