Division Problems with Remainder: A Study on Strategies and Interpretations with Fourth Grade Mexican Students

The present research focuses on analyzing how fourth-grade elementary school students (ages 9 to 10) solve and interpret the result of non-routine problems, precisely division measurement and division-partition with remainder. The methodology is qualitative, with a descriptive and interpretative approach. The information was collected using a questionnaire consisting of three problems (two of quotitive division and one of partitive division) and a clinical interview. The results showed the importance of using the division, multiplication, and addition algorithms to give a realistic answer to the problems. In the same way, it was possible to demonstrate the graphic strategy combined with counting to give a realistic answer to the problem. However, students were found to use division correctly but without an interpretation of the remainder or quotient. Likewise, they struggled to choose the correct procedure to solve the problem. These data suggest including realistic problems in mathematics classrooms to make sense of mathematical concepts in real life or the student's context. Likewise, this study provides implications on the mathematical problems that the teacher proposes in the classroom, where not only the division algorithm should be taught mechanically, nor focus on posing routine problems that lead the student to use a single heuristic resolution strategy. Essentially, the teacher is required to include real-world problems, where the student can awaken creativity to represent in different ways the understanding of a problem and, therefore, different strategies to solve it. In addition, that the student has the ability to check the result of the problem, with the conditions, situations or circumstances imposed by reality or everyday life.