Is the over-emphasis on conceptual math showing up in national test scores?

By now the serious harm to student learning caused by the pandemic may seem like old news. From Texas and Ohio to Tennessee, state test scores have dropped substantially for all students, however, those declines were uneven. The pandemic caused widespread drops in both reading and math, with much larger declines in math, which hit historically disadvantaged students the hardest. As schools set to the unenviable task of making up this lost ground, newly released national test results give reason to carefully consider how, particularly for math, they might best do so.

Since the 1970s, the NAEP Long-Term Trend Assessment (LTT) has tracked student academic performance, and it was last administered just before the pandemic. Those pre-pandemic results can be compared to the last LTT results from 2012. They show disquieting trends for the nation’s nine- and 13-year-olds: declines in both reading and math, with larger declines in math, driven mostly by low-performing students. Sound familiar?

Math scores declined for both nine- and 13-year-olds at the 10th and 25th percentiles — with 13-year-olds at the 10th percentile falling a whopping third of a standard deviation. Meanwhile, high-performing students saw no significant change. With the bottom falling and the top remaining afloat, the achievement gap is growing. And that was before the pandemic.

Via Twenty20

So, what fueled this widening math achievement gap? There’s no clear single cause; however, one contributing factor could be the marked shift towards conceptual math instruction that emerged around 2010. This shift stemmed from concerns that math instruction focused too much on fluency — learning how to solve problems — and not enough on conceptual understanding — learning why particular techniques and formulas lead to solutions.

Tom Loveless, formerly at the Brookings Institution, pointed to this shift in light of the LTT results: “To me, it suggests that beginning a decade or so ago, something went wrong with how we teach math to younger students. My own hypothesis is that an emphasis on conceptual understanding has gone too far, that without computational skills to anchor math concepts, students get lost.” Similar concerns have been voiced outside the LTT context.

Now, before I get too far ahead of myself or push Loveless past his hypothesis, it’s important to not uniformly ascribe drops in math to this single instructional trend. Conceptual understanding and fluency are both important parts of math education, and it could be that the shift to conceptual math instruction was not a problem, or was just one of several factors. However, if the shift toward conceptual math left fluency behind, then Loveless’ theory fits these results.

Moreover, it’s no great leap to see how such a shift would hit low-performers the hardest. An over-emphasis on conceptual understanding would hurt low-performers’ progress if fluency is a prerequisite, or perhaps more accurately, an anchor, for developing and articulating conceptual math understanding. Such challenges could be negligible for students maintaining grade-level performance math, but problematic for low-performers.

I am reticent to jump to conclusions regarding this instructional shift, but this potential explanation is worth attention right now for three reasons. First, this explanation fits with the low-performers’ scoring trajectory, while few others match the timing and subject matter of the major LTT declines. Second, this balance is well within educators’ control, which may be a welcome relief to teachers and schools often held responsible for forces outside their control.  Third, and most importantly, if an inordinate focus on conceptual math is hurting low performing students, educators need to adjust now, not because of what the last LTT showed us, but because of what the next round will show.

Typically scheduled every four years, the LTT for nine-year-olds was wisely moved up to capture the pandemic’s impacts on student learning. This is a great decision but, frankly, we already know what it will show: remarkably larger declines, just like those seen on last year’s state assessments.

Nearly all students took a hit during the pandemic, meaning schools have far more low-performing students than a few years ago. Math educators need to take a clear-eyed and pragmatic view on what it will take to get those students back on track, and that may mean shifting the instructional mix to privilege fluency over conceptual math instruction. This may be an unpopular view, especially among the vanguard of math education cognoscenti that pushed for more conceptual math instruction, but it will be a tragedy if math instruction does not strike the right balance for low-performers — especially now when schools have more of them to serve.

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