This article uses a cultural-developmental framework to illuminate the interplay between collective and individual activity in the mathematical reasoning displayed in a university Masters level lesson on fractals. During whole class and small group discussions, eleven students, guided by an instructor, engage in inductive reasoning about the area…

The educational benefits of challenge- or problem-based approaches to learning are now well established. Action Research (AR) and Action Learning (AL) together provide educators with an ethic, a research methodology and a pedagogical strategy for harnessing and developing the motive power of purposeful activity for reflective enquiry in teaching…

Technology has changed the practices related to teaching and learning mathematics in schools. The demand for learning mathematics in virtual environments is increasing in the 21st-century classroom. There has been widespread expansion of the use of technology in education. This column reviews three types of instruction--synchronous, asynchronous,…

Pragmatic, scalable and sustainable responses to persistent socio-emotional issues such as mathematics anxiety remain elusive. Artificial intelligence (AI) offers a promising approach by enhancing students' perceptions of competence, control, and value while transforming teacher-student interactions. This paper advocates for a research agenda…

Problem-based learning puts students in situations that suggest problems without providing instructions and available knowledge. Therefore, when using problem-based learning, students need to be flexible, self-disciplined, active and self-occupied with knowledge and turn the knowledge the teacher intends to impart into their knowledge. For locus…

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…

Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely…

This paper focuses on the importance of identifying students' Prior Knowledge (PK) for the teaching and learning of mathematics. Specifically, we present a framework that exemplifies the core elements teachers need to consider in relation to the purpose, design and implementation of learning experiences that enable PK to be activated and assessed.…

Transitioning from material to theoretical geometry is often considered a significant challenge in compulsory education. Over the last twenty years, research rooted in the Theory of Didactical Situations (TDS) has explored how material geometry can support the teaching and learning of theoretical geometry, promoting continuity in teaching. These…

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…

As COVID-19 continues to impact various business sectors, university administrators have steadily pushed for all academic units to resume on campus operations and activities; conversely, faculty and students have expressed increased interest in continuing online teaching/learning. We aim to mitigate this "tug-of-war" between…

This article explores the implementation of Olga Torres's Rights of the Learner (Torres's RotL) framework in a 100-level undergraduate mathematics course, particularly focusing on assessment practices. Torres's RotL framework offers a means to center students' voices, mathematical thinking, and humanity in the classroom. The article delves into…

One goal of inquiry-oriented instruction is student engagement with others' mathematical ideas. This paper analyzes a relatively short episode in which students engaged with others' ideas; the instructor facilitated engagement in order to support students in making mathematical progress. Students expressed some bafflement pertaining to the…

This paper explores the affordances of mobile learning in developing frameworks for discourse analysis. Specifically, this paper examines the commognitive analysis of classroom discourses in virtual learning environments (VLEs) and how it resolves the challenges of discourse analysis in face-to-face (F2F) settings. With the ongoing social turn of…

In March 2020, COVID-19 restrictions required our university courses to be offered in online mode only. This quick transition meant that lecturers were suddenly tasked with adapting their classroom-based teaching approaches and materials to the online space. For mathematics teacher educators (MTEs), whose on-campus classes were characterized by…