## Problem Solving [PS]

Problem Solving [PS]

**Quotes**

(The Alberta 10-12 Mathematics Program of Studies with Achievement Indicators 2008, Alberta Education)

*"Students need to explore mathematics through solving problems ..."* (pg. 2)

*"The main goals of mathematics education are to prepare students to: solve problems, etc."* (pg. 4)

*"Students develop a true understanding of mathematical concepts and procedures when they solve problems in meaningful contexts."* (pg. 8)

*"If students have already been given ways to solve the problem, it is not a problem, but practice."* (pg. 8)

**Thoughts on Problem Solving**

If at all possible, I try to facilitate problem solving by avoiding direct instruction and have students work on problems and investigations that guide them toward certain conclusions.

I frequently have students working in small groups on the board to solve a problem in order to promote an environment of taking risks, asking questions and posing conjectures.

**Investigations**The following examples ask students to look for patterns and then make conclusions.

- M10C Investigate Integer Exponents
- M10C Function Notation
- M10C Investigate Slope Intercept Form
- M20-2 Operations on Radicals (Addition & Subtraction, Multiplication, Division)

**Lesson Flow**In the flow of my lessons I often present a problem first and then debrief with the students afterward. It is often amazing what the students can come up with when presented with a problem and then their work can be a basis for discussion during the debrief. The debrief time also provides a time to formalize their work and I find the class is usually more interested in what you have to say since they are invested in the problem. The following are some example problems I've used:

**Applying Assignments**Applying Assignments are usually made up of problems that the students have not seen before and allow them to apply their skills. A description of Applying Assignments is available here.