Fingers, Digits, and Baby Math

Whoever would have thought that being able to count would have been a survival advantage? Or that using our fingers to count would have implications for how our brain developed?  I’ve been reading How the Brain Learns Mathematics (David Sousa), and there are some interesting tidbits that support the recent changes in approach to how we teach math.

1)  Brain research shows that the area of the brain that activates when we move our fingers is closely connected to the area of the brain that gets busy when we count.  This is not likely a coincidence as when we first learned to count, we probably used what was most handy (no pun intended..well, maybe a little), and so those parts of the brain developed in close proximity to each other.  It also explains why the word digits refers to both our fingers and numbers, and why one of the most commonly used number systems is base ten. Get it?  Ten fingers?  Ones, tens, hundreds, thousands – I’ll stop now.

2)  Babies as young as 18 months and animals have been found with the ability to differentiate between basic amounts such as 2 and 3.  They consistently take about a second longer to look at images that have three objects over images that have two. The supposition is that the ability to discriminate quickly between amounts gave us a survival advantage by being able to determine if we should fight or flee, based on the number of predators we were facing:  “Hmmm… one tiger.  I can take that bad boy.”  Or, “Three tigers! Yikes! I’m outta here!”

The implications for our teaching is that our most basic sense of number has to do with the quick recognition of visual amounts and tactile interactions with concrete objects.  That’s why it’s so important to start with manipulatives and visual representations before moving to the symbolic squigglies that we have come to recognize as numbers.  That’s why so many students find success with using the base ten cards, rather than learning to count by rote or by number line, as advocated by Trevor Calkins and his Power of Ten program.  It connects children’s innate ability to be able to discriminate amounts as we learned in the caveman days with the base ten context that we came up with by using our fingers.  Cool, huh? 

So, intead of starting with teaching students to count to 10 or 20, start with the ten cards, and have students quickly learn to recognize what the amounts are based on the visual representations.  They can then play games like “War”, where they have a stack of the cards, flipping them down one at a time, and winning the pair based on whose amount is larger.  I’ve also seen teachers work with students on simply learning to put the cards in order like a number line, or by flashing two cards at a time, having them identify which is the larger or smaller amount.  If you’re not sure what the ten cards look like, visit www.poweroften.ca

That’s also why it’s important to continually connect operations back to place value and the use of manipulatives such as base ten blocks.  Let students play with their understanding of place value to help them develop their personal understanding of how to perform operations before teaching them the rules.  I once watched a grade 1 student perform subtraction with 3-digit numbers.  It’s not that he was a math prodigy or that someone had drilled him on mathematics since he was a toddler.  He was just allowed to figure it out based on what he knew about place value.  By the way, he did it from left to right, starting with the hundreds.  But he did it correctly, and he was able to repeat his strategy with success.

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