There is/was a twitter thing on integers today. Someone spent two weeks talking about meaning, and then … students went to “adding the opposite.”
I suggested that sometimes the meaning background made the ‘rule’ easier to remember. I had earlier in the day recalled that azaleas and rhododendrons like acid soils, and had reflected that were it not for having learned some understanding of pH and the smells and feels of the soils, that would have been a ‘random fact that falls out of the brain. This inspired me to suggest that while the students resorted to “adding the opposite,” the meaning stuf fmight make that easier to remember.
The response was that basically meaning was great but students couldn’t remember the meaning stuff… which made me recall the other reality: so much “this is to help add meaning!” and strategies for learning are, from the student perspective, one more stupid thing to memorize. I posted that when this happens, I chuck the ‘add meaning’ and got a “good for you!” reply. Erm… whatever.
However, I’m not satisfied with that, because giving up so easily on building meaning in means that a whole bunch of students persist in in believing that math is a thing to be memorized and survived, so they do the academic bulimia thing and regurgitate to pass tests and never digest and build things, and the teachers and they just assume that … they’re not math types. YOu know, the whole thing that Jo Boaler and WithMathICan are fighting. Even if they’ve taken a pledge to learn from mistakes,we need to structure the learning so they can learn that way. Otherwise the pledge is just another thing to recite that has no meaning, like those “things to help add meaning!” in the math book…