Happy Spring! Yes, this is a picture of my niece, I thought it was appropriate being that it is the beginning of spring and she is using her finger to help her explore one of the wonders of Spring. . . a ladybug! Part 1 of “Fingers as Math Tools” showed her using her fingers in front of a wall of pumpkins! Time flies, but the discussion on “Fingers as Math Tools” continues on! In part 2, I discussed what we could infer about a child’s understanding of number if they were flashed a dice dot pattern card for 5, then a triangle dot pattern for 3, and then asked them how many dots in all? The student popped up a finger pattern for 8 (five fingers on one hand and three on the other) and counted up to eight looking at their fingers.
What if we presented the child with the same problem and instead of popping up a finger pattern they sequentially put up their fingers, one at a time, and counted from one to eight while extending each finger? In the following video clip I ask the student a similar question. I put two cloths down and ask the student to pretend there are 6 cookies under one cloth and 3 cookies under the other cloth. Then I ask how many cookies we have all together. Watch what the child does with his fingers.
Cool, right? He counts sequentially from one to nine on his fingers underneath the table. If he was still at the beginning stage of developing an understanding of number, he would need to have perceptual or concrete items (dots, finger patterns, etc.) in front of him to count. We can infer that he has had enough experiences counting that he does not need the concrete items in front of him. He can visualize the counters, and his fingers act as substitutes for the thing to be counted. This is important because it shows the material he is able to count is becoming more and more abstract. Eventually students in elementary school have to engage in mathematics that is very abstract. As teachers we need to make sure we attend to where students are in their progression of understanding number, so we can help them construct their understanding of number in a way that is meaningful to them. If we move to the abstract too quickly our students will not have a good foundation to build on.
Imagine what insight we have into a child’s construction of number just by noticing how they are using their fingers. I think about the disservice we do to our students by telling them not to use their fingers to help them solve problems. I know that I was very guilty of doing just that as a teacher. I thought if I didn’t let my students use their fingers it would help them memorize their math facts quicker. The research suggests otherwise. The more I read and understand the work of Dr. Leslie Steffe, the more I believe in his trajectory of how students construct their understanding of number. What’s next in the progression of how students use their fingers as math tools? Look for my next blog post to find out more!