A key part鈥攖hough surely not the only part鈥攐f early-grades math is ensuring students get the basic arithmetic functions down and, beyond that, making sure they鈥檙e able to swiftly and automatically recall addition number combinations and the times tables.
Those skills help kids advance when multidigit arithmetic, fractions, and long division enter the picture鈥攁llowing them to focus on more complex problem-solving instead of simple computation.
Nevertheless, a surprising number of misconceptions about fact fluency abound. One common debate鈥攚hich probably stretches all the way back to the introduction of the abacus, let alone calculators, computers, and Google鈥攃oncerns whether kids really need to know the multiplication tables when those facts are readily at hand elsewhere. (Hint: They do.)
Mini-Course: Teaching Math
In a recent 澳门跑狗论坛 survey of about 300 math educators, most agreed that it鈥檚 鈥渆ssential鈥� for students to have fact fluency in order to work on higher-order, conceptual math problems. But more than a quarter said that it was 鈥渉elpful, but not essential.鈥�
EdWeek interviewed researchers and reviewed dozens of studies for this explainer. Read on鈥攐r jump straight to the bibliography at the end.
Why does math fact fluency matter?
The basic reason why math fact fluency matters, cognitive scientists say, is that it frees up brainpower or working memory to do more complex mathematical work鈥攍ike figuring out how to structure a multistep word problem, model a solution, or puzzle out systems of equations. It鈥檚 harder for students to do those things when they鈥檙e simply trying to work through basic arithmetic.
Also, being able to automatically recall math facts seems to be especially important for multiplication: Students have fewer rapid backup strategies to lean on in multiplication if they haven鈥檛 stored the times tables in their long-term memory.
For single-digit addition, kids can get pretty fast using strategies like 鈥渃ounting on鈥� from the highest number being added (i.e., 6+5 is counted as 鈥�7, 8, 9, 10, 11.鈥�) This becomes impractical in multiplication.
鈥淲hen you don鈥檛 know 6x8, and you鈥檙e doing an algebra problem with multiplication, you have to take the time and attention to add 8 and 8 and 8 and 8 and 8 and 8,鈥� said Robert Siegler, a professor of psychology and education at Teachers College, Columbia University. 鈥淎nd, ultimately, you can鈥檛 regenerate these forever, as the math gets more complicated.鈥�
Research finds that fluency in these facts is linked with progress in later grades; multiplication in particular is linked to success with fractions, a common tripping-up point for many young students.
How does math fact fluency develop?
There鈥檚 a generally accepted understanding that students鈥� knowledge of the addition number combinations begins by counting up all the digits in a problem and evolves to the more conceptual understanding that whole numbers can be 鈥渄ecomposed,鈥� or broken down or recombined, in a variety of ways. All these stages appear to help students secure the answer to number combinations in their long-term memory.
Many students learn their addition facts without explicit instruction in these strategies, but those with math learning disabilities will need more intensive help. A variety of approaches based in helping kids hone those strategies are promising (see the next heading for details).
In general, there鈥檚 much less research on how math fact fluency develops in multiplication. The limited available evidence suggests that there are fewer universal strategies that transfer.
Students generally find 0 and 1 multiplication facts easy because they鈥檙e effectively rules-based: Any number times 0 is 0, and any number times 1 is itself. Students tend to skip-count the five鈥檚 time tables (5, 10, 15, 20, etc.) And students can use a decomposition strategy for nine鈥檚 by remembering their 10鈥檚 facts and quickly subtracting 9 from each. Other combinations seem to be somewhat harder to learn and harder for students to store in their long-term memory for instant retrieval.
That is partly why timed exercises are so associated with multiplication: It鈥檚 a way of assessing whether students are truly recalling from memory or whether they鈥檙e still using the backup strategies.
What are the best ways to develop fact fluency?
Frustratingly, there isn鈥檛 a clear answer here. Most of the research derives from interventions for students with math difficulties, and those studies use a mix of approaches, so it鈥檚 hard to identify which element makes the most difference.
, for example, researchers compared four different approaches: one was traditional drill work, in which students were shown simple addition and subtraction facts in a computer program and asked to restate them, with a visual aid embedded. In the others, students received explicit teaching beforehand in counting-up or decomposition strategies, in some cases with explicit help practicing and with work on word problems mixed in. All those approaches seemed to be helpful and were linked with improved fluency.
There is far less direct research on multiplication strategies and how they contribute to fact fluency. One study found in comparing two different approaches鈥攐ne a traditional approach focused on memorization, and a second that integrated some strategies, including number-line work鈥�
Are timed exercises bad for kids? Do they cause math anxiety?
Timed exercises are often used as a way to measure whether students have committed math facts to memory. They seem to be especially popular in multiplication, which is generally harder for students to master.
They鈥檝e also gotten a bad rap over the years, as some educators question whether they could cause or exacerbate students鈥� math anxiety. But there鈥檚 no conclusive evidence on that point鈥攎ostly because there are no empirical studies that directly try to measure the question.
Math anxiety shows up even in young students and Anecdotally, both students and teachers recount feeling stressed when taking timed tests, but it鈥檚 less clear that the tests themselves trigger math anxiety or inaccuracy. One study found that on a basic arithmetic test, though another found for students with high anxiety on timed vs. untimed exercises.
The difficulty of the math鈥攁nd whether it鈥檚 being graded鈥攁lso seems to affect matters. A meta-analysis on math anxiety found that it did not interfere with students鈥� accuracy on simple math problems as much as when problems It also found that these links were higher at the secondary level, rather than at the elementary level.
Some educators point out that if done badly, timed exercises can exacerbate disparities among students.
鈥淚n too many classrooms, those 鈥榤ad minute鈥� type things are creating a dichotomy,鈥� warns Dylan Kane, a 7th grade math teacher in the Lake County district in Leadville, Colo. 鈥淭he kids who know most of the facts and are developing that automaticity and long-term memory of the facts. [But] the ones who don鈥檛 know them are deriving them on their fingers and skip-counting. And if you derive it once and don鈥檛 achieve it from memory, you鈥檙e not developing it very well.鈥�
A better approach, some teachers say, may be to individualize timed exercises so students are motivated to improve their own time, rather than being compared with one another.
