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Rich Mathematics Problem Solving
Problem Solving forms the Basis of Effective Math Programs
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
Rich Problem-Solving- Sounds Like:
Students using the content specific vocabulary
Teacher chatting with each group checking to find out if they are on right track
The noise level would have peaks (degree of loudness) and valleys (degree of quietness)
-peaks when they have a great idea that they want to share with their group members
-peaks when they are discussing a concept
-peaks when they get excited about a concept and
-valleys when they are deep in though
-valleys when they are listening to each other
-valleys when they do not understand and are waiting for assistance
Rich Problem-Solving- Feels Like:
Positivity flowing through the classroom (through positive student behaviour)
Learning taking place in the classroom
Rich Problem-Solving- Looks Like:
Students actively engaged by participating
Students having various facial expression
The classroom may be a bit dishevelled (with desks out of place, papers and writing utensils disorderly on the desks)
Student work displayed in various places
Which Picture Shows The Rich Math Problem Solving Task ?
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
Picture Two- Student-Centred, Not Static, Student Engaged
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
www.edu.gov.on.ca/eng/teachers/studentsuccess/FoundationPrincipals.pdf