Using mobile puzzles to exhibit certain algebraic habits of mind and demonstrate symbol-sense in primary school students

Abstract Given the growing concern for developing students’ algebraic ideas and thinking in earlier grades ( NCTM, 2000 ) it is important for students to have experiences that better prepare them for their formal introduction to algebra. Mobile puzzles seem to be an opportunity for exhibiting certain algebraic habits of mind as well as for demonstrating symbol-sense which might support students in their transition from arithmetic to algebra. These puzzles include multiple balanced collections of objects whose weights must be determined by the solver. The arms/beams must be perfectly balanced for it to hang properly. Therefore, they represent, in a pictorial way, systems of equations. Each arm/beam that balances two sets of objects (representing variables as unknown “weights”) represents an equation. The data derived from Grade-6 students who were asked to solve a collection of tasks reflect the presence of the “Puzzling and Persevering” and “Seeking and Using Structure” habits of mind. At the same time these data incorporate instances of some main components of symbol-sense such as “friendliness with symbols”, “manipulating and ‘reading through’ symbolic expressions”, and “choice of symbols”. Also discussed is the way this experience contributes to an intuitive application of the conventional rules for solving equations that will be later introduced to the students as the standard algebraic “moves”.

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