#830: Symbol Grounding and Re-Grounding in Balance and Movement: Insights From Children’s Mathematical Compositions

In teaching mathematics, educators often seek to address the "symbol grounding problem"– the challenge of giving meaning to symbolic expressions. One avenue for addressing this challenge involves coordinating symbolic expressions with bodily experiences. Extending and integrating prior work on embodied design for symbol grounding and on balance metaphors in the teaching of algebra, we explore grounding math concepts in the bodily sense of balance, focusing specifically on the additive inverse principle. We conducted 9 semi-structured clinical task-based interviews with a developing design, the Balance Number Line, in which children use arithmetic symbolic expressions and a physical number line to compose and convey a set of bodily rocking movements to other children. We used multimodal video analysis of coordination across semiotic media (including language, gesture, arithmetic symbolic expressions, the number line, and hand and body movement) to examine whether and how children grounded arithmetic symbolic expressions in bodily activity, particularly with regards to the bodily sense of balance. We found that (1) children grounded numbers both to balance states, treating positive and negative integers as symmetrically organized around 0, and to hand movement trajectories on the number line, enacting operations in a left-to-right frame of reference, and they progressively integrated these perspectives, and (2) children dynamically re-grounded symbolic expressions during moments of mathematical transitions and communicative difficulty. Our findings suggest that symbol grounding is dynamic and contextual, rather than primarily a progression from concrete to abstract.