John Benson at Angles of Reflection has a post–a very important one–that’s been sitting at the top of the blog for a long time. Every so often I re-read that and think about it. It offers a telling vignette of how students are taught a rich technique for addition (“near doubles”) but do not use the technique. The students still revert to standard procedures of addition to “get the answer.” Then they tack on the new technique, which means they aren’t really learning about the structure of addition.
This explains something that has troubled me for some time. I frequently hear from parents that their child is not challenged by the curriculum that is being offered in their school. When I have looked at the curriculum I find that it is often very rich and full of many challenges. Perhaps the reason for this disconnect is that when the student looks at the material, the only thing the student is thinking about is how can I get this done and get a right answer, while I am looking at how many different things a student can learn from the variety of approaches taken.
I think the key to cutting off answer-getting in students is to notice that what they want is a good grade for just having the answer, so the teacher strategy is to give a middling grade for just having the answer, and a better grade for employing new strategies.