Problem-solving in mathematics works in a similar fashion. This higher-level of performance is only possible because the foundational skills have been automatized. Different chords and note progressions are executed with minimal conscious thought, freeing the musician's working memory to infuse the music with emotion or improvise with different tempos and dynamics. However, with practice and repetition, piano playing gradually becomes more automatic. Initially it takes concentration to strike the proper key with the correct finger at the right moment. For example, a novice piano player will find it laborious to play even simple songs. Proficiency in any field, not just mathematics, is built upon a foundation of automatized knowledge. This is a diversion that pulls attention away from the actual problem, consumes space in working memory, and increases the risk of error (e.g., a student who counts to 22 while using a counting-up strategy to calculate 3 x 7).

In contrast, students who haven’t memorized math facts must temporarily interrupt their higher-level problem-solving processes to manually calculate (or type into a calculator) the product of 3 x 7. Simple math facts, such as 3 x 7 = 21, can be retrieved effortlessly and instantly from long term memory. This allows them to better focus their intellectual energies on the problem at hand. By having key math facts and procedures immediately accessible in long-term memory, students need not waste cognitive resources on low-level calculations. Fundamentally, our working memories are extremely limited in size, while our long-term memory is vast. (2023) paper provides a compelling explanation of how memorizing certain math facts facilitates deep thinking and advanced reasoning. Isn't rote learning the antithesis of deep thinking? With calculators readily available, what is the point of having students memorize math facts? The counterintuitive relationship between memorized math facts and deep thinkingĬalls for “more memorization” may seem counterintuitive. Research also indicates that low-achieving math students experience significant sustained improvement in standardized test scores after developing an automatic recall of math facts ( Pegg, Graham & Bellert, 2005, Stickney, Sharp & Kenyon, 2012 ). Mastery of math facts has been linked to enhanced math learning and problem-solving performance in elementary schools (e.g., Cumming & Elkins, 1999, Lin & Kubina, 2005 ) and even predicts academic success at the college/university level (e.g., Powell et al., 2020, Hartman & Nelson, 2016 ). This finding has been demonstrated across different grade levels and student populations. Studies conducted since 1989 have consistently shown that students are more likely to succeed in mathematics when they develop automaticity 1 in basic math facts. In fact, they may have made deep thinking and problem-solving harder for students to do. However, there is increasing evidence that their new standards were shortsighted.

Implicit in NTCM’s 1989 recommendations was a belief that mathematics instruction should refrain from memorization-related activities in favour of deep thinking, reasoning and problem-solving. Today, it’s not unusual to find middle and high school students who don’t know their multiplication tables. states and Canadian provinces modified their curricula in response (Hartman, Hart, Nelson & Kirschner, 2023). The NCTM’s recommendations were influential and many U.S. At the same time, NCTM suggested that teachers reduce the time allocated to the rote memorization of math facts and algorithms. These standards recommended the use of calculators at all grade levels and emphasized the development of reasoning skills. However, a shift occurred in 1989 when the National Council of Teachers in Mathematics (NCTM) introduced new math teaching standards. During the 1960s and 1970s, children were expected to memorize fundamental math facts and algorithms. The article begins with some historical context. The paper offers a review of the topic and explains why research now suggests that a limited amount of memorization is highly desirable. Should children learn math facts (e.g., 4 + 9 = 13 and 7 x 3 = 21) by rote? In other words, should students rehearse these facts until they are fully committed to memory?Ī recently published paper, Designing mathematics standards in agreement with science, written by Hartman, Hart, Nelson and Kirschner (2023), brings us closer to resolving the debate. For decades, educational experts have been divided over the value of memorized math facts.

Memorize multiplication tables