Problem solving presentation

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 4,6

Problem solving in Mathematics

- Solve a problem solving problem 

- What is problem solving and what are problem solving strategies

- Struggles from students 

- Problem solving in Math lessons

What is the answer to the problem?

A: 17

B: 19

C:20

D:21

E:23

What problem-solving strategy did you use?

Do it/do the problem

Arrange your information in a different way

​3​​1​​m=​5​​1​​m+3−1

​15​​5​​m=​15​​3​​m+3−1

​15​​2​​m=2

2m=30

m=15

Algebraically 

Problem-solving

To solve a complicated and challenging problem, problem solving skills are needed to organize and process the given information correctly. 

With every problem you need to understand the situation (context), the necessary mathematics and the skills to work with the necessary mathematics. 

Source

Helden, H. van, Konings, T., & Krabbendam, H. (2019). Probleemoplossen en wiskunde voor de lerarenopleiding en Wiskundedocenten (2nd ed.). Ten Brink Uitgevers. 

Polya's problem solving steps

George Polya wrote a book ('How to solve it') in which he describes that solving a problem happens in the following 4 phases: 

1. Understanding the problem

2. Choosing a problem-solving strategie

3. Executing your strategie

4. Checking your answer

Source

Polya, G. (2014). How to solve it. Princeton University Press.

Which phase do you think most students struggle with?

1. Understanding

2. Choosing a strategy

3. Executing strategy

4. Checking your answer

Problem solving strategies/heuristics 

1. Draw it! (draw a representation of the situation) 

2. Make a systematic list. 

3. Elimination 

4. Reason with a matrix 

5. Find a pattern (Criteria B) 

6. Trial and error

7. Divide the problem in subproblems

8. Solve an easier version of the problem (or 'Use easy numbers') 

9. DO the problem. 

10. Work backwards

11. Use Venn-diagrams 

12. Use algebraic methods

13. Present the information differently 

14. Change your perspective

15. Use (other) graphic methods

16. Use specific materials 

Often there isn't just 'one way' to solve something

Source

Helden, H. van, Konings, T., & Krabbendam, H. (2019). Probleemoplossen en wiskunde voor de lerarenopleiding en Wiskundedocenten (2nd ed.). Ten Brink Uitgevers. 

Student struggles 

Why spend so much time on problem-solving

Student struggles 

Student struggles 

How can you choose a strategy if you don't know which strategies there are? 

Student struggles

Last year I focused on discussing a couple of the 16 problem-solving strategies and applying these in different problems. 

After familiarizing with the different strategies 

Problem solving in math lessons