"Fostering Mathematical Thinking and Problem Solving"

Mathematical thinkers are:

• Fluent
• Flexible
• Confident
• Curious
• Pattern Seekers
• Reflective

There are two different styles of teaching:

1. The teacher believes there is only one way to solve a problem.
2. The teacher believes there are multiple ways to solve a problem.

Techniques we should promote within our classroom

• Ask students to investigate and report
• Create questions that require deep thinking
• Value both the process and the product of math problems
• Have students share reasoning and/or their solution in order to build on other's ideas and to consider more than one approach.
• Allow time to reflect on problem solving
• Elicit discussion

What is a problem performer?  This student relies on routine and cannot solve beyond the boundaries they or their teacher have set up.

What is a problem solver?  This student is a mathematical thinker.  They can apply their knowledge and skills to problem solve in challenging problems.  

When students give an answer that is incorrect, ask "Well, tell me what your thinking is" or "How did you arrive to that answer?" or "I see where you had a misconception."