In my last blog, I reflected on my experience at the California Mathematics Council’s Southern Conference in Palm Springs and our presentation, “Don’t be Quick to Count On!”. Referenced throughout the conference were the Mathematics Teaching Practices from NCTM. One of these practices that resonates with the work of my team of research associates is, “Elicit and use evidence of student thinking.” We are reading deeply and working to understand the research of Dr. Les Steffe. He presented young children with different counting situations to see how students constructed their understanding of number. We have re-enacted some of his counting situations with students here in the San Joaquin Valley.
While studying video of kindergarten students that we have worked with, I have observed how they use their fingers. This provides us with evidence of their thinking. “Hmm . . .,” I hear you say. “All young children use their fingers when they are counting.” You are right, they do use their fingers, but have you ever noticed how they use their fingers? How children use their fingers is very interesting, especially when you consider that fingers are math tools children have access to all the time!
This reminds me of the CCSS Standard of Mathematical Practice, #5, “Use appropriate tools strategically.” This is interesting to think about, right?! I know a lot of kindergarten teachers that use dot pattern cards to help students “subitize”, quickly recognize numbers to 5. Let’s say you flash the domino five-dot pattern to a student and then flash a triangle three-dot pattern, and ask them how many dots altogether? How do you see students using their fingers? Do they:
- Pop up a finger pattern for 8, showing 5 fingers on one hand and three on the other and say “8”?
- Pop up a finger pattern for 8, showing 5 fingers on one hand and three on the other and say a number other than 8?
- Pop up a finger pattern for 8, showing 5 fingers on one hand and three on the other and then use a finger on one hand to count each finger up to five and use a finger on the other hand to point and count to eight on other hand?
- Count from one up to eight sequentially, popping up one finger at a time?
- Use their finger to tap out the pattern you showed from one to eight either on the table or in the air?
I have seen students do all of these and more! How students use their fingers in a counting situation can tell you a lot about where that child is in their construction of number. Are students using their fingers strategically? I would argue, absolutely!! In Dr. Les Steffe’s research he documented many hours of observing children counting and was able to define a certain trajectory children may follow when coming to construct an understanding of number. This trajectory includes how they use their fingers.
I hope to share more with you about this trajectory, and the student behaviors we observe, especially the strategic use of fingers! Unit next time, keep an eye on those fingers!