Relating Effective Representations and Hypothesis Production in Arithmetic Problem Solving

Producing hypotheses is very important in problem solving in order to understand the problem's aim and the relations among the data. However, a resolution process can also be viewed as a sequence of interpretations and productions of external representations of various nature. We discuss the relations between hypothesis and representation production in problem solving in elementary school, viewing a resolution process as a sequence alternating representations and hypotheses. These hypotheses and representations are strongly connected with each other since each hypothesis can give rise to a representation, and each representation, working as additional problem data, can give rise to a new hypothesis which is influenced by the characteristics of the employed representation system.