<I>I HAVE FOUR LEFT AND DON’T KNOW WHAT TO DO WITH THEM</I>. A STUDY ON DIVISION WITH REMAINDER PROBLEMS IN 1ST OF ESO PUPILS

Abstract

Division-With-Remainder problems are particularly complex as suggested in many works. The aim of the present research was to establish whether students’ difficulties in these problems came from an inadequate initial representation or from an inadequate final interpretation of the numerical answers. We also wanted to determine whether types of remain-ders could be grouped into two blocks depending on whether the answer was directly matched to one of the terms of the division or not. To this end, we tested forty-nine secondary students with a mean age of 12 years and 10 months. The participants solved Partitive and Quotitive Equal-Groups problems involving four Types of Remainder: Remainder-Not-Divisible, Remainder-Divisible, Remainder-as-the-Result, and Readjusted-Quotient-by-Partial-Increments. Our data showed that: (a) although the selection of division as the resolution procedure was very high in both Models of Division, Partitive problems were easier than Quotitive ones; (b) the percentage of correct interpretations was higher than the percentages reported in other researches; and (c) success in problems whose answers were the quotient or the remainder was higher than in Readjusted-Quotient-by-Partial-Increments problems. To conclude, the main difficulty of students when solving Division-With-Remainder problems seems to be in the inadequate initial representation of the problem.