# Rich Mathematics Problem Solving

## Rich Problem Solving Must Include:

Metacognition--By seeing how others solve a problem,students can begin to reflect on their own thinking and the thinking of others to adjust their own way of thinking.

Reflecting---Good problem solvers regularly reflect on their own thought processes. This allows them to switch to a different strategy and rethink the problem if what their doing Is incorrect.

The Four-Step Problem-Solving Model--This model gives students a process to apply their math knowledge during problem solving activities.

The most commonly used problem-solving model is George Polya’s Four-Step Model: understand, understand the problem, make a plan, carry out the plan and look back to check the results.

## Common Problem Solving Stratagies:

-Making a model

-Picture diagram

-Looking for a pattern

-Guessing and checking

-Making an organized list

-Making a table

- Chart making

## Characteristics of a Rich Math Task:

- Curriculum based

- Multiple strand/ cross- curricular

- Open- ended with no obvious answer

- Include math processes

- Is collaborative

- Gives students a voice

- Provides opportunity for learning through many vehicles

- Allows for multiple entry points

- Engages students and makes them talk about math

- Asses through observation, conversations and product

## Picture One - Teacher Directed, Static, Lack of student Engagment

This may be a representative of a rich math task as it has the vocabulary, the display of anchor charts and reference to what the students did the day before. This photo does not show the actual student work, it is all the teacher. The question is not open-ended therefore it does not allow for much discussions. What it does allow is for the studennts to follow the teacher's formula.

## Picture Two- Student-Centred, Not Static, Student Engaged

This is may be consolidation of a rich math task. It allows for many entry points within solving the problem students work in evident, the student is engaged, her voice is present through her work. It allows for students to use a strategy they are comfortable with while taking risks in solving the problem. Discussion is evident on the board with the various responses being written with various formulas.

## References:

Ontario Math Curriculum Document Grades 1-8, 2005

http://www.edu.gov.on.ca/eng/curriculum/elementary/math.html

Paying Attention to Mathematics Education K-12