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Fluency and flexibility in mental computation

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Fluency and flexibility in mental computation

Think Mentals 17/8/23

Have you ever tried moving 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?

Just like moving furniture, students in a maths classroom can respond to challenges in different ways when the first strategy they try doesn’t work. There is a key difference between a student who simply reproduces mental computation strategies quickly and one who applies strong number sense to select an appropriate strategy. When students have a good knowledge of different strategies, along with the ability to choose and apply the most appropriate strategy to a given problem, this is referred to as flexibility in mental computation.

Teachers need to both teach the strategies 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.

Students develop strong number sense and fluency when they learn a variety of mental computation strategies. Students develop flexibility when they are encouraged to find their own ways to solve problems and critically evaluate the effectiveness of those strategies. This is where Think Mentals comes in.

When introducing a new strategy, a Think Mentals lesson begins by posing a problem and asking students how they would solve it. After solving the problem, students share and discuss the strategies they used. This encourages students to make observations about how different, or perhaps more effective, strategies can be used.

Facilitating risk-taking and discussion in the classroom is known to develop fluency and flexibility in mental computation. A scaffolded approach that encourages students to explore and discuss their thinking – coupled with explicit teaching – is a recipe for success.

After learning a new strategy on day 1, students explore problems throughout the week that challenge them to apply a variety of mental computation strategies. Providing opportunities for students to solve a range of problems and evaluate the effectiveness of their chosen strategies supports students to develop flexibility.

Students who consistently struggle with mental computation often tend to rely on a more limited number of strategies than those who excel. Adopting a whole-school approach such as Think Mentals provides a common language for mental computation strategies in the primary years and ensures students are regularly exposed to familiar strategies. In addition, Think Mentals provides plenty of revision opportunities to ensure learning is consolidated.

A student who has good mental computation flexibility can make a sound guess at which strategy would be most effective to solve a problem. They can also pivot quickly to another strategy if the first one isn’t working. A carefully scaffolded program such as Think Mentals equips students and teachers alike with the tools they need to develop fluency and flexibility in mental computation.


Rathgeb-Schnierer, E & Green, MG 2019, ‘Developing flexibility in mental calculation’, Educação & Realidade, 44(2), 75–86, doi:10.1590/2175-623687078.

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