Struggling With Math? Practice Leads To Progress
In his latest blog post, Hampton Tutors Coach Tim Barnes discusses a fascinating study of math skill development in kids over time. The results suggest that, when it comes to learning (and therefore teaching) math, routine and consistency are key.
What kinds of brain changes occur when you learn how to solve a new math problem? A large group of researchers at Stanford have recently published their results of scanning kids’ brains over years of math development. They looked for large-scale structural differences that tease apart different aspects of learning such a complex set of skills.
This is one of the first longitudinal studies of brain connectivity in developing children relative to a task; these studies are especially difficult to set up because participants move away or drop out, and the experiment lasts longer than the typical length of both a university research position and a government grant funding cycle. The alternative of scanning kids of all ages at one point in time is much more tempting, but is almost useless because one cannot truly disentangle the general effects of age and the specific effects of each child’s unique development schedule.
The researchers measured three general classes of variables: they measured each kid’s general math and reading aptitude with a standardized test (Pearson WIAT-II) at each visit; they measured their speed at performing specific math problems in the brain scanner; and they measured brain activity with functional magnetic resonance imaging (fMRI) while the subject did math problems or lied passively in the scanner.
A statistical test showed that the subjects’ standardized test scores generally stayed the same, so they assume that the kids generally all developed their math skills at a similar rate. Because the subjects have to hold still in the scanner, the types of math problems that can be done in the scanner is limited; in this experiment, simple equations were shown (2 + 3 = 7) and the subject had to respond whether the equation was correct or incorrect. Since this was a fairly simple task for most kids aged 7 to 14, brain connectivity profiles were compared by how quickly they answered the question (reaction time / RT), from 2-3 seconds near 7 years old to about a half second at 14.
These efforts to analyze the “effective connectivity” between math-related brain areas over time are truly heroic; they’re able to piece together an interesting story about how kids’ brain connectivity changes with age and math ability, but results like this should always be held very loosely.
The researchers show that, while doing math, certain brain areas’ activity patterns become more or less similar as the subject gets older. They focus on connections with an area whose overall activity level is correlated not just to age, but also to math aptitude: the intraparietal sulcus (IPS). This area, otherwise known to process quantity, becomes more collaborative on this task with areas that respond to the forms of letters and figures (ventrotemporal occipital cortex / VTOC), while simultaneously collaborating less with prefrontal cortex (PFC), which is otherwise associated with high-level reasoning and cognitive control.
In other words, math skills may develop by making calculations more habitual and automatic. The authors believe that these changes are related to general math ability, because a similar study on a specific 8-week training didn’t show any changes like these; the changes are faster than those expected by general genetic-driven brain development from aging; and older kids with dyscalculia have connectivity profiles that resemble those of the younger kids in this study.
These results corroborate one of our earlier posts that suggest that math skills are related to making certain math forms and processes instinctive. As a tutor, one should not be afraid to incorporate a moderate level of rote practice into teaching math skills. At the same time, if math skills are dependent on quickly memorizing the visual form of a calculation, these results are another call to being as consistent as possible with math notation when learning a new concept.