# Teach Math Like a Maker

### New book shows teachers how to supplement teaching math with the 3D models and hands-on projects.

by Joan Horvath and Rich Cameron

Maker education typically focuses on learning how to make something, like programming an Arduino or using a 3D printer. However, we think one of the greatest opportunities in school makerspaces is using making to teach math. Math is typically taught as an abstraction, a language, or some other construct that may appear arbitrary. Students learn math first as a prerequisite, and only later learn the physics, chemistry, or engineering that uses it. We see this as both depressing and demotivating for all concerned.

Traditional math teaching requires careful scaffolding so that students learn algebra techniques they will use at each stage. However, starting with a hands-on model and discussing concepts qualitatively first can upend that order. For example, there is no reason an elementary student cannot understand the basic concepts of calculus like the relationship between an integral and a derivative if it is taught with LEGO bricks and 3D prints. We have taught kids as young as nine this way. They may not be able to state the algebra or symbolic formulations, but they have a framework to hang grade-level ideas onto that they think is cool. And if they think they know a bit of calculus, that gives them a little swagger that might take them through the bumps in third-grade math.

We postulate that students fall apart in math, particularly calculus, for several reasons. One is just its fearsome reputation. Another is that there are a few guiding principles and then a lot of special cases. It is common to beat all the special cases to death, without spending enough time making sure students understand the core principles first.

Teachers need to see how much their students know. In math, this involves an answer. Beyond an answer, though, teachers ask math students to “show their work.” Showing work can be challenging for students who are very intuitive. They may be able to get to an answer by using mental modeling or techniques they develop on the fly. Since much of what we do as makers teaching math is about developing intuition, it will not always follow that students can then move to doing a problem a particular way. They should be able to get to an *answer*, but the route may not be the same as one derived purely from algebraic manipulation.

If the point is for the student to get good math intuition to build on later, where possible it will be more motivating for all involved for the student to describe the problem *the way they solved it *rather than the way the teacher prefers to solve it. This can particularly be a problem if the student has leapfrogged the current topic and is thinking about the issue more broadly than it is being taught.

Discussion with the student to see how they are thinking about a problem solution (which might not be the same way a teacher thinks) is more powerful than just having the student copy a standard method exactly and then reconstruct it by rote. If discussion is not practical because of the number of students, the student can perhaps sketch or use some other method to justify the path to their answer. Or students can explore these models together and share ideas for a bit of "peer review" before an authoritative up or down assessment.

Our new book, *Make: Math Teacher’s Supplement* gives concrete suggestions on how to supplement teaching math with the models and projects in our Make: Geometry, Make:Trigonometry and Make: Calculus books. By all means, use school maker space time to teach kids about 3D printing. But then let them use that knowledge to build tools to learn about math, science and other topics more intuitively. We’d love to form a community learning how best to make this work. Drop us a line at nonscriptum.com/contact!

Adapted and condensed from *Make: Math Teacher Supplement, *Joan Horvath and Rich Cameron, Make: Community LLC, 2024* *(available at makershed.com and other retailers).

Joan Horvath and Rich Cameron are the authors of the books noted in this piece, as well as other books, and LinkedIn Learning courses. They are the co-founders of Nonscriptum LLC (www.nonscriptum.com) where they consult on many aspects of making and learning.

Joan and Rich will be presenting at the MakerEd Education Forum on September 27 & 28.