I like working with teenagers for a lot of reasons. One such reason is because it is usually quite easy to get bold, absolute statements out of them.
For example: “I don’t get ANY of this.” (emphasis not mine…).
It’s tricky business handling that statement because most of the time, the author of that quote genuinely feels that way. That doesn’t make the it true, but if he or she is already feeling like all the attempts at math are turning up wrong, combating their perception by simply saying it’s false is probably not the best approach.
I enter into evidence the following photo:
I gave these two problems as part of a short formative assessment. I saw the answers shown above a bunch. Most of my classes were lamenting the assessment because, “They don’t get any of this.”
Which, as I said above, couldn’t be farther from the truth. Those two answers show quite a lot of understanding, actually. There is a single mistake that led to incorrect response in both cases. That student was unable to distinguish the shorter leg from the longer leg. That’s it. Fix that and the answers get better.
And when I show them the answer to those two, many of those bold, absolute thinkers are likely going to think, “Yup, I knew it. It’s wrong. I knew I didn’t get any of this.”
At least I know that going into the discussion. Now, if I can just convince them that understanding is a spectrum more than a light switch.