In getting ready for the summer tutoring season, we once again have had several discussions with parents regarding preparation for math in the upcoming year. One of the things we have noticed over time is that there seems to be a trend locally to introduce students to sophisticated math concepts at an earlier and earlier age. The trend has got us thinking about why that might be and, whether it reflects something that promotes overall genuine academic mastery in math.
As a person that took Algebra 1 in 9th grade, today’s local community would likely consider this author to be tracked for “regular math,” or even a bit behind. Yet, the author was considered very good in mathematics when he was young and went on to major in Aerospace Engineering (where he took 5 calculus classes) as an undergraduate at a prestigious engineering school. Later, the author went on to a Master’s Degree program at Stanford University in what is probably best described as “applied math.” In other words, despite his “lagging behind” in high school by today’s standards, mathematically, he’s had more training than many people and has done “okay” in that department.
We encounter student after student that is taking algebra 1 in 7th grade, many of whom are not mathematically mature enough for the precision that solid mathematical thinking requires. Despite that fact, the local climate for math achievement seemingly holds taking a class like algebra 1 at an earlier and earlier age as desirable. What is the rush? Why is it that pushing down the age at which algebra is taught (and thus advancing through the math ladder earlier) is desirable when many students are simply not ready?
One thought is that a reason for this “push-down” is a response to the regular reports that among industrialized nations, the United States is not fairing as well in math achievement as we, its citizens, would like. Couple that fact with the regular warnings that are issued about maintaining worldwide technological leadership as a nation being critically dependent on our ability to produce a student body that is proficient in math, and one can see the connection. But is this response misguided? Is the reason that we perform worse than some of our industrialized peers really attributable to the fact that children in other nations are seeing sophisticated math concepts earlier than ours?
Certainly another motivator, at least in Silicon Valley, is one of competition. It’s no revelation to characterize Silicon Valley as a highly competitive place, but we wonder whether some of that competitive spirit is manifesting itself in a way that may not be optimal if our goal is to raise as many children as we can with legitimate mathematical competency. We wonder whether the drive for competitive edge, rather than doing what may be best for most students, is powering some of the push-down.
There is no doubt that there ARE students that live here that are indeed capable of digesting Algebra 1 in the seventh grade. There are a great many highly intelligent, educated and motivated individuals that live here, so it is highly likely that there are a higher proportion of children that live here who can perform, and even excel in math at early ages. But it seems to us that the response to that likely fact should be to enrich the lives of those students where appropriate. Instead, what may be happening is that the push to have those children be enriched and do advanced work within the school setting is “seen” by parents of a variety of children, some of whom may be ready for that level of work, and some of whom may not. The rush to ensure that the child is “keeping up” ends up resulting in a child being placed in a class (often at parental insistence) that may not be appropriate. Thus, advanced math begins to “creep down” to a lower grade level and ultimately this may not be helpful.
The problem with both of the aforementioned phenomena as a response to wanting our children to excel in math is that a lot of kids end up finding themselves overwhelmed and stuck on a “hamster wheel” of results-driven, i.e. grade-driven performance. Far too often the result is that kids compensate by seeking learning strategies that maximize a grade without enabling them to truly and deeply assimilate some of the more important connections in math. Hence, we end up educating a legion of students whose mastery of rote strategy is very high, but whose capacity to draw connections and thus become better, more capable math problem solvers is never given a chance to flourish.
Furthermore, and we see this a lot too, many children are never given the chance to see the beauty in math and the power of becoming math proficient. At the end of the day, many students see it as just another “thing that needs to be done” so college admission is made easier. That result seems antithetical to the goal of raising more of our children to be truly mathematically literate and is in fact, somewhat akin to “proof by contradiction” (If you’ve studied and appreciated math, those last words will seem familiar).