The submitter of this mistake notes,
This mistake brings up the concept of teaching with keywords to me. I asked the student to tell me how he got his answer; he pointed to the word “total” and said that he needed to add. I’d like to know what ideas educators have to intervene when a student is already clearly looking for keywords and is not making sense of the problem.
What do we mean by “make sense of a problem”?
Are we imagining an all-math skill, tools that can be used to make sense of any math problem no matter the topic or age of a student? Something like “read the problem carefully!” or “draw a picture!”?
Or are we imagining a local skill, some way to make sense of this problem and problems like it? Something like…well, I’m not exactly sure what would help someone make sense of this problem. Maybe, “if you see names, you might be comparing!” or “if you see a lot of numbers in a problem, rewrite them in a list so you can focus on what the problem is asking”?
I suppose that I’m inclined to think of keyword mistakes as a lot like applying the distributive property where it doesn’t belong or other “over-extending” mistakes. Generalizations are smart things to do, and a keyword generalization is a smart thing to think also, and it’s usually correct. Knowing that this mistake exists, I might create a set of problems all that contain the word “total” with some being summing up problems and others being compare problems and so on. My reasoning is sort of simple: this kid thinks that “total” means add ’em all up, so let’s provide him with counterexamples and then urge him to make a new generalization.