The problem is that the normal pace of development for some students means their brains are physiologically not capable of understanding algebraic abstractions. Worse, once students have tried and failed to make sense of the material, they may conclude that they “just can’t do math” — a potentially self-fulfilling prophecy in subsequent courses. I heard that claim all too often over the past few years.
In the study of math, we now know, timing matters a great deal. As children mature, they become more capable of complex cognitive functioning. They add perceptual, discriminatory and evaluation skills to their cognitive repertory through experience.
To oversimplify the neuroscience, the cortex, or outer layer of the brain, matures from back to front. Parts of the brain associated with more basic functions, such as motor and sensory functions, mature first, followed by areas involved in spatial orientation, speech and language development. Areas involved in attention, evaluation and motor coordination develop last.
What does this have to do with algebra? Importantly, imaging studies have shown that late-developing areas are extensively involved in abstract reasoning. While imaging studies are not yet (and may never be) capable of determining a specific age at which adolescents are most able to learn concepts like those in algebra, we can expect that this human attribute — just like height, weight or IQ — will approximate the famous “bell curve” distribution across the population. Some students will develop early, and some late, and those who develop late are at risk due to the push-down of algebra into middle school.
Classrooms in Fairfax provide anecdotal evidence that supports this idea. Thomas Edison High School, where I taught, enrolled 1,187 ninth graders between 2008 and 2010. Of these, 435 took a remedial course called Algebra 1 Part 1, which was designed to strengthen basic arithmetic skills and introduce abstract concepts at a slower pace. In other words, at this one school, fully 36 percent of incoming ninth-graders were deemed unable to handle full-blown Algebra 1.
So what’s the take-home message? Just as teachers need to adjust for the different styles of learning exhibited by various students, curriculum administrators need to be aware of the different capacities of students to deal with abstract reasoning. This doesn’t refer to textbooks, materials or teaching approaches. It is simply that the physiological brain development of students varies.
Course offerings should take this into account, and, in particular, provide alternatives to Algebra 1 in the eighth grade.