In my previous blog I wrote about the characteristics of perceptual and figural counters, which are two of five counting stages Leslie Steffe, Ph.D. identified through his research. Simply covering counters can be a powerful way to encourage students’ development of abstract units. In this blog we will look at counters of motor units. Counters of motor units are much more likely to successfully solve problems with missing addends, so if your students are unsuccessful with missing addend word problems it is possibly because they have not developed a sophisticated enough unit to count (motor unit).
A child counting motor units uses movement to count, wheither it is pointing, putting up fingers, or tapping the table. They isolate their motor activity as the thing they count. A counter of motor units notices the kinesthetic (proprioceptive) signal, not the actual finger or manipulative that they are pointing at. The motor act is a substitute for the perceptual and/or figural representation.
Steffe writes, “Since the motor act is intentional as well as independent of the perceptual items, and since as proprioceptive sensation it has a beginning and an end, the child may begin to attend to it and thus create it as a unitary item.” *
Here is an example of what a counter of motor units may do with a problem where one of the addends is hidden.
Problem: There are seven of twelve cars hidden.
Teacher: There are seven toy cars hidden under the cloth. How many cars are there altogether?
Student: May utter 1,2,3,4,5,6,7 while sequentially putting up seven fingers. Pause and continue the counting act while uttering 8,9,10,11,12 and sequentially putting up the rest of his fingers and then re-extends two of the fingers used in the first seven.
Many people discourage the use of fingers in math. Using their finger through tapping them, putting them up simultaneously or sequentially is an important part of their journey to understand number. I do believe that if they are using them for too long it is not beneficial, but counters of motor units is a powerful developmental stage because now a child can count anything – they can create a motor unit to represent math problems!
In my next blog we will continue to look at counters of motor units. We will look at how they might solve missing addend problems.
* Steffe, Leslie (1983) Children’s Counting Types, p.55.