We recently attended the annual meeting of the National Council of Teachers of Mathematics, NCTM. This year’s conference was in San Antonio, Texas. We were mostly a group of research associates from the AIMS Center. The size of the conference (over 7000 attendees) and the wide range of presentation topics worked together to create a dynamic atmosphere.
One of the “big ideas” of the conference was how to elicit student thinking. One way is to ask for students’ responses in class. Young students are sometimes even eager to give responses, and tell you what they’re thinking. There is a problem, as I see it, not in getting student responses, but in interpreting student responses. When a teacher views responses only from their adult perspective, the children’s responses can sometimes seem to be illogical and even nonsensical.
Here’s an example of student thinking that a teacher might shut down without realizing what is going on. My team has been recently working with a student who did not know multiplication. She was beginning to skip count, and she was quite limited in that. To solve a particular problem we gave her, she needed to figure out the value of ten 3s. She said she couldn’t count that high by threes. Instead, she proceeded with 2,4,6,…, 20, 21,22,23,…,29,30. What she did was replace each 3 by and a 2 and a 1. Then she counted ten 2s followed by ten 1s. This was a brilliant scheme that a child came up with to accomplish her goal. In a normal classroom setting, the teacher may have stopped her quickly because she was not counting by 3s.
Six attendees from our group discussed our take-aways from the conference. We had collectively participated in at least five dozen of the various workshops and other sessions. We all agreed that the workshop presentations were mostly traditional, generally given from an adult perspective, and gave little if any credence to math from the child’s point of view. We also agreed that we had all been in that traditional education mold prior to our work in researching how children learn math.
A classroom lesson may seem to be very interesting, inspiring, and well designed to an adult, but at the same time it might be just the opposite to a child. How do we get teachers to consider the mathematics of children? That is one of our big challenges at AIMS. If you are a teacher, you will encounter situations where student thinking may be occurring, but you will have to be patient and aware to notice evidence of that thinking. Have you ever thought about the mathematics of children?