I have a student in algebra 1 who has been solving basic equations by guess and check, and he shuts down when he sees a more complicated equation. Weeks into the unit he still didn’t know how to solve using opposite operations. Today I took him aside to show him the function machine method I learned last week. He was quickly successfully solving problems, thinking about inverses! At the end of class he said, “Now I get it!”
Another teacher’s PreCalc class was struggling with transformations of functions. I showed him the variable substitution method and his students said, “Why didn’t you show us this before??”
It sure is nice to find something that clicks for kids.