The Secret To Success On The PSAT: Knowing That 5+2=7

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The PSAT includes some pretty sophisticated math. But new brain-imaging studies show that students who are well-versed in very basic single digit arithmetic—and I mean very basic, as in 5+2=7 and 7-3=4—are better equipped to achieve high scores on the PSAT (and, by extension, the SAT). ScienceDaily reports:

“In findings published January 4 in The Journal of Neuroscience, fMRI scans performed on high school seniors found a significant link between their brain responses while solving extremely basic, single digit calculation problems and their scores on the PSAT.

Students who scored better on the math section of the PSAT generated greater positive activation in a brain region in the left side of the brain, called the supramarginal gyrus, which is known to be linked to fact retrieval, while students who scored lower produced more activity in an area in the right side of the brain, called the intraparietal sulcus, which is involved in quantity processing and more effortful problem solving.

‘Essentially, this means that those high school students that don’t do so well on the PSAT use more problem solving strategies when they are doing very elementary sums and subtractions,’ says Daniel Ansari, a psychology professor at Western University. ‘If you are a high school student and you are using brain circuits that we know are associated with fact retrieval and fluency, we see evidence that you are also going to score better on the math portion of the college admission test. There is a clear link between fluency and high level abilities—being fluent at basic math counts.’

This new knowledge is important from a math education perspective, concludes Ansari, because traditionally, debate rages between the ‘drill and kill’ style approach versus more conceptual, problem-solving based pedagogy. It is now clear that both methods are important in elementary education. These findings suggest that the way in which the brain is organized for single digit arithmetic calculation predicts performance on more complex math skills, illustrating the critical role that arithmetic fluency plays in building mathematical proficiency among students.” (Read more here.)

Let’s repeat that again for emphasis: It is now clear that both fact-based and conceptual methods are important in elementary education.

You must know your math facts to be able to do advanced math well. At the same time, knowing only facts and not the conceptual relationships connecting them leads to a shallow and inflexible approach to the subject.

I hope this will settle the long-running debate between the two sides. But I doubt it.

 

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3 Responses to “The Secret To Success On The PSAT: Knowing That 5+2=7”

  1. I wonder what this says about classical education.

  2. Tim Hudson says:

    There is significant confusion about the means and ends of mathematics learning. This research study only validated the importance of curricular goals (the ends) that everyone agrees on. But there are some unfounded conclusions being drawn from this research regarding instructional implications (the means).

    The research showed “a clear link between fluency and high level abilities.” We’re all agreed that fluency is the goal – though I wouldn’t put “fact retrieval” and “fluency” on the same level of importance (I’m not fluent in Spanish, but I can retrieve the fact that ‘casa’ means ‘house’). I’ve spoken with countless adults who memorized their math facts up to 12×12 but need a pencil or calculator to solve 13×7. They may have some fact retrieval, but that’s not fluency.

    This research looked at which 12th graders taking the PSAT were fluent and which students weren’t. It concluded that students who knew their facts and had conceptual understanding at the time of the test were more successful. The only conclusion to draw from this research is that we need to ensure students reach a certain point of fluency and conceptual understanding. Thus the ‘ends’ we want are clear: fluency, concepts, and facts. No one debates these, and the research showed their importance.

    There’s no data in this study, though, about how this fluency was developed in each student back when they were in elementary school (and including anything since 7th grade). So the debate arises because conclusions are drawn from this research about the means and methods by which fluency is developed, conceptual understanding is cultivated, and facts are acquired. The statement “It is now clear that both fact-based and conceptual METHODS are important in elementary education” does not appear to be substantiated by the research findings. The only thing that is clear from the research is that fact-based and conceptual OUTCOMES are important in elementary education.

    Despite being a widespread and prevalent assumption, it’s misguided to believe that the only way students can acquire the facts and use them fluently is through “drill and kill” methods. That’s not how young children become fluent with vocabulary and grammar in one or more languages. Students fluent in arithmetic say, “there aren’t that many facts to remember because many of them are related and you can figure things out really fast using those relationships” (as an example, most adults know 33×2 instantly, but they didn’t memorize their 33′s). Students lacking fluency think, “I’ll never learn all these facts – there are too many to remember.” For these students – who this study says will later be unsuccessful on the PSAT – they need to learn that mathematics is about more than memory. They shouldn’t become adults who need a calculator for 13×7.

    We always have to be clear about the means and the ends. The outcomes aren’t being debated. Just the methods. And it appears that this research only shed new light on the importance of the outcomes.

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