This article presents a mathematical modeling activity for students related to the process of memorization in which students collect their own data to drive their model development, parameterization, and validation. Engaging in the data collection gives them insight to critique and evaluate various models. This task is a low-floor high ceiling…

During their first physics courses, most students struggle with mathematical concepts that are used but not fully understood, for example, the appearance of infinity in introductory physics exercises. In many cases, these concepts are critical to understanding the underlying physical phenomenon. Typically, most books do not place much emphasis on…

Much of the education research on implicit differentiation and related rates treats the topic of differentiating equations as an unproblematic application of the chain rule. This paper instead problematizes the legitimacy of this procedure. It develops a conceptual analysis aimed at exploring how a student might come to understand when and why one…

In activities based on proof without words (PWW), we developed, students are given a PWW--a diagram that alludes to the proof of a mathematical theorem. The students work collaboratively to construct a proof alluded by the PWW, and then each student writes and submits a proof attempt. In a 3-year design-based study, we investigate and develop…

Background: South African learners face the double disadvantage of living in low socioeconomic conditions with access to few resources and attending schools with challenging learning conditions. Mathematics performance reflects such conditions with extreme performance gaps between wealthier and poorer learners. The need for early intervention is…

This article argues the importance of teaching students about the philosophical and mathematical underpinnings of Australia's superannuation system as an example of a real-world problem context. It also provides a rationale for teaching financial modelling and decision-making in ways that respect the diverse financial realities represented in…

This paper aims at contributing to the debate in Mathematics Education about the understanding of the dynamics of students' group interactions by proposing an interpretative lens, which defines four modes of participating in a group on the basis of different kinds of utterances, gestures, postures, and glances that each student makes. We apply…

The article discusses the role of body movement, perception and kinaesthesia in mathematical thinking and accounts for the virtuality of mathematical concepts. A first person experience with a graphing motion software (WiiGraph), which involves ample body movements and is used to draw a circle, is presented. To study the unfolding of the…

This lecture reports on aspects of a larger research programme focused on studying mental mathematics in elementary and secondary mathematics classrooms. It specifically addresses an unplanned aspect that became salient through the work conducted in these classrooms. In this research programme, mental mathematics sessions are designed on a variety…

School life in England (and beyond) is temporally structured, with learning planned as a time-limited activity, both within lessons and across units of work. Discourses of performativity and measurement pervade school life in many societies and, what we call "regulated time" controls school-based learning. In particular, primary…

This paper argues that critical mathematics education requires reflective knowledge, which lies outside of mathematical and technological knowledge, and which can be generated through philosophical inquiry in the classroom. Philosophical inquiry can provide "thinking tools" for questioning, challenging and critiquing implicit assumptions…

Educational institutions are more concentrated on preferable measured outcomes rather than theoretical ones. Measuring subject knowledge obtains through written examination is easy, even as skills such as critical and logical thinking, decision making, problem-solving ability, creative thinking are difficult to measure. The education field is…

This article presents theoretical knowledge, sample activities, and reflections from the implementation process on how teachers can benefit from the Variation Theory to help students enhance their mathematical comprehension. In this context, "congruence of triangles" was conceptualized as an object of learning. Critical aspects were…

Verification and validation are essential aspects of mathematics and beyond in STEM, but these constructs are not consistently defined in research nor in curricula documents. In this theoretical paper, we argue that verification and validation are largely characterized as binary judgments by teachers and researchers about what students do. We then…

Non-mathematics specialists' competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students…