1. What is problem solving?
Considered the most complex of all intellectual functions, problem solving has been defined as higher- order cognitive process that requires the modulation and control of more routine or fundamental skills.

2. Is Problem Solving Your Goal in Teaching Mathematics?

3. Often Our Dilemma
Maintaining a balance between the development of concepts and skills AND the modulation and control of these concepts and skills through problem solving

4. A Possible Solution to Our Dilemma
Teaching About Problem Solving
Teaching For Problem Solving
Teaching Via Problem Solving

5. What is meant by Teaching Via Problem Solving

6. NCTM Principles and Standards, 2000
Solving problems is not only a goal of learning mathematics but also a major means of doing so…

7. Teaching Via Problem Solving
Van de Walle’s Three-Part Lesson Planning: Teachers: Before, During, and After Students: Explore (Show and Share) Connect Practice (Reflect)

8. Teaching Via Problem Solving
Teach in ways that students tell you what you used to tell them!

9. Teaching Via Problem Solving
Each learner constructs meaning in his/her own unique way. A learner, therefore, must be actively interacting with the idea. That is, he/she must be thinking (inducing, deducing, reasoning, sequencing, classifying, finding patterns and relationships). It is the quality of this interaction that is crucial to the development of understanding.

10. What is meant by Teaching For Problem Solving

11. Teaching For Problem Solving
Mathematics concepts and procedures in school mathematics are used in the world. These applications should be front and centre in the study of any concept or procedure, NOT treated as an afterthought.
For example, all units on addition and subtraction should centre on the different structures of story problems and their solutions.

12. As teachers, we cannot over estimate the role story problems play for most students to see the relevance of a math concept, and the very essence of the concept.

13. What is meant by Teaching About Problem Solving?

14. Teaching About Problem Solving
Polya’s How to Solve It
4-Step Process
Understand the Problem
Make a Plan
Carry Out the Plan
Look Back

15. Teaching About Problem Solving
If this technique fails, Pólya advises not to give up:
"If you can't solve a problem, then there is an easier problem you can solve…find it.”
"If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"

16. Understanding the Problem
What information are you given? What are you asked to find or show?
Can you restate the problem in your own words?
Can you think of a picture or a diagram that might help you understand the problem?

17. Understanding the Problem: The 3-Read Strategy
Five hundred people are lined up outside the Apple Store by 7 am. Since the store doesn’t open for an hour, three of the staff at the store decide to distribute an iPhone brochure to every 2nd person in line, an iPad brochure to every 5th person in line, and a gift certificate to every 7th person in line. If they all start distributing at the head of the line, how many people in line get all three things?

18. Five hundred people are lined up outside the Apple Store by 7 am
Five hundred people are lined up outside the Apple Store by 7 am. Since the store doesn’t open for an hour, three of the staff at the store decide to distribute an iPhone brochure to every 2nd person in line, an iPad brochure to every 5th person in line, and a gift certificate to every 7th person in line. If they all start distributing at the head of the line, how many people in line get all three things?

23. Problem Solving Permeating Your Teaching
Teaching About Problem Solving
Teaching For Problem Solving
Teaching Via Problem Solving ✔ ✔ ✔

24. MathPower
Reasoning, communication, problem solving too; All the connections we can make are central to what we do. Let’s have our students know and use, and love mathematics more, Ready to face the world alone confident and sure.
Math Power for everyone – that’s the mission we’ve begun Yes, it’s Math Power for everyone –It’s the greatest gift we’ll give.