Q&A: Can You Teach a Math Class on the Basis of Projects Only?

Cross-posted from here.

Question

Can you teach a math class on the basis of projects only, as opposed to more traditional exercises?

Answer

Not really. Sure, projects can be useful for pulling a lot of skills together to do something cool and exciting. That’s valuable. But the thing is, students need to acquire the component skills first. Most student’s can’t learn component skills on the fly in the context of a bigger project – they need plenty of practice on each particular skill, where lots of scaffolding is provided at the beginning and then gradually removed.

For example, let’s say you want to do a project where students sketch an image by graphing a bunch of straight lines in Desmos. Obviously, going into the project, students are going to need to know how to represent points in the coordinate plane and find the equation of the line between two points. They should also know how to manually create the graph of a given linear equation (otherwise they’re not going to understand what Desmos is actually doing for them, and they won’t be able to debug their equations if they run into issues). They’ll need to be comfortable different formats of equations of lines, including $x=\textrm{constant},$ $y=\textrm{constant},$ $y=mx+b,$ $y−h=m(x−k).$

There are tons of component skills here and you can’t teach this all in the context of the project. Each of those component skills has to be built up beforehand. And it takes plenty of time and practice to build them up. Most students are going to need a worked example and a handful of practice problems (with feedback) on each separate case of each component skill (separate cases involving positive numbers, negative numbers, fractions, decimals, etc.). If they don’t get this practice, then they’re going to be totally overwhelmed by the project, spend a ton of time working unproductively, and ultimately learn little to nothing from it.