I am having a few issues with our new resource’s attempt at actualizing the recommendations made by the NCTM and the WNCP in order to philosophically align itself with current theories of learning. I deeply appreciate that research supports the idea that students need to construct their own knowledge for deep understanding to occur. I also firmly believe that this construction needs to be made relevant to the students for them to truly engage with the topic at hand.
However, when both the relevance and the constructing are done in primarily artificial ways, I just don’t see the point. For example, to introduce the idea of polynomials, alge-tiles are highly relied upon. The tiles do provide a nice visual for students, and can be easily manipulated to illustrate concepts. To get students using the tiles, the resource uses “games” to get students attention. Well, I don’t know about you, but “let’s pull a handful of alge-tiles out of a bag and then draw both their pictorial and symbolic representation, whee!!” is about the lamest game I’ve heard of yet. This is not relevance. This isn’t even fun past the first throw of the tiles. (Even then it’s likely only fun because you’re throwing something.)
Now, don’t get me wrong, I have no idea how to introduce like terms in an authentic way that would be both relevant and motivating at the grade 9 level. Not yet anyway. (When I do, I have a sneaking suspicion I might be in the business of making lots of money.) But, this is not it. There is nothing to “discover” when the text outlines what the different tiles represent and how to use them. As of yet I have not encountered an alge-tile in my life outside trying to teach students polynomials and cannot imagine when I would pull them out to pictorially represent a situation. There has been no “need” created here, there are no other options that might call upon some problem solving, there is simply compliance wrapped up in a “fun” package.
I have issues with this because I think it misses all the critical pieces that make new theories of learning and engagement so powerful. It’s false advertising. It trivializes what is meant by “deep learning” for both teachers and students. As someone who is desperately trying to see how math could fundamentally look different in my classroom, this fake fun is doubly dangerous. It is both toxic in the staffroom and borderline insulting for both myself and my students. This gives the critics of “new math” the ammunition they are looking for – that the new math has no standards. It also doesn’t help the supporters of math reform envision math in truly new ways. I could have supplemented my old lectures with the introduction of some alge-tiles(and sometimes I did!). I could have had “game” days on Fridays all along. I would, however, still be teaching stuff.