A Saturday morning, in a small abacus class above a stationery shop. The ceiling fan turns slowly over a dozen children sitting cross-legged on a blue durrie, each with a wooden frame of beads. The beads click in quick bursts, like the first rain on a tin roof. Then the teacher says, “Close your eyes,” and the clicking stops. The room goes quiet, but not still. Small fingers flick and pinch in the air, moving beads that are no longer there. A girl near the window whispers the answer first.
Where did that sum get done? In her head, we would say. Yet her hands were busy the whole time, and a few months ago the beads under them were made of wood.
A notebook that remembers
In 1998 the philosophers Andy Clark and David Chalmers asked a large question in a short paper. Where does the mind stop and the world begin? Picture two people going to a museum. Inga remembers the address. Otto cannot trust his memory, so he carries a notebook everywhere and believes what it says without a second thought. Clark and Chalmers argued that the notebook does for Otto what memory does for Inga. If some part of the world does a job we would call thinking were it done inside the head, then it is part of the thinking. They called this the extended mind.
Under the right conditions, the notebook is not a helper standing outside Otto’s mind. It is one of the places where his mind is. It takes the idea that thinking is not only in the head one step further, out through the skin and into the things we hold.
The hand that thinks ahead
The evidence that we think through things is more ordinary than the philosophy. In 1994 David Kirsh and Paul Maglio watched people play Tetris. Players kept turning the falling blocks on screen rather than in imagination, because a turn on screen took about a tenth of a second and a turn in the mind far longer. Kirsh and Maglio called these epistemic actions, moves made not to reach the goal but to make thinking easier, faster or more reliable.
Children do this all day. One counts on her fingers, wipes the slate with her palm and tries again, pushes three pebbles aside to see what is left. Susan Goldin-Meadow and her colleagues asked children and adults to explain maths problems at a blackboard while holding a list of words or letters in memory. When they were free to gesture as they explained, they remembered more of the list. Moving the hands lightened the mind’s load.
The abacus shows the same thing over years. Michael Frank and David Barner studied children in India trained in mental abacus. Their sums held up under spoken distraction that throws most of us off, which suggests they were calculating with a picture of the beads rather than with words. Barner and his colleagues then followed 204 children in a Vadodara school for three years. Those who learnt mental abacus gained more in arithmetic than children given the same time on ordinary extra maths, though mainly those who began with stronger spatial working memory. The training did not make children cleverer in general.
What this changes about the child
If the mind can reach into the slate and the bead frame, then a child who counts on her fingers is not cheating. The teacher who says “do it in your head” is asking the child to set aside part of her thinking equipment. Sometimes that is fair, because the abacus children show that outside beads can move inside. But the inner abacus is built from months of practice on the wooden one, and the hands remember the route. The journey from a tool held in the hand to a sign carried in the mind passes through the body.
Where this series parts ways
The usual case for the body in education is instrumental. A good tool gets faster answers and better marks, and finger counting is a crutch to drop early. The extended mind is easily sold the same way, as a reason to buy gadgets. This series reads it differently. Fred Adams and Ken Aizawa argue that being closely coupled to a thing does not make it part of cognition, and the objection deserves weight. Whatever the final answer, for a growing child the line between hand, object and thought is not fixed. So the question is not which tool raises scores. It is what kind of thinker forms in partnership with that tool. A slate the child moves is a different partner from a screen that moves for her, which is why the debate over handwriting and typing deserves patience.
Think again of the girl by the window. One day the wooden frame will be gone from her life, and something of it will stay in how she reaches for a number. Which things are we putting in our children’s hands today, and whose minds will they quietly help to build?
Put it into practice: P31 Counting with steps, claps and jumps · P32 Measuring with hands, feet and strides · P34 Number lines children stand on
Read next: R11 Gesture as thinking: what the hands know before words · R36 Vygotsky: tools, signs and learning between bodies
Notes
- Andy Clark and David J. Chalmers, “The Extended Mind,” Analysis 58, no. 1 (1998): 7–19. https://doi.org/10.1093/analys/58.1.7
- David Kirsh and Paul Maglio, “On Distinguishing Epistemic from Pragmatic Action,” Cognitive Science 18 (1994): 513–549.
- Susan Goldin-Meadow, Howard Nusbaum, Spencer D. Kelly and Susan Wagner, “Explaining Math: Gesturing Lightens the Load,” Psychological Science 12, no. 6 (2001): 516–522.
- Michael C. Frank and David Barner, “Representing Exact Number Visually Using Mental Abacus,” Journal of Experimental Psychology: General 141 (2012): 134–149.
- David Barner, George Alvarez, Jessica Sullivan, Neon Brooks, Mahesh Srinivasan and Michael C. Frank, “Learning Mathematics in a Visuospatial Format: A Randomized, Controlled Trial of Mental Abacus Instruction,” Child Development 87, no. 4 (2016).
- Frederick Adams and Kenneth Aizawa, “The Coupling-Constitution Fallacy,” in The Bounds of Cognition (Malden, MA: Wiley-Blackwell, 2008), 88–105.