"There is no one way"

Friday, April 18, 2014


In some schools and communities teachers face a tremendous push for hyper-acceleration of certain students. As I mentioned in my previous post the pressure comes largely from parents, but they are often supported by students and administrators. Many parents believe that hyper-acceleration will help their child's college applications. Many students' self-image is intimately related to being "ahead" in math, as they have received so much praise for this in the past. Many administrators encourage hyper-acceleration in response to parental pressure, and in their attempts to compete with other schools. Such competition is seen as an economic imperative for private schools, and for public schools, it is a way to reduce the hemorrhaging of middle class students into private schools.

None of these motivations have anything to do with high quality math education. In fact, more often than not, hyper-acceleration undermines student learning. In this post, I will present some examples of hyper-acceleration, and try to explain why they are counter-productive.

* While some algebra is a must before high school, moving the entire Algebra 1 course in its 1970's form down the grades is a serious mistake. It shuts the door in the face of many students, and promotes superficial rote learning for the rest. (I wrote about this issue at greater length in my analysis of the Common Core.) I have worked with many, many kids who "did well" in a traditional Algebra 1 in middle school, but in fact learned nothing. When being interviewed to decide on what course they should take when they start high school, they struggle to remember the most elementary techniques, which they once knew by rote. In many schools, rote learning yields good grades, but unfortunately it does not stick.

* Many parents and students want to skip geometry, which they see as slowing down the march to calculus. Or else, almost as bad, they would like to dispose of the topic quickly in a summer course. Yet geometry is a fundamental component of cultural literacy the world over; it is necessary for further work in mathematics, including trigonometry and calculus; it fosters a strong visual sense, which is crucial in many careers, such as architecture, chemistry, and design; it is a part of math where students look at the big picture, literally and figuratively. Note that it is often the students whose strengths lie in the memorization of algorithms, not in problem solving or reasoning, who are most eager to skip or rush through that course. Yet they are the students who need it most!

* While calculus can be a legitimate topic for 12th grade, little is gained by teaching it earlier, and much can be lost. I once visited a BC Calculus class where a 10th grader stated that it was obvious that log(a) + log(b) = log(a+b). Such a misunderstanding is normal in 10th grade, but not so much in BC Calculus. Moreover, schools that allow early calculus have to find something to do with their hyper-accelerated 11th and 12th graders. The solution is typically to offer college-level courses with college textbooks and pacing, thereby making it difficult for students to develop an in-depth understanding of the material since most of them are, in fact, not much more mathematically mature than other kids their age. Colleges quite rightly do not offer credit for those classes, and students end up having to retake them, if they haven't been totally turned off to math by then.

OK, you say, too much acceleration can be bad. But how do I suggest schools deal with students who are not challenged by grade-level math, and are bored? I presented a partial answer in my last post, and will return to the question in my next one.


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