About a year ago, Miles Kimball Noah Smith published a column in The Atlantic entitled “The Myth of ‘I’m Bad at Math’”. Clearly this touched a number of nerves, and provoked a comment debate that continues today. I did an earlier post on this topic. Today, there were a couple of new comments added that stimulated me to think about this issue in a new way, so I thought it might be interesting to share these thoughts more widely, in hopes that this discussion might develop into wider dimensions.
The starting point was the idea that what we currently teach under the label “math” is really a collection of a lot of different things, only loosely related even at the foundational level – calculation, approximation/estimation, representation, visual math, number and set theory, logic, computer science at the very least. The name of “math” becomes associated with all of them. The inevitable is that if a kid is slower than average to catch onto any part of this diverse skill set (and of course half the kids will be below average, with a substantial portion well below), then s/he gets the idea that “I’m poor at math” and consequently loses interest in anything that is labeled as “math”, even if s/he might actually excel at those other parts.
As an example, I can offer an N=1 case study – i.e., me. I was pushed ahead a grade level in the middle of first grade, largely because I was reading at the 5th-6th grade level. That was hardly a sign of genius – I just loved reading, and was seriously curious. As a result of this push, I basically missed the entire introduction to calculation that was the foundation for all “math” until junior high school (yes, it was that long ago). I resisted being labeled s “poor at math”, but I knew that I had to do some serious work to catch up. It wasn’t until fractions in probably 5th grade that I felt myself really up, and it was always in my mind associated with lots of hard work (and thus not fun). This was all in the pre-calculator era; the thought of delegating even a single long division to eight decimal places to any kind of machine was instantly labeled as “cheating”.
It was not until I got to geometry in 11th grade that I really found a part of math that WAS fun. I tend to be strong visually, and this was the first part of “math” that could be comprehended with the eye (at least, as math was then taught). I was also able to grab onto the little bit of set theory we were given. But calculations were still a major chore. When I got to college, I resisted taking the basic intro math class, opting instead for the easier version. It was well taught, and for the first time I grasped some of the real ideas behind math, including number theory and calculus.
I never really overcame my “math phobia” until I first encountered statistics in graduate school. One part of math I had always been very good at was approximation, and the concepts of probability suddenly became intuitively obvious. Fortunately, my class was one of the first to use statistical computing as a core aspect of the class, and I jumped onto computing like the last squirrel onto the last nut on Earth. I (he said modestly) excelled at statistics, largely because I could delegate the calculations to the computer. I also learned a fair amount of conversational Fortran in the process. I’ve been able to teach statistics (largely in the form of applied data analysis) for a long time and to a lot of people who came in with the old phobia. To me, data analysis is real fun, finally.
I apologize if the long case study seemed excessively narcissistic, but I am the person I know best and whose Tale I can best relate. The point is this: it would be much more effective if we could divide up and separately name some of the major components: distinguish among calculation, approximation, number theory, representation and logic, computer science at the very least – all different, and likely to appeal to different kinds of kids. It’s likely that almost every kid will be able to excel in at least one of these. Simply by making this division and banning the use of the term “math until secondary school at least, we could probably eliminate most of “math phobia”, and thus enable a lot more kids to at least get in the door of the mathematical kingdom, where they might find more such things.
It’s a fact of human life that in the primitive tribal societies that kids mostly inhabit, the highest status tends to be awarded to the physically strongest and most adept. Unfortunately, the kids who do manage to overcome the teaching and “get” math tend to be more the “geek” type who do little in the physical domain except embarrass themselves (e.g., yours truly). Thus, math becomes further associated with the kind of person that most of the kids aspire not to be. If we could find parts of math that appealed to the jocks and let them excel at it, then some of this association of “math” wigh “geeks” might also be broken.
Words and labels matter. It’s how human being store information and link ideas, particularly abstract ones. So we ought to be very careful in how those labels are set, and how kids associate them. It’s more likely that we can improve on mathematical knowledge in the general population by disaggregating mathematics than by lumping still more things into an already tainted intellectual bucket.