Schools generally track students starting in third or fourth grade based on their ability to memorize the multiplication table from zero to ten with speed and accuracy. When you consider your own education in math, you’ll probably find a nice example of how that process works.
Those who measure 2-digit multiplication memorization skills in 9 year olds usually have no training whatsoever in assessing innate mathematical talent. The fact that they feel any inclination to do that in the first place tells us as much. They often create learning and testing conditions that are detrimental to understanding and that render their assessments useless.
There are a few simple facts that one should make this obvious:
· Memorization of the multiplication table is not a mathematical skill; it is a memorization skill. (When one is taking a multiplication test for speed and accuracy, one is not thinking mathematically but simply demonstrating the ability to memorize abstract symbols in relation to one another. The multiplication table test is the intellectual equivalent of memorizing state capitals or baseball team mascots.
· A person can be taught to recite the multiplication table without understanding the concept of multiplication.
· In stressful situations, the autonomic nervous system creates the fight or flight impulse that overrides the parts of the brain that attend to memory and recall.
· When humans are asked to perform a memorization task, their accuracy decreases when they are given a time limit, when the stakes are high and when others are watching… in other words when the situation is stressful.
A timed, in-class multiplication test that impacts a student’s grade or course placement will, therefore, not provide any information about the student’s mathematical ability; it’s not even a good way to measure memory and recall. Repeated implementation of such an exercise is a form of educational malpractice.
More damaging than the timed, public, high-stakes multiplication test itself is its special power to ruin of the school experience many students.
The academic tracking that often results from such testing frequently extends to classes other than math and can launch capable students into academic pathways that stifle their potential, diminish their confidence and limit their options in life.
Many schools still set up schedules to accommodate “stronger” and “weaker” students as determined by their math class placement- a characteristic often traceable to multiplication tests in 3rd or 4th grade. So students who do not memorize symbols quickly and accurately when they are 9 years old, often find themselves permanently placed in classes across the curriculum that do not challenge them and in which expectations for deeper understanding are low. (Please recall that high expectations is the single most powerful factor in influencing student achievement. https://visible-learning.org/hattie-ranking-influences-effect-sizes-learning-achievement/ )
Multiplication table memorization tests are often the first step on a long journey of bad math instruction. Math education in some parts of California still emphasizes accuracy and the ability to apply algorithms rather than conceptual understanding, much less experimentation or creativity. Course progressions are arbitrary and were designed years ago as barriers to separate students into divergent tracks rather than as opportunities to learn and grow. (Ever wonder why Algebra 1 comes before Geometry and Algebra 2 comes after that?)
In this system, teachers often fail to see the potential of students who might excel in math and make significant contributions because they are focused on the ability to calculate and get correct answers, independent of conceptual or practical understanding. This emphasis frustrates many college teachers who receive freshmen who are fast and accurate with equations but who have trouble communicating, modeling or representing concepts visually.
What we offer to students and what we tell them about math has an enormous impact. Countless students pass through our classrooms each year and I fear that we underestimate their potential, causing them to underestimate their own. Consider the somewhat famous story of Maryam Mirzakhani who nearly gave up on math in middle school but went on to become the first woman to win the Fields Medal in 2014.
Mirzakhani did poorly in her mathematics class that year. Her math teacher didn’t think she was particularly talented, which undermined her confidence. At that age, “it’s so important what others see in you,” Mirzakhani said. “I lost my interest in math.” The following year, Mirzakhani had a more encouraging teacher, however, and her performance improved enormously.
I highly recommend reading the full article not only to understand the impact of high expectations from teachers but also to get a better understanding of what mathematics really is:
So what do we do? Don’t we have to get our middle school students ready for the high school math track? Unfortunately, we still do. Until the whole system changes, we do need to ensure that our kids get to high school prepared for grade level math and that does means speed and accuracy… but it doesn’t mean just speed and accuracy and it doesn’t mean tracking based on those things.
Let’s start with what we shouldn’t do: No timed, public multiplication tests for grades. We can stop doing that right now. Middle grade teachers need to ensure understanding but should not hold kids back from deeper concepts because they don’t meet an arbitrary speed & memorization benchmark. And that doesn’t mean that we shouldn’t teach kids their multiplication tables; that can be very helpful. But let’s recognize math fact memorization as a tool for further work and growth rather than a learning objective and certainly not as an indicator of capacity to learn math.
Next, let’s re-think our understanding of what math really is. Math is not the ability to make quick and accurate calculations any more than history is the ability to recall state capitals. Math is the logical study of pattern, shape and quantity and math education should be about facilitating growth in that area. Schools need to understand that and do our best to keep the door to math understanding wide open for all students.