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.
Highlights
This paper illustrates variations of mathematical reasoning of 43 elementary school children identified as having low achievement in mathematics as evidenced through their problem solving in equal sharing tasks
We sought to identify the ways of reasoning apparent in 43 children’s partitioning strategies in equal sharing tasks
“No Linking between the Number of Objects and/or Parts to the Question Context” was defined as a response that did not show a link between the numerical value in the question posed and the children’s partitioning
Summary
This paper illustrates variations of mathematical reasoning of 43 elementary school children identified as having low achievement in mathematics as evidenced through their problem solving in equal sharing tasks Addressing this problem is important because illustrating the ways of reasoning these children do possess (as opposed to describing what they do not know or a level of performance they do not have) can inform the field about the potentially rich mathematics in which these children can engage. As participation in mathematical practices hold implications for children’s later mathematics performance [1], beginning conversations on how researchers and teachers might support such participation seems essential These conversations stand in sharp contrast to much of the current special education literature base and recommendations for mathematics instruction for children who experience.
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