Why learning basic number facts still matters

An expectation of mathematical proficiency embedded across the Australian Curriculum (Version 9.0) is the development of mathematical fluency (Australian Curriculum, Assessment and Reporting Authority [ACARA], 2024). In Foundation to Year 10, fluency in Mathematics involves efficiently selecting appropriate procedures, accurately recalling number facts, and readily applying conceptual knowledge and understanding (ACARA, 2024). Within broader educational discourse, fluency is often associated with the concept of memorising number facts.

One of the most common questions I hear from parents is whether students still need to learn their times tables and basic number facts when calculators are readily available. It's a fair question, however if we want students to students to think critically, solve complex problems and apply mathematics in meaningful ways, then the ability to respond rapidly, accurately, and with minimal cognitive resources is essential (Skinner & Daly, 2010).

The ability to quickly recall basic number facts remains one of the foundations that supports higher-level thinking. When we refer to basic number facts, I am referring to operations involving addition and subtraction (for example, 7 + 8 = 15 or 15 − 8 = 7), multiplication tables, and operations with fractions. These are the building blocks of successful learning in Mathematics in both the Primary and Senior Years.

So why is it important to be able to automatically recall these basic number facts? The answer lies in how our brains process information. Research in cognitive science and educational neuroscience shows that working memory, the cognitive space we use to think about problems, is limited. With respect to learning new information, our working memory can only remember about 7 elements, however when we try to process newly acquired information, such as when we perform a calculation for the first time, that capacity reduces to 3-4 elements (Sweller, 2024). Long-term memory on the other hand has no know limits. Once information has been stored in long-term memory, it can be retrieved and used in working memory without being constrained by the same capacity limitations that apply when learning or processing new information (Sweller, 2024).

When students have to stop and calculate basic facts every time they encounter them, a significant portion of their working memory is used on those calculations. There is less capacity available for developing conceptual understandings, identifying patterns or solving more challenging problems. An analogy would be trying to read a novel while sounding out every word letter by letter. It is possible, but it would be slow and exhausting. Learning in Mathematics works in a similar way and when basic facts are more readily able to be retrieved from long-term memory, students are more are more likely to learn related concepts.

Reducing the cognitive load on working memory when learning new information is one of the key reasons fluency has been identified by the Australian Curriculum as an expectation of mathematical proficiency. Students who can instantly recognise that 8 × 7 = 56 or that 7 + 8 = 15 are able to devote more cognitive resources to manipulating fractions, solving equations and problem-solving. Basic number facts become tools rather than obstacles.

Fluency with number facts doesn't develop through discovery, it requires regular, structured practice over time (Kirschner et al., 2006). Several studies have found that one of the most effective ways do develop automatic retrieval of basic number facts is peer-practice – that is saying facts aloud - and daily retrieval where students repeatedly recall information from memory. Retrieval activities help students strengthen their recall of facts more effectively than any other approach. The act of repeatedly retrieving information helps build stronger and more accessible neural pathways associated with long-term retention (Breneman-Smith 2024; Haebig et al., 2021).

The good news is that supporting numeracy development at home doesn't need to be time-consuming. Regular short practice sessions are more effective than long ones. Five minutes a day, has been shown to be a powerful way to transfer information to long-term memory. Encouraging children to say facts aloud rather than simply reading them from a page, helps strengthen memory and improves recall speed. Games can help too. Card games, dice games and simple mental maths challenges often provide valuable practice without feeling like formal study. Through my youngest son's interest, I have recently discovered just how much basic arithmetic is involved in the Pokémon Trading Card Game!

At Somerset College, we want students to develop both fluency and conceptual understanding. These aren't competing goals; however, strong number fact knowledge provides a foundation that allows students to engage more deeply in conceptual understanding with critical thinking, reasoning and problem-solving.

The mathematics our students encounter in secondary school and beyond becomes increasingly sophisticated. Algebra, calculus, statistics and mathematical modelling all place demands on working memory. Students who have automatic access to basic facts are often better positioned to manage those demands because their attention can remain focused on the concepts rather than the calculations.

Australian Curriculum, Assessment and Reporting Authority. (2024a). Mathematics proficiencies. https://www.australiancurriculum.edu.au/resources/mathematics-proficiencies/

Australian Education Research Organisation. (2024). Developing maths proficiency [Explainer]. https://www.edresearch.edu.au/... [1, 2]

Breneman-Smith, S. L. (2024). Quasi-Experimental Study of the Impact Spaced Practice and Retrieval Have on Mathematical Fact Fluency in Third-, Fourth-, and Fifth-Grade Students. Doctoral Dissertations and Projects.

de Bruin, K., Kestel, E., Francis, M., Forgasz, H., & Fries, R. (2023). Supporting students significantly behind in literacy and numeracy: A review of evidence-based approaches. Australian Education Research Organisation & Monash University. https://www.edresearch.edu.au/...

Haebig, E., Leonard, L. B., Deevy, P., Schumaker, J., Karpicke, J. P., & Weber, C. (2021). The neural underpinnings of processing newly taught semantic information: The role of retrieval practice. Journal of Speech, Language, and Hearing Research, 64(8), 3195–3211. https://doi.org/10.1044/2021_J...

Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75–86. https://doi.org/10.1207/s15326...

Skinner, & Daly. (2010). Improving Generalization of Academic Skills: Commentary on the Special Issue. Journal of Behavioral Education, 19(1), 106–115. https://doi.org/10.1007/s10864...

Sweller, J. (2024). Cognitive load theory and individual differences. Learning and Individual Differences, 110, Article 102423. https://doi.org/10.1016/j.lindif.2024.102423