Physical models in mathematical problem solving: a case of a tetrahedron problem

Physical models of geometric figures can be considered useful manipulatives for solving solid geometry problems. In this paper, roles such models play in the mathematical problem solving process are explored by analysing one solver's solving process closely. Analysing the data from the viewpoint of the solver's structures of problem situationsand focusing on the phase where the solution's main idea was generated, the following model roles were found: (i) the conflict between the solver's expectation and the state of models realized by the operations on them could facilitate the solving process; (ii) the operations on the models could naturally generate new elements although it was the solver's role to give sense to these new elements. These roles, especially the latter one, suggest similarity between model functions and diagram functions in mathematical problem solving.