Sometimes it’s helpful to let students name things first.

For example, I usually begin algebra without introducing a whole lot of new vocabulary up front. So, we’ll be discussing an equation, and a student will try to make a point about the “coefficients”—but since we don’t have a name for coefficients, the student is struggling to get everyone on the same page. At that point, I’ll ask the student to describe the parts of the equation she is referring to, and to give them a name. From that point on, any time we refer to that part of the equation, we use her name.

This way, students get to act as explorers. When they discover some new territory, they get to name it. And since these names have context within this particular class, they are easy to remember, and no one is struggling to figure out what the name means or where it comes from because we know exactly who named it and why. By reducing cognitive load (how much we have to think about in the moment), students are able to put more of their focus on solving the problem or understanding what’s going on.

Later, once students are familiar and comfortable with identifying and manipulating the parts of an equation, I’ll let them know the boring names that mathematicians use—which most of them already know.

By the way, you didn’t cover one of the more important concepts (and my personal favorite): “terms”. Math might have been a little scared to bring it up at the end.