Traditionally, teaching problem-solving in mathematics includes presenting students with “closed problems” that encourage them to follow a single procedure to reach a single outcome.
I’m moving away from this approach in my class. Instead, I’m encouraging students to approach math problems with many different strategies for reaching a single solution. I’m also asking them to help establish a context for specific mathematical problems so that they can see the real-world application of the math skills they’re developing.
Here’s how I do it:
- First, I listen closely to students to discover the subjects students are interested in and what they care about.
- Next, I pose questions asking how they would approach a particular problem and facilitate their research in the interest area.
- Then, I introduce ways they can apply math skills as part of a related project.
For example: When one student became interested in helping polar bears, I turned this interest into an opportunity for problem solving for the whole class. Through questioning, I was able to lead the students to discovering and solving open-ended mathematical problems related to this real-world project.
Open-ended problem solving is important because kids want to come up with their own ideas when they solve problems. Providing this opportunity makes me feel like a “true teacher.” I’m not giving students answers, sharing procedures, or telling them how to do things. Instead, they’re learning through their own process—one I facilitate by asking questions. And, my whole classroom community benefits: I can more easily give extra time to students who need more foundational, procedural practice and students who are ready to engage more have the opportunity to do so.