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A lively debate on an online teaching forum has spurred me on to think further about the use of fingers and hands in education. In particular the use of fingers in maths and counting.
There seems to be a bias against using fingers for counting, yet using hands and fingers for tasks such as recalling the number of days in a month or for electromagnetism and the cross-product of vectors in Physics is a common sight and seems to be widely accepted.
A recent publication has encouraged the use of finger counting in primary schools as a method of improving general mathematical ability.
It seems this is quite a hot bed of contention with the neuroscientists and math educational researchers not always coming to the same conclusions.
Even though neurocognitive and mathematics education research agrees that children make use of finger-based numerical representations, they disagree on the consequences of reliance on such numerical representations. On the one hand, the neurocognitive literature suggests that embodied numerical representations, including finger-based ones, are important in numerical cognition in general. On the other hand, mathematics education research recommends the reliance on external representations, including finger-based ones, only as an aid in the transition to mental representations of numbers.
Moeller et al Front Psychol. 2011; 2: 328.
While I delve further into the research I thought I would present one of the most useful ways of using fingers in math that I have encountered. But first an explanation as to why I think it is so useful.
Multiplying and the Times Table
Some recent research run by education tech firm Flurrish and published in the Guardian shows a pattern that is recognisable to many math educators. There seem to be holes in knowledge when it comes to knowing the times’ table- or more importantly being able to do multiplication problems independent of running through the tables in order.
The plot above shows a heat map of the multiplication problems with the hotter (red) squares representing the problems that the children struggled with most. The hardest multiplication being six times eight (and eight times six), which students got wrong 63% of the time.
As we can see it is those pesky multiplication problems between 6 and 10 that are the real issue for students- and so onwards to one of my favourite uses of fingers in mathematics: Once you know your simpler multiplications (2, 3, 4) then this method will help you always remember your times table (6 to 10) using finger multiplication.
Here is a handy (excuse the pun) video by MindYourDecisions on youtube explaining the technique.
Experiment with all the combinations- and see how quickly you can move away from using your hands. I should point out that 6 x 6 and 6 x 7 (7 x 6) can be tricky using this method- and I would recommend memorising these separately.
As with all these techniques, some techniques work better for some than others. So give it a go and see if it helps! If you found this post helpful please subscribe below to be informed of any new blog posts, as they become available:
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I’ve taught math in the US for over 20 years and I’ve never seen this finger strategy before! Many of my high school students know the strategy for multiplying by nine. I think I’ll show them the 6-10 technique.
That’s good to hear…. let me know how they get on.