Unit Coordination

“Sixteen!” My grandson shouts, sitting on the floor smiling, fingers extended. We had been playing with his toy cars. He counted out nine, gave them to me, and I put them behind me out of his sight. He then counted out seven more, gave them to me also, and I hid them under a nearby pillow. I asked him how many cars I had together. He counted to nine, extending fingers, stopping when he had said nine. He then pulled back his fingers and continued counting 10, 11, …,16, while extending seven of his fingers for a second time. This was new for him and he was excited. I have seen him grow in his efficiency using fingers. The fact is, fingers are tools children use in mathematics. ⁽¹⁾ There is an ever-increasing wealth of information pointing to the importance of finger usage by young children in mathematics. Some teachers think that finger usage for students is an indicator of immaturity, and they encourage students to abandon the practice as early as possible.

Teachers know kids use their fingers in various ways but may not know what the differences are, what they mean, or how to use what they see to help students. The complexity and variations of finger usage are often missed. The earliest use of fingers for mathematical purposes is usually the counting of fingers. This is seen when a child is asked: “What is 5 and 2?” We’ll see them pop up five fingers, on one hand, a two on the other, and then count all the extended fingers to determine a total. ⁽²⁾ There are variations in this type of usage. ⁽³⁾  But it can’t stop there. ⁽⁴⁾ The Common Core Progression documents affirm this by stating, “Using fingers is not a concern unless it remains at the first level of direct modeling in later grades.”

One advancement in a child’s use of fingers is their use for monitoring. Monitoring means the child uses their fingers to keep track of their counting. Often, finger patterns become the tool used to monitor counting. A child counting-on may continue their counting five more counts by filling a finger pattern for five to signal an end to their counting. ⁽⁵⁾ These same finger patterns also assist children to monitor counting backward to determine when to stop in situations involving takeaway. ⁽⁶⁾  In “change unknown” situations, a child may use their fingers to keep track of the counts, such as from 12 to 19, recognizing the finger pattern for seven upon the completion of the counting activity and realizing the finger pattern represents the unknown addend in the problem.

Continued development of finger usage is seen in their use of fingers when counting composites. In one situation we use children build towers with cubes and then those towers are hidden. For example, five towers with three cubes in each tower. The teacher can then ask for the total number of cubes. We saw children develop the ability to count the groups of three with fingers on one hand while keeping count of the number of towers on the other hand. ⁽⁷⁾ Children’s finger usage is even seen in our early work with fractions.(8) The important point is that the use of fingers should grow along with the sophistication of children’s mathematics. I will continue to encourage my grandson to use his fingers in ways that reflect the growing sophistication of his mathematical thinking and in the process, I hope to see many more of his smiles and his enthusiasm.

For further reading about finger usage:

1. “Handy Little Fingers as Counters”, Wilma Hashimoto October 30, 2017
2. “Finger Pattern Adding Schemes: Sums Less Than Ten”, Beverly Ford, May 24, 2017
3. “Fingers As Math Tools – Part 2 Let’s Get Tapping”, Elin Anderson, February 15, 2017
4. “Counting and Fingers”, Grace Florez, May 16, 2018
5. “Mathematics of Grace: Figurative Mental Material”, Beverly Ford, April 5, 2017.
6. “Takeaways from Subtraction Part 2: Take Away or Not to Take Away” David Pearce, January 30, 2018.
7. “What Every Student Needs to Know for Multiplication (Part 1)”, Elin Anderson, October 31, 2017.
8. “Composite Units and Fractions”, Brook Lewis, March 28, 2017.

References:

Progressions for the Common Core, State Standards in Mathematics (draft), The Common Core Standards Writing Team, 29 May 2011.