I don’t know exactly how I wound up being a math teacher when I think of all the crappy math teachers I had. In fact, I cannot point to a single pre-college math teacher and say, “He/she was a really good teacher.” I went on to study the subject because I had natural ability in it – whatever that is – and I always knew I wanted to be a teacher. So, I guess in some sense, I wanted to become the math teacher I never had, one who dared to break the stereotype and turn kids on to the subject.
One math teacher I had reduced everything we studied into a series of steps to follow. For every problem type, she had six or eight steps that, if followed accurately, would produce the answer. It was a cookbook of math she was offering, a recipe for every problem type. She thought she was a great teacher for doing this, it seemed to me. I suspect she had absolutely no idea that this kind of teaching is problematic in two significant ways.
First, this method provides virtually no conceptual understanding. There is no sense of why things work as they do, no sense of the connection to other math (or to real-life), and no sense of discovery or wonder. Math is reduced to procedural knowledge and “learning” it this way essentially becomes memorizing the steps with complete disregard for the why or the what if. Nobody cares why it works and the mentality of the students becomes: just do A, B and then C and you’ll get the answer.
The second problem I see with this kind of math teaching is that there is no long-term retention once the test is over. Since kids aren’t really learning any concepts, they quickly forget the memorized steps to this problem or that problem. Why wouldn’t they? It is the concepts that underlay the procedures that give meaning to the procedures and aid in retention. But these kids who dutifully study these collections of recipes generally pass the course. And when they do, they move up to the next course where they invariably struggle because their background is spotty at best. This unfortunate situation is exacerbated if they have a real math teacher in the next course who won’t give them recipes for everything. In fact, it’s the second teacher who gets grief because the students now have to think and are not being spoon-fed with a steady course of steps. Often, the students are very vocal saying things like, “Mrs. Soandso gave us steps last year and it really helped. Can you be more like her? She helped us.” Even parents chime in with a similar request. It may not be until the following year when the second teacher is appreciated for teaching concepts along with those procedures and making her students think and apply and wonder.
It seems to me that the underlying issue is the propensity for teachers – particularly in math – to break everything down for kids. (Often this is done out of sheer frustration.) On the surface this is sensible and even prescribed by many educators. I do it, you do it, we all do it. But if we never put the pieces back into the cohesive whole to which they belong, the students never see the interconnections and never see the big picture. That is, they never get the concept. When we never put it back together into something more complex, we leave our students forever floundering in low-level thinking. It is not possible to ascend Bloom’s Taxonomy by only breaking it down and never rebuilding the bigger, harder concepts from the little understandings. I think this is where we often fail our kids. To a point, breaking it down is fine – just don’t stop there. And don’t mistake learning steps from a recipe for learning math anymore than you would mistake learning to type for learning to write. dven.
