Given the prominence of group work in mathematics education policy and curricular materials, it is important to understand how students make sense of mathematics during group work. We applied techniques from Systemic Functional Linguistics to examine how students positioned themselves during group work on a novel task in Algebra II classes. We examined the patterns of positioning that students demonstrated during group work and how students' positioning moves related to the ways they established the resources, operations, and product of a task. Students who frequently repositioned themselves created opportunities for mathematical reasoning by attending to the resources and operations necessary for completing the task. The findings of this study suggest how students' positioning and mathematical reasoning are intertwined and jointly support collaborative learning through work on novel tasks.
The authors of this study conducted an exploratory study of the teaching and learning processes of a tutor and a student with a mild intellectual disability (MID) while working on two-step equations. The researchers focused on situations in which the participant was likely to struggle with memory and processing as well as the challenges of the mathematics tasks with which he was presented. The student benefitted from his own use of strategically organised work on pencil and paper as well as the teacher's use of gestures and strategically asked questions designed to promote his progress, yet not interfere with his critical thinking. While the student did experience some challenges, this study demonstrated a case in which a student with a MID solved and discussed two-step equations successfully.
From a social semiotic perspective, students' use of language is fundamental to mathematical meaning making. We applied thematic analysis to examine students' use of geometric and contextual ideas while solving a geometry problem that required them to determine the optimal location for a new grocery store on a map of their local community. Students established semantic patterns to connect the problem context to geometry. Groups differed in how they used geometry in their discussion of the solution, in particular with how students used distance to describe the location of a new grocery store. Overall, students' knowledge of the problem context served as a resource for them to establish geometric meanings. Thematic analysis, which describes the connections in students' talk between out-of-school and discipline-specific knowledge, highlights ways in which instruction can build upon students' prior experiences for the purpose of learning in school.
The researchers conducted a qualitative case study to describe the experiences of two seventh grade students with mild intellectual disability as they engaged in mathematics word problems involving proportions. The researchers analyzed student performance in large group settings and with individualized instruction to gain perspective on the students’ tendencies with challenging mathematics content. During the teaching sessions in this study, one of the participants initially struggled with the proportions word problems, but demonstrated success after teachers connected new information in the tasks to students’ long-term memory and utilized gestures and diagrams to facilitate the students’ processing of information. Another participant succeeded more easily with proportions word problems which, along with the success of the other participant, provides support that students with a mild intellectual disability can succeed with challenging topics, such as proportions word problems.
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