Today I gave my 8th graders a summative exam of the algebra topics we've been covering. This mainly included solving for x as well as solving for y to set up a y=mx+b linear equation.
They have not been terribly attentive, to say the least, to the activities we do in class, so it was with some level of trepidation that I decided to give them the exam. I am not a believer it testing for testing sake, nor for holding grades or exams over my students' heads as threats. But I have to admit that my student culturally go there without me doing anything.
Anyway, many of them showed serious misunderstandings of variables and constants, of fractions and of the algebra tiles we've been using. I saw in front of me the many various misunderstandings of algebra that are interfering with their deeper math education. My admin as well as the parents will quickly tell me that it is my fault: that I am not telling them "how to do it". I will say that it is not the "how" that is holding them up, but the "why". They'll say that I must not be explaining the "why"well enough. I will have to consider this carefully, because every teacher should be humble enough to realize that they are not walking on water when it comes to presenting material. But down inside I know I follow all the best practices associated with conceptual learning, and still my students resist (at times, reject) it.
So it all gets me thinking of the intersection between mass culture and education. If my students and families are hell bent on the "how" (because they learned it that way and because that is the "only" way math should be taught), but I am putting my foot down and insisting on justification and conceptual knowledge, then we find ourselves irreconciably miscommunicating.
It gets me thinking, too, about at what level we, as American educators, can hope to really teaching a rigorously conceptual math program along the level of Singapore Math. This is what I wrote in an earlier post:
When is the next plane to Singapore leaving?