There is very little satisfaction in just being given the answer. In some ways that is a negative trade off of the internet. You can always find the answer to a question (what's the formula for circumference of a circle or how to calculate the law of sines), but you don't get that same sort of satisfaction in having worked out the solution yourself.

There is great satisfaction as well as deeper learning in discovering the solution to a problem. This is why I love inquiry-based learning. As a teacher, it's hard not to give the answer.  I know how to solve a system of equations.  I could just show my students how, but then students would not discover and internalize the solution.

Getting started with inquiry-based learning in your class can be easy.  Here's three quick strategies you can implement today:

1. Find the pattern:  Give students open-ended problem solving opportunities such as in this activity in which students work out the meaning of circumference and developing a formula. I could just tell them what it is, but by finding patterns by the examination of multiple circles, students understand what circumference means and rarely have to memorize the formula because students determined the pattern by themselves. By the end of the inquiry activity, students can write the formula for circumference and literally find pi.
2. Show examples but not define: In this case, students work with a concept. We don't define or name the concept until the end when students write their own definitions. In this inquiry-based activity on volume, students compare the space taken up in a box by by unpopped kernels of popcorn and then the same number of kernels popped. Students decide how to measure and define this. At the end we name it volume, and students write definitions. Later, when they are working out formulas with different 3-d shapes, they have a clear recognition of what volume is.
3. Create a problem, determine a solution:  Design projects and problems that have broad parameters and lots of opportunities for students. Because of the open nature of the projects, students will encounter problems unlike ones they have seen before. For example several students wanted to include churches in their medieval villages in this integrated geometry project.
The churches were in the shape of Roman crosses. This presented two problems: how do you create a net for a cross and how do you determine the surface area and volume of the structure? Although I was more than willing to help, I absolutely refused to show anyone "how" to do it. Students discussed, failed, tried again and figured it out themselves. They all didn't come up with the same strategy, which is as it should be.

I love inquiry-based learning because once students get used to it (and many don't like it initially), students discover that they can problem solve and find solutions. I (nor the internet) am the sole ways to find answers. Inquiry-based learning is empowering and builds confidence. And everyone can do it.

For more tips on using inquiry-based learning in your math class, check out this short video.

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.