Limerick has been interested in different base systems for several months now; he’s enjoyed playing place value games in bases other than 10, converting between bases, counting in alternate bases, and so on.
The other day he came up to me and told me that he’d figured out a new way to count on his fingers. Holding up the pinky finger on one hand, he told me that was 1. Just the ring finger extended was 2; the ring and pinky together was 3. The middle finger on its own was 4, middle and pinky together was 5, middle and ring together was 6, and middle, ring and pinky all at once was 7.
It may be easier to see his logic with 0’s and 1’s, where a finger curled down represents a 0 and a finger extended represents a 1.
00000 00001 (one pinky extended)
00000 00010 (ring extended)
00000 00011 (pinky and ring extended)
00000 00100 (yeah, this one looks wrong, but he’s six so he has no clue)
00000 00101 (middle and pinky)
00000 00111 (middle, ring, and pinky)
And so on.
It’s binary! Assigning each finger one place in the binary place value system, he figured out how to count on his fingers to 1023 (which would be all fingers extended). In addition to showing how natural this aspect of mathematics is to him, it also shows a good foundational understanding of computer science – because electric signals are either on or off, just like Limerick’s fingers could either be extended or curled down, and therefore represent data in this same bitwise manner. It is so amazing what kids can think of and create when they are given the chance to deeply explore something they love.
(We tried developing a base 3 counting system but found it was too difficult to keep some fingers folded only halfway down when the fingers next to them needed to be extended or completely curled – someone with more fine motor control might have more luck though!)