“Young children reinvent arithmetic. Spontaneously or by imitating their peers, they imagine new strategies for calculation. They also learn to select the best strategy for each problem. The majority of their strategies are based on counting, with or without words, with or without fingers. Children often discover them by themselves, even before they are taught to calculate.”
― Stanislas Dehaene, The Number Sense: How the Mind Creates Mathematics
Fact Fluency
Fact fluency plays in to number sense as it provides an achor to computation, comparisons, and place value (especially as it relates to the distributive property).
Brooke Newsome
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If you want to see benefits of fact fluency taught through reasoning and number sense, not just memorization, take a look at this presentation!
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Reynaurora Resendez
Math coaches and instructional specialists, need a handout that's easy-to-read and packed with support for best practices around fact fluency? Click below for one that's ready to go!
AJ Barnes
If you are looking for research-based arguments in support of fact fluency taught using number sense and reasoning, this article has you covered.
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Written by AJ Barnes
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It's been years since the beginning of the Covid-19 pandemic, and society is still trying to get back to “normal.” Schools have returned to in-person instruction, but students, teachers, staff, administrators, and parents are all likely to agree that just because school is “back in business” does not mean that school is “back to normal.”
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Students across grade levels and demographic groups have shown declines in math achievement scores since the pandemic (Walton, 2023).
A common remark made by teachers and parents is that students do not know their times tables or basic math facts. In response, it is tempting to advocate for a “back to basics” approach where students use algorithms to solve arithmetic problems under drilled and timed conditions. However, research should caution us to go down this path.
Teachers, administrators, parents, and policymakers may find themselves in unchartered territory as we recover from the pandemic. The pressure of standardized testing and making up for “learning loss” due to the pandemic may lead many to advocate for practices like fact drill worksheets and timed tests of times tables. But there is a rich set of research that can point us in
the right direction.
A critical part of students’ success in mathematics has to do with number sense.
Number sense is the ability to work with numbers flexibly.
Students who have strong number sense use strategies such as using decomposition, “making ten,” and compensation, to name a few.
Students with strong number sense also use known facts. Math facts are important, but, “math facts themselves are a small part of mathematics and they are best learned through the use of numbers in different ways and situations.” (Boaler, 2015)
When students are labeled as “low performing,” it is tempting to recommend “drills” and more and more practice of addition and multiplication facts. The thinking may be that if children practice math facts enough, eventually they will stick. Yet facts memorized through rote techniques do not tend to stick (Kling & Bay-Williams, 2021).
Furthermore, multiple research studies suggest that “Low achievers are often low achievers not because they know less but because they don’t use numbers flexibly – they have been set on the wrong path, often from an early age, of trying to memorize methods instead of interacting with numbers flexibly (Boaler, 2009). This incorrect pathway means that they are often learning a harder mathematics and sadly, they often face a lifetime of mathematics problems. (Boaler, 2015)
Fluency is a stated goal in almost all math curricula. However, we should be cautious to conflate fluency with speed. The speed at which someone speaks a language should not be used to judge the fluency with which they speak it. Some of the most eloquent orators speak slowly and deliberately. Like so, the speed at which someone does mathematics should not be used to judge the fluency with which they do it. Not only are some of the greatest mathematicians some of the slowest thinkers, but research suggests that timed tests and assignments may cause students to develop anxiety and negative identities around mathematics (Boaler, 2014). Timed tests also do not reliably measure students’ efficiency and accuracy with math facts, especially for young children whose fine motor capabilities are still developing (Kling & Bay-Williams, 2021).
Instead of timed tests, mastery progress charts for 0s, 1s, 2s, etc., and endless worksheets, teachers and parents can engage in a variety of strategies to develop fact fluency in students. Interviews, Quick Looks, Number Talks, and games are just some of the activities that educators and parents can use to cultivate number sense in children (Boaler, 2015; Kling & Bay-Williams 2021).
Plus, they are much more enjoyable!
As we all continue to recover from the pandemic, let us use research to re-think the ways that we help students master their math facts.
In the long run, it will be worth it!
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References
Boaler, J. (2014). Research suggests that timed tests cause math anxiety. Teaching children mathematics, 20(8), 469-474.
Boaler, J. (2015, January 28). Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts. YouCubed. https://www.youcubed.org/evidence/fluency-without-fear/
Kling, G., & Bay-Williams, J. M. (2021). Eight Unproductive Practices in Developing Fact Fluency. Mathematics Teacher: Learning and Teaching PK-12, 114(11), 830-838.
Walton, E. (2023, November 9). Performance declines in basic mathematics and reading skills since the COVID-19 pandemic are evident across many racial/ethnic groups. NAEPPLUS+. https://nces.ed.gov/nationsreportcard/blog/pandemic_performance_declines_across_racial_and_ethnic_groups.aspx