Broadening Participation

This editorial is part of a special issue of Investigations in Mathematics Learning Critical Approaches that was inspired by a Disability in Mathematics Education working group.

The authors fuse Universal Design for Learning (UDL), differentiation, and talk moves into three key planning and pedagogy considerations.

This paper seeks to provide a resource for prospective DRK-12 awardees by identifying some of the theories that current and recent DRK-12 awardees are using in their research on broadening participation.

This study reports results from 113 students and three science teachers from two low-income urban middle schools participating in SciLG. It highlights the role of students’ views of themselves as competent, related, and autonomous in the garden, as well as their engagement and re-engagement in the garden, as potential pathways by which garden-based science activities can shape science motivation, learning, and academic identity in science.

Exploring how children’s conceptions might advance through their implicit knowledge provides a fundamental view into children’s mathematics and elucidates possible alternative definitions of “learning difference (LD)”. I present an evolving theoretical framework that depict children with LD’s knowing and learning as nascent understandings that emerge from a real-time negotiation of meaning within “small environments” of instructional intervention. These negotiations are supported, or not, by the teacher’s propensity to engage in the knowledge of children and use teaching to construct shared goals for learning. Implications of the work include new ways educators might define LDs as a complex phenomenon that reflects how children’s knowledge of mathematics advances, or not, through a shared cognition grounded in children’s unique knowing and learning.

Cognitive differences intrinsic to children with learning disabilities (LDs) have historically led to deficit assumptions concerning the mathematical experiences these children “need” or can access. We argue that the problem can be located not within children but instead as a mismatch between instruction and children’s unique abilities. To illustrate this possibility, we present the case of “Jim,” a fifth-grader with perceptual-motor LDs. Our ongoing analysis of Jim’s fractional reasoning in seven equal sharing based tutoring sessions suggests that Jim leveraged his knowledge of number facts and alternative representations to advance his reasoning.

In this study, we challenge the deficit perspective on mathematical knowing and learning for children labeled as LD, focusing on their struggles not as a within student attribute, but rather as within teacher-learner interactions. We present two cases of fifth-grade students labeled LD as they interacted with a researcher-teacher during two constructivist-oriented teaching experiments designed to foster a concept of unit fraction. Data analysis revealed three main types of interactions, and how they changed over time, which seemed to support the students’ learning: Assess, Cause and Effect Reflection, and Comparison/Prediction Reflection. We thus argue for an intervention in interaction that occurs in the instructional process for students with LD, which should replace attempts to “fix” ‘deficiencies’ that we claim to contribute to disabling such students.

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