This work is an exploration of upper elementary students' sense making around four conventional representations of function: equations with algebraic notation, Cartesian graphs, function tables, and natural language. The cornerstone to the empirical work is a task called the Function Puzzle, where students are given 16 cards representing four…

Argues that tables, graphs, and diagrams extend language's power by exploiting the Euclidean possibilities which a text suggests. Notes that graphic display elements form no compatible natural set and that their value and visual elements are decisively disparate. Concludes that graphic displays are unlikely candidates for unitary theoretical…