Mind the Black Box

Here at the AIMS Center, a central focus of our attention is the mathematical thinking of children. It should not be surprising that children do not think like adults. While as adults we agree in theory, our actions consistently seem to contradict this truth. The habitual act of laying our own mathematical thinking onto children is difficult to break. But difficult does not mean impossible. Piaget seemed to believe that it begins with a de-centering of oneself. He describes this as “Egocentrism [which] signifies the absence of both self-perception and objectivity.” (The Construction of Reality in the Child, pg. xii) How can an adult attend to and interpret the mathematics of a child without consciously putting aside her own mathematical thinking?

Last month in a teaching episode with a child my expectations were brought to disequilibrium. The auditory task that was planned seemed simple – have a child count the number of times I clapped my hands. Watch the video below to view what happened.

Perhaps you can tell by my pause that I was stunned. I had labeled the task simple, but that was my mathematics thinking, not the child’s. She counted 4, yet reproduced my three claps exactly. What does this mean? How do I clarify for her the item being counted? What task can I prepare for next time that will give me more information about her temporal (rhythmic) pattern ability?

Every time I bring a mathematical task to a child, I strive to have a mindset that puts aside my own mathematics. Their thinking is like a black box and, as a detective, my goal is to gain information on their location in their mathematical journey and decide what opportunities I can provide to help them move forward. The task provided is thoughtful but it is not magical.  It does not alone pour math knowledge into their brain, any more than I could by telling them how to solve a problem and have them mimic back my words and actions.

In error, at times, we overly stress the task and ignore one of the most powerful factors in the equation of learning – the teacher. When a teacher embraces her role as researcher, she transforms herself from merely being a source of knowledge. Every child brings a unique set of experiences to the table, and this is what makes a teacher’s job a formidable, never-ending project. Our goal is for the black box of each child to achieve clarity. Reaching towards that goal, we become better at knowing how to provide mathematical experiences in which a child can construct their mathematical knowledge. Like anything worth doing it takes time, patience, and perseverance among other aspects, but the outcome is tremendous.

Imagine a child who has mathematical confidence, a child who is a problem solver, and whose logic and reason are sound. Imagine a classroom of such children, a school, a city, etc. It is an honor to be a part of a Center that is striving to see this dream come true.


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