My IB Mathematics course has started out well, with a successful introduction of functions, domain and range and composite functions. So maybe I started getting too cocky and didn't spend enough time on today's lesson - on inverses. Whatever the reason, it felt like hitting a wall. While students happily solved questions such as "what's k(x) if h(x) = 5x and h(k(x)) = x?", they could not even start on the very similar question "what's the inverse of h(x) if h(x) = 5x+3?" Even with me explicitly explaining the connection, by definition, to the previous question, students were dumbfounded by these developments.
Now I'm the one who's a bit stuck. Do I give an extra class on inverse functions - this would break my planning and mean I'm lowering my standards a bit. Or do I send them to the math study hall and go on with my planning, hopefully managing to fit in inverses now and then again? I'm leaning towards the latter but would really like to figure out what went wrong (and how to fix it). Maybe the language just got to abstract? Riley at Point of Inflection has a series of posts I probably should have read more carefully.
Ah well. "Where you stumble, there lies your treasure", is this nice saying I've always liked. Maybe there'll be something superbly useful in this mess somewhere.