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,…

After about two years of emergency remote teaching during the pandemic, the teaching of mathematics is slowly returning to (what used to be called) "normal." However, after the period of mostly teaching online, there is uncertainty about the extent to which we will return to the way we were teaching before. In this survey paper we…

Representation is an important element for teaching and learning mathematics since utilization of multiple modes of representation would enhance teaching and learning mathematics. Representation is a sign or combination of signs, characters, diagram, objects, pictures, or graphs, which can be utilized in teaching and learning mathematics.…

This paper explores how different schools of thought in mathematics education think and speak about preparing mathematics for teaching by introducing and proposing certain metaphors. Among the metaphors under consideration here are the unpacking metaphor, which finds its origin in the Anglo-American school of thought of pedagogical reduction of…

Mathematical identity is a socio-motivational construct known to be a predictor of mathematical achievement. Students who identify positively with mathematics are more likely to pursue advanced courses and Science, Technology, Engineering, and Mathematics (STEM)-related occupations. Although mathematical identity is shaped by a myriad of internal…

This study describes preservice teachers' beliefs about teaching mathematics for social justice (TMSJ) after experiencing a two-part professional development (PD) workshop on the subject. The research question is: To what degree does a PD experience, designed by a preservice teacher, influence preservice teachers' beliefs about TMSJ? The lead…

A practice-based engineering degree, in which students worked on real-world, team-based projects from day one and throughout their course, was designed to address the need for employability skills in a rapidly changing world. Teaching mathematics in this way required a very different approach to the lecture-exam based model prevalent in most…

The objective of this article is to identify the meaning attributed to the didactics of mathematics and what are the criteria with which an improvement in the teaching and learning process of mathematics is based, future teachers of mathematics, belonging to universities in three different countries (Brazil, Chile, and Ecuador). The qualitative…

Research on LTs remains a central topic in mathematics education. In this plenary paper, I argue that LT-based research needs a hard re-set if it is to play a role in creating more equitable and anti-oppressive experiences for historically marginalized students. I begin with an overview of LT-based research presented during PME-NA plenary…

Traditional lecturing is the dominant method of teaching mathematics in undergraduate mathematical courses in many countries, whereas active student-centered approaches such as inquiry-based learning have been shown in some instances to be more effective. Most teaching resources (inquiry-based tasks) available at the tertiary level are related to…

What is the connection between advanced mathematics and teaching secondary mathematics? I address this question, drawing on insights from the Special Issue on "Personal Mathematical Knowledge in the Work of Teaching" ("CJSMTE" 13(2), 2013) and reflecting on my personal teaching experience.

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…

Over the past two decades, there have been calls to integrate Education for Sustainable Development (ESD) across all subjects in the primary and secondary curricula. However, researchers have argued that sustainability and mathematics education remain largely unconnected in actual classrooms. The question of what sustainable mathematics education…

In this paper, we offer a novel framework for analyzing the Opportunities for Reasoning-and-Proving (ORP) in mathematical tasks. By drawing upon some tenets of the commognitive framework, we conceptualize learning and teaching mathematics via reasoning and proving both as enacting reasoning processes (e.g., conjecturing, justifying) in the…

Mathematics is pivotal in the contemporary technology-driven world. However, poor mathematical performance continues to be a concern in many countries. Guided by Mathematics in a Cultural Context (MCC) framework, this article investigates the similarities, differences, and potential reasons behind early numeracy achievement in South Africa and…