Inferentialism has emerged as a valuable theoretical resource in mathematics education. As a theory of meaning about the use and content of concepts, it offers a fresh perspective on traditional epistemological and linguistic questions in the field. Despite its emergence, important inferentialist ideas still need to be operationalized. In this…

In recent years, science, technology, engineering and mathematics (STEM) approaches in education have received growing attention in the political arena and in educational research and practice. A concern consistently raised in the research literature regarding interdisciplinary STEM education is that the role played by mathematics is understated…

According to commognitive conceptualization, development of mathematical thinking, whether historical or ontogenetic, requires periodic transitions to mathematical discourse "incommensurable" with the one that has been practiced so far. In this new discourse, some familiar mathematical words will be used in a new way. Historically, such…

Learning standards such as the "Common Core State Standards for Mathematics" [CCSSM] (NGA Center & CCSSO, 2010) advocate that we develop students' algebraic thinking "beginning in kindergarten." Such a tall order requires innovative approaches that re-imagine what teaching and learning mathematics means for the elementary…

Calculus education research on integration is coalescing around the theme that teaching integration based on quantitative reasoning is crucial for robust understanding of and usage of integrals. This paper contributes to this International Journal for Research in Undergraduate Education special issue on the teaching and learning of definite…

The theoretical reflection on the nature of school algebra and the development of algebraic thinking from the first educational levels is a relevant topic in mathematics education. In this paper, we first summarize and clarify the positions held on this topic by two theoretical frameworks: the Theory of Objectification and the Onto-semiotic…

The development of the mathematical concept of the infinite, through the reflections that arise from personal notions and perceptions and the analysis of some ideas of Galileo and Cantor, invites us to investigate the relationship between intuition and formalization for the understanding of the said concept. This paper aims to observe and describe…

Fractions are an imperative skill for students to master to achieve success in future mathematics concepts and classes. Yet many students, especially those experiencing math difficulties and/or characteristics of emotional and behavioral disorders, continue to exit elementary school without a concrete foundation of fractions skills required to…

"Epistemological justification" is a way of thinking that manifests itself through perturbation-resolution cycles revolving around the question "why and how was a piece of mathematical knowledge conceived?" The paper offers a conceptual framework for constituent elements of epistemological justification. The framework provides:…

A theoretical model describing young students' (Grade 3) arithmetic-algebraic structure sense was formulated and validated empirically (n = 130), hypothesizing that young students' arithmetic-algebraic structure sense consists of five distinct but correlated factors; structure in numerical equivalence and word-problem modeling, structure in…

Teachers and teacher educators have been sharing strategies and resources for implementing mathematics routines in National Council of Teachers of Mathematics (NCTM) journals for years. A less commonly shared mathematics routine, especially with young learners, is "Clothesline Math" (Shore, 2017, 2018). In this routine, teachers create…

We introduce, motivate, and exemplify a proposed theoretical construct guiding the design and facilitation of collaborative geometry activities, conceptually generative perspectival complementarity (CGPC). Participants in CGPC activities learn content by negotiating their respective perceptions of situated features they manipulate to accomplish…

New perspectives on executive functions propose a greater involvement of context. These perspectives have implications for research in mathematical cognition. We tackle the problem that although individuals clearly exercise inhibitory control in mathematical contexts, researchers find that the relations between inhibitory control and mathematics…

Research studies are abundant in pointing at how the transition from additive to multiplicative thinking acts as a core challenge for students' understanding of proportionality. This said, we have yet to understand how this transition can be supported, and there remains significant questions to address about how students experience it. Recent work…

The evolution of mathematics coincided with advancements in its teaching. The 19th and 20th centuries marked a pedagogical revolution in mathematics education. This paper argues that Bruner's (1966) model, Gagné's (1985) taxonomy, innovative teaching methods emphasizing research and problem-solving, and the inclusion of data analysis topics have…