Doing vs Understanding

Posted: February 6, 2016 in Uncategorized

This past week I had my Pre-AP students working in groups to create a lesson that they are going to teach their classmates. We did this last month, but the concept this time is a little more difficult. Each group was assigned a 3-dimensional solid. In their group, they needed to learn about their solid, figure out how to teach the surface area and volume, and also have a small assignment (practice) for their classmates.

What is the purpose of having them do this instead of just telling them the formulas of each? Well, everyone gets tired of hearing the teacher talk all the time, but I feel that if I just say, “plug the numbers into the formula and solve” then the students are just doing math. I don’t want them to “do” math like it’s a job, I want them to discover and understand what they are doing.

While groups have been working this week, I was not sitting at my desk (I don’t have one) ignoring the students while they worked. I sat down with each group and looked at their solid. We discussed the shapes that make up the faces and how to find the area of each. We also discussed how to find the volume and practiced a little.

The prisms and cylinders groups have their shapes down. They understand how to find Screen Shot 2016-02-06 at 9.26.40 AMthe surface area and volume of each. The cylinders even found out how to type π on a Chromebook. They even used Google Draw to create their own images and not just using images that they find on the web for their presentations. They are creating 3-dimensional objects on a computer!

Now, we all know that pyramids and cones have a little more difficulty in their formulas. However, when I sat down with their groups and we looked at the solids, they see the different faces and they know how to find the area of each shape. So when they go to find the surface area, they just think about the shapes that make up the solid.

When I was talking with cones and pyramids about the volume, they knew to multiply by 1/3. I asked them why, and there was silence. So I told them to go on a field trip with me, and as we left the room, I grabbed the prism (for pyramids group) or a cylinder (for cones group) and walked down the hall to the water fountain. I shared with the students that they the two solids in my hands had the same base size and the same height. I asked a student to fill up the pyramid/cone with water, then pour it into the prism/cylinder. As the student was filling the pyramid/cone a second time, I always had someone in the group have it click!

We were discovering as a group why you multiply by 1/3. (It’s because 3 pyramids/cones volumes fit inside the prism/cylinder.) I also encouraged them to use rice and to use this demonstration when they teach their peers.

You see, when I can empower students to teach their peers and their ideas and not just mine, their peers listen more. It also helps the students have a strong understanding of one solid to be able to help their classmates when they are having difficulty.

Also, as a math teacher, I know that if you understand how to find the surface area of a prism, the cylinder makes sense (and vice versa). If you understand how to find the volume and the relationship between the prism and pyramid, then the relationship between a cylinder and cone is better understood.

So you see, as students are learning their solid, it will help them understand another solid that is being taught by a different group. If I just stood and gave the formulas of each, then students would get confused and I don’t feel would fully understand the concepts.

What do you think? Is this a great way to teach or should I just stand at the front of the room telling them the formulas and how to plug the numbers into them?

For some more explanation, you can check out the video below. We do not work with spheres, but you can see how it ties in as well.

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