If you've ever taught a math class, then you've probably encountered the following scenario: you're showing the class a cool proof (like why an inscribed angle always has half the measure of its arc), and you get asked: "Will this be on the test?" You're demonstrating how math is a consistent framework and that even the hardest facts are derived from simpler theorems. But your students just aren't interested. And from their perspective, this makes a lot of sense. Students have many demands on their time (some related to education, some not), and they're really just trying to optimize their schedules.
And so with our lessons, we tried something a little different. We know students aren't interested in working through proofs all the time. But sometimes they're genuinely curious, or they already passed the quiz and are now returning to see why the rule they memorized actually works. So we try to leave it up to the student to choose: if you want to work through a proof, click here; to just do practice problems, click here instead.
Here's an example from our lesson on inscribed angles:
After a student sees the rule in action and plays with an interactive, he or she can decide whether to work through a proof or skip ahead. If they opt for the proof, they'll work with general angles and prove it for themselves.
Otherwise, practice problems it is!
While it's nice that we give students the choice, we're really hoping they'll elect to work through the proof. They'll get more experience with geometric proofs, get more practice with algebra, and convince themselves that the rule truly works. So how many students decide to work through the proof?
Using our analytics dashboard (which comes with our authoring tool, QuickBranch, for you content authors out there), we found that of the 1701 students who made it to this point in the lesson, 987 (or 58% of them) decided to work through the proof. And of those, 779 (~78%) made it all the way through the proof. We found similar rates in other lessons as well, like the Pythagorean theorem. More often than not, in our self-paced learning environment, students will choose to work through the proof.
When they're asking "Will this be on the test?," it's not that students don't care or don't want to learn. It's that their time is limited, and they're trying to optimize. If you free them from these constraints, and let them come back to the proof when they feel motivated or incentivized to really learn it, they'll choose to do so.
So when it comes to material that won't be on the test, trust your students and give them the choice. They may surprise you.