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Why fluency and flexibility matter in mental computation
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Why fluency and flexibility matter in mental computation
Think Mentals 4/11/26
Australia’s maths results have been making headlines. One in three students is failing to reach proficiency in maths,1 and this year’s NAPLAN showed Year 3 numeracy at its lowest point since 2023.2 Behind those numbers are young learners still building the foundations they’ll rely on for the rest of their schooling and beyond. An important factor in foundational numeracy is what a student does when a maths problem doesn’t go to plan. How do they use their mental computation toolkit to move forward?
Think about the last time you moved furniture. Did you panic when your oversized couch wouldn’t fit through the door? Did you hastily try different positions until you found one that worked, damaging the paintwork in the process? Or did you take a moment to consider your options and decide which approach would work best?
Students in a maths classroom face the same choice when their first strategy doesn’t work. Some keep pushing the couch. Others step back, look at the problem and choose a better way through.
What is flexibility in mental computation?
Flexibility in mental computation is a student’s ability to draw on a range of mental computation strategies and choose the most appropriate one for a given problem.3 There is a key difference between a student who simply reproduces strategies quickly and one who applies strong number sense to select the right strategy for the job.
Take 99 + 47. One student might split both numbers into tens and ones and add them separately. It works, but it takes several steps. A flexible student notices that 99 is just one less than 100, adds 100 + 47 and takes away 1 to get 146. Or consider 1000 − 998. Counting back would take forever, but a flexible student sees the numbers are only 2 apart and counts up instead.
Both students can get the right answer. The flexible student gets there more efficiently, with less cognitive load and less room for error.
What’s the difference between fluency and flexibility in maths?
Fluency is being able to carry out a strategy accurately and efficiently. Flexibility is knowing several strategies and being able to choose between them. Students need both, and the order matters.
The Grattan Institute’s Maths Guarantee report’s snapshot of effective maths teaching describes an approach where students develop fluency with one strategy before new strategies are introduced, and are taught which strategy is most useful to use at any time.1 In other words, fluency builds the toolkit and flexibility is knowing which tool to reach for.
Students develop strong number sense and fluency when they learn a variety of mental computation strategies. They develop flexibility when they are encouraged to find their own ways to solve problems and critically evaluate the effectiveness of those strategies.3
Why does flexibility in mental computation matter for primary students?
Flexibility matters because it helps students solve problems more efficiently, more accurately and with greater understanding. A flexible student isn’t just following steps. They’re looking at the numbers, noticing relationships and choosing a strategy that suits the problem in front of them. That habit strengthens number sense, reduces the load on working memory and builds the kind of confidence that keeps students persisting when a problem gets tricky. Research also recognises flexibility as an important part of mathematical expertise,4 so the benefits stretch well beyond mental computation into multi-step and complex application.
The opposite is also true. Students who consistently struggle with mental computation tend to rely on a more limited number of strategies than those who excel.3 When their one go-to strategy doesn’t suit the problem, they have nowhere else to go.
The good news is that flexibility can be taught. When students are given regular opportunities to learn, compare and discuss different strategies, they become more confident, capable problem solvers. That’s exactly the kind of strong early foundation that reports like Grattan’s and the latest NAPLAN results are calling for.1 2
How do teachers develop flexibility in mental computation?
Teachers need to teach the mental computation strategies explicitly and help students understand that there are multiple ways to solve a problem, and that some strategies will be more effective than others depending on the context.
Research backs up the value of comparison. Across classroom studies involving hundreds of students, those who compared multiple correct strategies gained greater procedural flexibility, often gained greater procedural knowledge, and sometimes gained greater conceptual knowledge than students who studied the same examples one after another.4 Regular comparison of alternative strategies is recommended, particularly once students have developed some fluency with an initial strategy, along with small group and whole class discussion about the similarities, differences, strengths and limitations of each approach.4
Facilitating risk taking and discussion in the classroom is known to develop fluency and flexibility in mental computation.3 A scaffolded approach that encourages students to explore and discuss their thinking, coupled with explicit teaching, is a recipe for success.
How can explicit teaching and practice build fluency and flexibility?
This is where Think Mentals comes in.
Students are explicitly taught a range of mental computation strategies that are easy-to-remember and effective to use. During Think Mentals lessons, teachers can encourage students to make observations about how different, or perhaps more effective strategies can be used to solve problems.
On day 1, students learn a new mental computation strategy and practise using only that strategy to build fluency. Then as the week continues, students explore problems that challenge them to apply a variety of previously learned strategies. Providing regular opportunities for students to determine which strategy may be the most effective supports students to develop flexibility.
Adopting a whole school approach such as Think Mentals also provides a common language for mental computation strategies across the primary years and ensures students are regularly exposed to familiar strategies. Plenty of built-in revision opportunities ensure learning is consolidated and repeatedly practised over time.
With national attention on mathematical outcomes, building fluency and flexibility in mental computation every day is a crucial and practical way that schools can strengthen students’ numeracy foundations that lead to better outcomes. A carefully scaffolded program such as Think Mentals equips students and teachers alike with the tools they need to get there.
References
Hunter, J, Haywood, A, Parkinson, N, Daniel, P 2025, The Maths Guarantee: How to boost students’ learning in primary schools, Report, Grattan Institute, viewed 6 October 2026, https://grattan.edu.au/report/maths-guarantee/↩
Australian Curriculum, Assessment and Reporting Authority (ACARA) 2026, Latest NAPLAN data shows improvements in national numeracy levels alongside areas for continued attention, Media release, 5 August 2026, viewed 7 October 2026, https://www.acara.edu.au/docs/default-source/media-releases/media-release-latest-naplan-data-shows-improvements-in-numeracy-levels-alongside-areas-for-continued-action-5-8-26.pdf↩
Rathgeb-Schnierer, E & Green, MG 2019, ‘Developing flexibility in mental calculation’, Educação & Realidade, vol. 44, no. 2, pp. 75-86, doi:10.1590/2175-623687078↩
Rittle-Johnson, B, Star, JR & Durkin, K 2020, ‘The case of comparing multiple strategies to improve mathematics learning and teaching’, Current Directions in Psychological Science, vol. 29, no. 6, pp. 599-609, doi:10.1177/0963721420969365↩