Productive Struggle: Fostering Deep Math Learning in Your Classroom with Discovery

Do you ever feel like you are working harder than your students? That they are just going through the motions of being a student? Getting students to think and problem solve can be difficult, but the payoff is huge.

Learning isn't always easy, but it's not the teacher's job to make it seem easy. Instead, our role is to create opportunities for learning that encourage students to grapple with mathematical concepts. In this blog post, we'll delve into the idea of productive struggle and explore a format for lessons to encourage inquiry learning.

Productive Struggle: The Key to Deep Learning

Productive struggle is the process where students face challenging problems or concepts that they don't immediately know how to solve. However, they approach these challenges with hope and confidence, believing that with effort and perseverance, they can arrive at a solution. This is a mindset that takes time to develop.

While not all students start with this level of confidence in math, it's a trait that can be nurtured over time. As educators, it's our duty to provide students with numerous opportunities to overcome mathematical struggles. With each experience, their confidence grows, making them more willing to take on more and more difficult problems.

The Discovery Lesson Format

Now, let's get into the nitty-gritty of creating lessons that ignite curiosity. Imagine a lesson that's more like a science experiment than a lecture. Here's a breakdown of this format:

Prediction:

Start with a prediction phase. Ask your students to make hypotheses or estimates about a problem. It's a low-pressure way to get them engaged and thinking about what's coming up. Plus, it's a sneak peek into their thought process, which is super helpful.

Experiment:

The core of the lesson lies in the experiment phase. This is where students actively work through the problem, often making mistakes, asking questions, and trying various approaches. It's a phase of active learning, where students are thinking critically. Hands-on activities or visual aids can greatly enhance this stage, especially when dealing with geometric formulas.

Conclusion:

After the experiment, gather your students for a group discussion. This is when you connect the dots, clear up any confusion, and collectively understand the math magic that just happened. It's like solving a puzzle together!

Extension:

Not all students make discoveries at the same speed. Offer extension activities that challenge students to think deeper. I like using error analysis, reversing the problem, or letting students get creative.

Why the Experiment Matters

Some might question whether spending time on experimentation is worth it when you could simply provide students with the formula. The answer lies in the depth of understanding and engagement that experimentation fosters. When students work through a problem themselves, they aren't just learning the formula; they are comprehending why it works. This is conceptual understanding, which is more enduring and valuable than rote memorization.

Conceptual understanding equips students to see the bigger picture, make connections between different mathematical concepts, and apply their knowledge creatively. It transforms them into problem solvers who approach challenges with confidence.

Encouraging productive struggle and discovery learning can transform your math lessons. It not only deepens your students' understanding of math but also instills in them the confidence and skills to tackle complex problems in the future. So, as you plan your lessons, consider how you can create opportunities for your students to engage in productive struggle!

I hope you’ve found these ideas helpful.

Discovery lessons are just one of the strategies I discuss in my online workshop: How to Teach Math without Telling Students Everything.