I'm always a little disappointed when students are stymied because they don't recognize a problem. "I CAN'T" is not part of our class, and students need to try.  But, I can't put such expectations on my students if I do not give them some tools to support their effort.

Part of education is empowering students to learn. I like to provide tools and strategies students can use to solve problems.   In math, problem solving strategies are an important part of a mathematician's tool box.

I start with problem solving strategies early in the year, posting random problems and then letting students just try things.

For example:

If we list all the natural numbers below 10 that are multiples of 3 or 5,
we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 50.

I emphasize that the important part is attempting the problem not necessarily getting to the right answer. This becomes especially important for my less confident and reluctant learners.

Once students start to open up to just giving it a go, I start introducing strategies.

I introduce a strategy with several problems. Students select a problem and then try that strategy out. Often I'll show, too, that there isn't only one strategy for one problem.

For example, look at the problem to the left. You could make a table, draw it, or find a pattern.

This flexible thinking is key to students owning their learning and empowering them. Instead of saying "I don't know how to do that" or "you haven't taught me that", students wonder how they can approach the problem.

Even if students don't always find a solution to the problems, students stretch their creative brains and give it a go - I think an important concept that extends far beyond the realm of mathematics.  Problem solving is a great way to help students to become more independent learners as well as to approach new situations.

Math Mondays is a bi-weekly blog post (2nd and 4th Monday of each month) sharing tips, ideas, resources, and products for teaching math.  If you have questions or think there is something I should include, you can leave me a message in the comments section below or at the store in the question and answer section.