Tom in his Halloween costume
Quick! What’s 14-8? Now 8×7? How about 96+7? And 96÷8?
Did you “just know” those facts, or did you have to figure them out?
This is the way we often think of measuring how well students “know their math facts.” We quiz them, out of context of any application of the fact, and expect them to be fast and accurate in their recall of the answer. The faster they can answer, the better they know them. These facts are often thought of as things that we “just have to memorize” so that we can be automatic. Keep practicing with those flash cards, right? You might be surprised to learn that the answer is…not really.
Merriam-Webster.com defines “fluency” as “the ability to do something in a way that seems very easy.”1 A student’s ability to be quick and accurate in their recall of basic math facts like addition, subtraction, multiplication and division is often referred to as “fact fluency,” and there is no question that it is important to a student’s success in both learning and applying math.
Brain scans comparing students who had achieved a certain level of fact recall fluency over time with those who had not (and were still using strategies to figure out the facts) show that those who are not fluent with these facts are using more parts of the brain to figure them out. Unfortunately, they are using the very parts of the brain that we would hope they would use to learn more complex procedures or concepts. Those who have established a more fluent recall of facts, actually utilize a different (and smaller) part of the brain, because they are simply recalling a fact, rather than figuring it out. This frees up the other parts of the brain for the more complex work we are asking them to do in class.2
While efficient fact recall is absolutely helpful, we may actually be making this more difficult when we encourage memorization and use timed fact tests as a part of our math instruction. Students use their working memory to apply facts in the context of a problem. Working memory can be shut down by the brain when it is under too much stress. Studies show that timed tests impair working memory performance in students of all backgrounds and achievement levels.3 According to some estimates, this often leads to some level of math anxiety among as many as a third of all students3. What is perhaps even more compelling is that other brain scans have shown that students who memorize facts process them in an entirely different brain pathway than those who learn them without memorization. Further, those who learn them without memorization were actually more secure with their facts and better at applying them.3
Rather than encouraging students to memorize facts and practice recalling them faster and faster, researchers and educational leaders suggest that fact fluency is best achieved by a sound “understanding of the underlying numerical relations”3 and repeated application within the context of an engaging “problem.” These might be real world situations (even if contrived), puzzles (such as those here), or games (like this). There may be times that a flashcard type of practice (like these) might be helpful, but these should be used without time constraints and only as practice after the conceptual understanding has been established.
More important than “just knowing,” might be the ability to figure out something new. Computational fluency goes beyond “fact fluency” and is even more important for students to develop than an easy recall of facts.
We’ll find out more about this next time. Until then, I’d really encourage you to read the full article that I’ve referenced several times here. I think you’ll find it compelling.
Take your time to figure this out mentally: 235×15=
Happy Math! And check me out on twitter @tompitttcs,
Tom
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1http://www.merriam-webster.com/dictionary/fluency
:the ability to do something in a way that seems very easy
2https://www.reflexmath.com/research
Video: Automaticity & The Brain
3https://www.scientificamerican.com/article/why-math-education-in-the-u-s-doesn-t-add-up/
Why Math Education in the U.S. Doesn’t Add Up:
Research shows that an emphasis on memorization, rote procedures and speed impairs learning and achievement
