In agreement with the main tenets of the anthropological theory of the didactic (ATD), this study uncovers dependencies between what students can learn, the established curriculum and the current state of mathematicians' mathematics ('scholarly mathematics'). One main result is that the mathematics taught, too often taken for granted by curriculum…

Earlier approaches to sense-making in mathematics have looked at the ways students comprehend a mathematical concept. Recent research suggests that some students make sense not only of mathematical objects that have a being, but also of objects that have yet to become. In such cases, learning mathematics is not just an act of comprehending a given…

In this dissertation, I report results from a study that investigated the impact of students' engagement in a series of tasks in an introductory proof course that was designed to stimulate their learning of reading strategies to support their comprehension of mathematics proofs. Specifically, I investigated the impact of the design of five…

Professional learning communities (PLC) have increasingly attracted attention in research on teachers' professional development. The aim of this study is to identify contradictions that can occur and be manifested in PLCs in mathematics. Identifying contradictions in PLCs are important, as the identification and resolution of contradictions are…

The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…

Tensions between constructivist learning theories and objectivist learning theories in online courses implicate a need for a theoretical balance. This article describes organizing and enacting tasks that elicit constructivist learning of mathematics in an online mathematics teacher education course. The results focus on a conceptual framework that…

The emergence of interactive mathematics software in the early 1990s has invited mathematics education researchers to consider ways that dynamic geometry environments (DGEs) might influence K-16 learners' growth of geometric understanding. This article examines the applicability of the Pirie-Kieren theory to trace this growth. Data for this…

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…

Positioning theory has been used in research to understand how elementary student teachers are positioned while working with their mentor teacher. While this research has identified four general positions, there remains a lack of clarity about these positions, particularly in how they differ. This study explores three contrasting student…

In this paper duality between real world phenomenon and mathematics will be discussed. This duality exists for many years which considerably remarked in the history of mathematics curriculum. One of the good potential for filling the gap between real world phenomenon and mathematical ideas would be modelling tasks which require performing the…

The problem addressed in this qualitative single case study is low mathematical achievement levels among students in grades K-4 in rural Vermont schools, based on district-wide and school-based progress monitoring assessments and Vermont's Smarter Balanced Assessment scores. The purpose of this qualitative single case study was to explore the…

In 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…

Virtual learning environments give students more autonomy over their learning than traditional face-to-face classes and require that students adapt the ways they consume and assimilate new information. One theory of this process is self-regulated learning, which is illustrated in Efklides' Metacognitive and Affective model of Self-Regulated…

This paper substantiates the notion of inclusive materialism by illustrating the role of signs and micro-perception in the learning process of multiplication. Inclusive materialism, offered by de Freitas and Sinclair, considers mathematical learning a process of becoming a learning assemblage, which embodies various materials in a Deleuzian sense.…

Exponential functions are an integral component of the secondary mathematics curriculum with which students struggle. Inherent difficulties students have had around the topic of exponential functions suggested a need for thinking about and examining the teaching and learning related to this content. This study presented the mathematical ideas made…