This work presents data from a study which aimed at verifying the performance of Elementary School 6th and 9th graders when solving eight multiplicative problems involving combinatorial thinking. The problems were different concerning the amount of variables and the amount of numerical digits used in factors. Therefore, through a clinical interview, we listed the main strategies and mistakes produced by 40 graders from two public schools (A and B) in the municipality of Campo Grande (Mato Grosso do Sul - MS - State) which were part of a larger research developed before. The observations reveal that the performance was better in problems with two variables and factors with low values. There was no alteration in the performance among the 6th and 9th graders. In general, the difficulties found were related to: 1) intuitive models students have when dealing with multiplication (especially the one including repeated addition); 2) the semantic structure of the problem; 3) numerical preferences regarding the quantity of numerical digits, ways of representing the problem and interpretation of verbal problem statements. Because multiplication is a very complex operation involving abstract cognitive processes in its solution, we believe that the teacher needs to know them to facilitate students' learning.
Mathematical learning; combinatorial problems; cognitive processes; Elementary School
