1. TEACHING MATHEMATICS Through Problem Solving
Amelia Buan
Grace Liwanag
Joan Rose Luib

2. The K - 12 Mathematics Curriculum

3. The K -12 Mathematics Curriculum Framework

4. What is a learner-centered lesson?
A lesson is learner-centered if it provides the learners plenty of opportunities to engage in higher order thinking skills.

5. What is a problem?
A problem is a mathematically unfamiliar situation that needs a solution but for which the problem solver has no readily available algorithm to use to solve it.

6. What is problem solving?
It is finding a solution to a problem.

7. Three types of teaching related to problem solving –SCHROEDER (1989)
Teaching for problem solving
Teaching about problem solving
Teaching through problem solving

8. Teaching for problem solving
Problems are given to the students after needed content and skills are taught

9. Teaching about problem solving
Understand the Problem
Devise a Plan
Carry out the Plan
Look Back
Problems are given to the students after general method of solving problems and the different strategies are discussed

10. Teaching through problem solving
Problems is given to the students at the start.
The problem is used as context to teach the topics as well as to develop skills and apply these skills to unfamiliar situations

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.

12. Experience Observation Critical Thinking Reflection Listening Applying
Analyzing
Synthesizing
Evaluating
Experience
Observation
Reflection
Listening

13. Questioning to Promote Critical Thinking

15. Prompts for Divergent questions
What if…?
Suppose that…?
How…?
Why…?
Given what you know about…, why…?
What can you conclude from…?

17. COLLABORATIVE LESSON PLANNING?
Learning Objectives
Assessments
Materials and Activities

18. Students vary in abilities, interests, attitudes, learning needs
Task
They approach the same learning task in different ways.

19. Why do we assess?

20. Assessment purposes Encourage Collaboration and Self Direction
Gauging Student Needs
Encourage Collaboration and Self Direction
Monitoring Progress
Checking Understanding
Demonstrating Understanding

21. TiMSS 2011 Mathematics Framework

22. TIMSS 2011 Mathematics Framework
Reasoning
Applying
Knowing

23. knowing recall recognize compute retrieve measure classify
Recall definitions
Recognize mathematical concepts
Carry out algorithmic
Retrieve information
Use measuring instruments
Classify objects/shapes

24. applying select represent model implement Solve routine problems
Select an efficient operation
Display mathematical information
Generate an appropriate model
Implement a set of mathematical instructions
Solve standard problems

25. reasoning analyze generalize integrate justify
Solve non-routine problems
Use relationships between variables
Extend domain to which result of mathematical thinking
Make connections
Provide justification to known mathematical results
Solve problems set in mathematical or real life contexts

26. Lesson Study

27. What is a lesson study?
Lesson study, a form of collaborative practice, is a school-based professional development initiative that aims to enhance teaching and learning through the methodology of professional sharing of practice (Burghes & Robinson, 2009)

28. Lesson Study Process L L B O Planning a Research Lesson
Implementation of the Research Lesson
Post-lesson Reflection & Discussion C O L B R A T I N

29. Phase One: Presentation of the Problem (10 minutes)
Phase Two: Developing a Solution (15 minutes)
Phase Three: Progress through discussion ( 10 minutes)
Phase Four: Summarizing ( 10 minutes)

30. The end