Variations of Reasoning in Equal Sharing of Children Who Experience Low Achievement in Mathematics: Competence in Context

Abstract

For children with persistent mathematics difficulties, research and practice espouses that an altered kind of mathematics instruction is necessary due to sustained performance differences. Yet, a critical issue in mathematics education rests in the question of why research locates the problem within these children. In this paper, we challenge a longstanding assumption about the type of mathematics children with low achievement in mathematics “need” along with how these children are positioned in terms of mathematical thinking and reasoning. Our aim in this work is to identify ways of reasoning evident in the partitioning activity of 43 fifth-grade children as they solved equal sharing situations independent of instruction over ten sessions. Results reveal three themes of reasoning that show a resemblance between these children’s reasoning and existing frameworks of reasoning in equal sharing problems found in prior research among children who did not show low achievement in mathematics. We discuss the results in terms of the problem of a continued conceptualization of low achieving students’ need for specific kinds of teaching and learning experiences and/or detached instructional experiences in school. We advocate for an increase in research that examines how teachers can support participation of these children in mathematics classrooms such that children might develop powerful mathematics conceptions.

Keywords

• mathematics learning difficulties
• low achievement
• fractions
• reasoning
• informal knowledge