# Good with digits – does the evidence point to using fingers for maths?

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- Good with digits – does the evidence point to using fingers for maths?

## Good with digits – does the evidence point to using fingers for maths?

Professor Jo Boaler of Stanford University has done much in the last few years to help highlight important ideas about mathematics education. However, she has been criticised for doing this in a way that dumbs down the research or reduces it to an overly simplistic model – something she appears to have done recently with the correlation between finger gnosia (ability to perceive or recognise one's own fingers) and mathematical development.

In an article in the Atlantic entitled "Why Kids Should Use Their Fingers in Math Class", Jo Boaler makes the case that using fingers to reason with is not only 'essential for mathematical achievement', but improving students' finger–perception quality makes them better at maths.

In the article she asserts that schools in the US 'regularly ban' students using fingers in classroom or call them 'babyish'. Professor Boaler doesn't clearly outline the age of the students her comments relate to in the article, which is a shame as this seems particularly relevant to the topic. If counting on fingers is 'babyish', the suggestion is that it is appropriate for young children but not older ones. Is there a right time developmentally to stop using fingers in maths, and if so, when?

Boaler cites this study by Berteletti and Booth, on children aged 8-13, which says that 'our results support the importance of fine-grained finger representation (i.e., finger gnosia) in performing subtraction problems'. However, it only used 39 children – perhaps due to the difficulty and expense of scanning them – and selected only those children who were already good at maths (scoring 85 or above on the Math Fluency test). There are other studies, which Boaler also references, which suggest that improving students' finger knowledge or even just encouraging them to gesture more can lead to improved maths performance. There is a fascinating link here between the way that we learn to count and represent number and the areas of the brain that control our fingers.

However, Bertelleti and Booth also concluded that "against our initial hypothesis, we did not find finger motor activation to be related to skill." They could not find evidence in this admittedly small sample that using motor areas of the brain correlated with getting questions wrong – or right, or even that the harder problems or those with larger numbers activated the brain more. They expected this to happen, because previous research has shown that children who experience more difficulty with maths rely on finger-based strategies more – but for them, a possible explanation was that "children were relying on some finger-based strategy irrespective of problem size, but the use of this strategy did not yield better performance."

If Boaler wishes to recommend that all children be allowed – indeed encouraged – to use their fingers in mathematics, it is worth considering if there are particular conditions or stages in which this is actually helpful, rather than just accepting it as a universal benefit. Whilst banning finger use seems both ill-advised and hard to enforce (hand-sitting is impractical, and fingers will twitch whether you threaten detention or not), does the research really suggest we should all be doing it, all the time?

Almost all children, all over the world, use their fingers to do early maths. At least one study shows that adults do, too – at least, they use the same parts of their brains, even if their fingers are kept firmly in check. But does it actually help us calculate successfully? It's time we investigate more thoroughly, in order to see if Boaler is right and we should embrace finger-counting at every level, or if there are benefits in gently encouraging pupils to move from digit-waggling towards a purely mental representation of number, at some appropriate time.

The key here is to look at age and skill variables – the study on adults was on psychology students with no specific mathematical background, and the Berteletti and Booth study was on children of roughly homogenous (high) previous mathematical ability. Is there something about the way some brains process number concepts from the physical into the abstract that helps a mathematician become successful?

There is, of course, evidence to suggest that using fingers to calculate from scratch, rather than memorising basic facts, means students never become fluent in mathematics. The 'added cognitive load from inefficient methods of computations (such as counting on fingers) that arise from a lack of automaticity often leads to procedural errors and difficulties in learning new procedures' (DeMaoribus 2011). There is a widespread acceptance of a progression in mathematics that flows from the concrete to the abstract, from the procedural (counting) to retrieval (declarative) (eg Pruther and Alobali, 2009).

The research here is interesting – but not, as Boaler suggests, straightforward - because it reveals a gap still being bridged between neuroscientific and mathematical educational research. Whilst 'neurocognitive researchers conclude that successful finger counting and finger-based arithmetic serve as building blocks for later numerical/arithmetical development', 'the failure to abandon finger-based representations is seen as one possible reason for children's computing errors in second grade' (age 7-8)(Moeller et al, 2011). Much of the latest research in this area therefore seems to conclude that the use of fingers is one of several representations of mathematical objects that are proxies for later, more complex understanding of the relationships and properties that exist independently of these objects themselves – they are a useful anchor, but should not be allowed to drag on the ship once it sets sail. In our view, uptake of Boaler's suggestions must be tempered according to the emerging outline of finger-counting's potential boundaries for usefulness. There is a need for continuing research to help map this boundary more fully so that finger-counting can play an optimal role for each student in the development of mathematical understanding.

**Lucy Rycroft-Smith**

*Research and Communications, Cambridge Mathematics*