How much knowledge is enough knowledge?

The semester has started and I am confronted with the same question the AIMS Center is currently wrestling with: How much knowledge is enough for a teacher to know to make effective decisions with students? We read research by researchers who have been spending years if not decades studying how students come to learn to think multiplicatively. The level of detail is deep, but again, how deep is deep enough for a teacher?

These questions resonated with me as we began implementing small group activities in a local second grade classroom. Our students are working on tasks that ask them to think of numbers in three ways: (1) As representing the number of towers (groups); (2) as the number of cubes to build the towers (number of objects in each group); (3) as number of total cubes to build all the towers (the product).Thinking of these three ideas at the same time is what is asked of students when they work with multiplication

Coordinating multiple ideas at one time is not just what the students need to do, however, but also what the teacher needs to do. The teacher is thinking of the enactment of the activity for 4-6 different students. The teacher is also watching behaviors related to doing the activity and related to what the student might be thinking about while doing the activity. The teacher is also monitoring the behavior of all the students who are working (or supposed to be working) independently at centers. Since we don’t attend consciously to more than one thing at a time, our attention moves between these various tasks until, with enough experience, the teacher can go on “autopilot” with some of these tasks. But how much do you need to know before you can go on “autopilot” when it comes to watching students’ behavior to infer what they might be learning? Or to respond with an adaptation in the task you have given them?

I have seen teachers making adjustments during instruction that seem effortless, and when I ask them about those adjustments, some say, “I just knew to do it.” In the moment, they did not stop and think through that any more than I did this morning when I tied my shoes.

To get to the point that classroom teaching practices are like tying one’s shoes (for most of us), you must go through the process of deliberately thinking of that task enough that it eventually becomes automatic. If tying my shoes involved a hundred steps, would I ever be able to make that automatic in the face of all the other things I am learning to do as a very young child? How complex can the information be that we expect of teachers in the face of all the other things vying for their attention?

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