If there’s one simple trick that I think every teacher could master really quickly–and that would lead to more mathematical agency in classes, and students having deeper levels of understanding, it’s this:

Let students conceptualize something on their own before bringing in mathematical language and notation makes it more likely that the notation will aid in their understanding rather than provide another hurdle in learning.

I’m quoting Bowman Dickson there, and he’s got a whole post explaining how he did this in a calculus class. You should check that out. If it’s been a while since calculus (or if you never *took* calculus), that might be a bit overwhelming, but it shouldn’t be. It just means don’t teach vocabulary and symbols at the very beginning of class. I don’t know how many times I’ve seen that: a teacher up at the front, asking students to copy down definitions, which still mean *nothing* to students, and meanwhile they’re checking out one by one…

Just save them! Do the vocab at the end, rather than the beginning.