There is much debate on how best to be fluent with basic math facts, according to an article in Education Week.
Should students memorize these facts and drill them? Or can they learn by playing with numbers, practicing ways of finding the answers so they internalize them?
“Most people in the field will say: ‘Both, we need both,’” says Nicole McNeil, a professor of cognitive psychology who studies math learning at the University of Notre Dame. “But that doesn’t give any actionable feedback about what that means.”
A recent paper reviews the research on fact-fluency development and offers research-backed advice for classroom practice.
Here are four key recommendations from the paper:
1) Early number sense skills matter, and interventions can boost them
A foundation for fact fluency includes three early math milestones that occur in early childhood:
- Understanding “cardinality,” or the idea that the last number counted in a set of objects represents the quantity. For example, a child who counts 1, 2, 3 blocks in a bucket would know that the total number of blocks in the bucket is three.
- Comparing written numbers, or knowing, for instance, that the number 5 represents a smaller quantity than the number 6.
- Using addition strategies, such as “counting on” to add 7+3 by counting three up from 7, to reach the answer 10.
Schools and pediatricians’ offices should screen for these skills.
Also referenced is the “concrete-representational-abstract” method — teachers first represent a number with three-dimensional objects, then with pictures, and finally with numbers. “This process supports the transition from everyday understanding of numbers, relations, and operations to the more formal symbols used for communicating mathematical ideas,” the authors write.
2) Explicitly teach how to solve math facts
Some students may intuitively pick up on strategies for calculating addition and subtraction programs. Others won’t and need direction, says McNeil.
Some conceptual foundations of math can be absorbed through everyday experiences with numbers, she says. “But once we get to the formal mathematical symbols, those are human inventions, so learning how those symbols map onto meaning requires intentional instructional support to ensure they are learned well,” McNeil says.
Teachers can model some of these strategies, according to the paper, such as how to use 10 when solving 9+n addition facts. In working through 9+5, for example, teachers could say, “Think, what is 10+5 and then just subtract 1, because 9 is 1 less than 10.”
3) Structure practice intentionally
To recall math facts quickly students need to practice producing them. Research suggests practice should be short—2-10 minutes at a time—and frequent, several times a week.
Teachers should introduce new facts systematically, says McNeil. That could mean starting with foundational fact sets, like the 2s, 5s, and 10s times tables, or using another organizational strategy. Students should only practice 3-4 new facts at a time until they can recall them automatically.
4) Timed practice shouldn’t be high stakes
The National Council of Teachers of Mathematics says timed drills can “negatively affect students, and thus should be avoided,” although there’s no conclusive research showing that timed tests cause math anxiety. In its most recent math framework, the California Department of Education discouraged using timed activities.
Research shows when practice is a little stressful and challenging it can actually help the content stick better in students’ memory. Several studies show that students’ speed and accuracy with math facts improved when they participated in time-pressured practice.
McNeil offers some cautions. Timed practice helps improve speed once students are already accurate, she says. Teachers should only introduce timed practice of math facts once students can reliably produce the answers correctly.
And time pressure should be limited to practice. High-stakes timed tests are a “bad idea,” she says.
Education Week
