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Item Enhancing Our Theoretical Lens: Second-Order Models As Acts of Equity(PME-NA, 2023) Hackenburg, Amy J.; Tillema, Erik S.; Gatza, Andrew M.; School of EducationIn this theoretical paper, we respond to a call for all Mathematics Education researchers to become equity researchers (Aguirre et al., 2017) by articulating how equity is foundational to making second-order models of students’ mathematics. First, based on prior research, we view equity to be about power and respect. We define an act of equity as acting on social boundaries with the intent of changing them in order to address known inequities. Second, we explain why making second-order models is an act of equity, showing how it respects students and can affect power in research settings. Third, we demonstrate how attention to social identity categories and social identities can enhance current second-order models to better support acts of equity.Item Generalization across Domains: The Relating-Forming-Extending Generalization Framework(2017-10) Ellis, Amy; Tillema, Erik; Lockwood, Elise; Moore, KevinGeneralization is a critical aspect of doing mathematics, with policy makers recommending that it be a central component of mathematics instruction at all levels. This recommendation poses serious challenges, however, given researchers consistently identifying students' difficulties in creating and expressing normative mathematical generalizations. We address these challenges by introducing a comprehensive framework characterizing students' generalizing, the Relating-Forming-Extending framework. Based on individual interviews with 90 students, we identify three major forms of generalizing and address relationships between forms of abstraction and forms of generalization. This paper presents the generalization framework and discusses the ways in which different forms of generalizing can play out in activity. [For complete proceedings, see ED581294.]Item Three Facets of Equity in Steffe's Research Programs(2017-10) Tillema, Erik; Hackenberg, AmyThe [National Council of Teachers of Mathematics] NCTM research committee made a recent, urgent call for mathematics education researchers to "examine and deeply reflect on our research practices through an equity lens." With this in mind, we use this paper to reflect on the ways in which Steffe's work has contributed to three facets of equity. We also suggest opportunities for researchers working within this framework to deepen their commitments to issues of equity. [For complete proceedings, see ED581294.]