In my last blog, I highlighted various ways you have probably observed children using their fingers when they are counting. In this blog I will continue that discussion and show you how observing the way children are using their fingers can help you understand where a child is in their construction of number.
I pointed out CCSS Math Practice Standard 5 is, “Use appropriate tools strategically” and fingers are tools that children have immediate access too. Our research team has also been reflecting on the NCTM teaching practice of, “Build procedural fluency from conceptual understanding.” Let’s revisit the problem I posed in my last post: you flash a student a dot pattern with a domino five pattern, then flash a dot pattern with a triangle three, and ask the student, “How many dots altogether?” If the student popped up a finger pattern for 5 on one hand, and then a finger pattern for three on the other, and then counted from one to eight they are probably a still a counter of perceptual items. Per the research of Dr. Leslie Steffe whose research we are studying, children who are perceptual counters need to have concrete items in front of them to count. In this example the student has had enough experiences with dot patterns to be able to subitize five and three and use their fingers as replacements for the dots, but they still need to have something concrete in front of them to count. When presented with a task where they had to add two groups, in this case the dot patterns for 5 and 3, the student could not add those numbers in their head because they haven’t created a mental record or template for those numbers yet.
An analogy I can make is learning to tap dance. Yes, tap dance! It has been a hobby of mine for awhile and learning a new sequence of tap steps is much like learning a sequence of numbers. When I am learning a new sequence of steps I must start at the beginning of the sequence, I cannot start in the middle of the sequence. Even more than this, I need to have my teacher right in front of me showing me the steps with the music. The next step would be to practice the sequence of steps but still have the mirror in front of me to see if I was doing the sequence of steps correctly. The mirror and the teacher are concrete items in my learning! At this point I might be able to pick up the sequence from the middle and not the beginning. Each week he adds a few more steps until we have learned a whole dance. Only after months of practicing would I consider performing on a stage in front of an audience without a mirror or the teacher in front of me.
Students who are constructing their understanding of number need many experiences counting concrete items to be able to create a lasting mental image of that sequence in their mind. Using your fingers (and toes!) to count is a good thing!