This work intends to disseminate a didactic experience in mathematics, in times of pandemic, in an emergency remote teaching situation, at the Portuguese School of Cape Verde, using the Desmos digital platform. The topic addressed was the study of the volume of geometric solids. The main objective was to contribute to the learning of mathematical…

Mathematical modeling is a challenging and creative process. If one considers only interim or final solutions to modeling problems or interviews modelers afterward, often only their "explicit" models are accessible -- those expressed in work products or evinced in verbal and written reflections. The inner world of tacit knowledge and its…

In this article we examine the nature of inter-semiotic and intermodal construction in the exposition of a solution for a geometry rider. In the tradition of hermeneutic phenomenology, this case study involved an exploration of the oral discourse and visual texts used in a mathematics lesson. This research was intended to contribute to the…

The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of…

Visualisation plays a critical role in the teaching and learning of mathematics word problems. It is an essential tool for enabling learners to create meaningful mental pictures necessary for solving mathematical problems. Appropriate visualisation requires good reading skills, English proficiency and an understanding of mathematical vocabulary,…

Although buoyed by the induction of a democratic government, and the high ideals of our constitution, the South African education system has in many ways not met the expectations of its people, in this case, the mathematics education community. With the birth of an expansive intended curriculum came the monitoring of the outcomes through systemic…

This paper uses a multilevel analysis of mathematical reasoning rooted in Cultural Historical Activity Theory to examine how mathematical discourse and student reasoning about linear functions developed across 3 weeks in a ninth grade bilingual algebra class. Despite the teacher's expertise teaching with a conceptual focus, and her stated…

Metacognition encompasses knowledge and regulation that, through reflection, sustain problem solving behaviour. How metacognitive awareness is constructed from reflection on metacognitive knowledge and regulation and how these reflections enable metacognitive skills for Mathematics problem solving remain unclear. Three secondary schools…

Classroom discourse is central to fostering mathematical practices, but we still have much to learn about how the detailed work of teaching can support students to engage in the range of mathematical practices set out in the Common Core. This study examined mathematics discussions in four inquiry based secondary mathematics classrooms to…

Professional development (PD) programs often evaluate their impact on teachers' learning by assessing teachers either individually or in groups. The goal of this paper is to illustrate the variety of paths teachers might follow as a result of working in groups within online PD settings. Data are drawn from a PD program for grades 5-9 mathematics…

This article investigates the coconstruction of student identity and engagement in the case of a 9th grader in a project-based algebra classroom that afforded students a great deal of autonomy. The focal student, Terrance, utilized classroom resources to serve both project-related and social functions as he interacted with his peers during…

In this article, the author provides insight into the pedagogical processes for delegating mathematical authority to students, through the use of specific classroom structures, as a means to strive toward equity. Employing qualitative methods, the author analyzes transcripts of classroom video, along with field notes and teacher and student…

Middle Years students often do not see mathematics as useful. Authentic and real mathematics tasks and artefacts are frequently advocated as arresting this situation. However, often such experiences are contrived and lack authenticity. This paper reports on how a group of Middle Years students used mathematics and technology to engage in a real…

In this article I explore high school students' perspectives on working together in a mathematics class in which they spent a significant amount of time solving problems in small groups. The data included viewing session interviews with eight students in the class, where each student watched video clips of their own participation, explaining and…

Against the backdrop of half a century of research in mathematics problem solving, Polya's last stage is especially conspicuous--by the scarcity of research on it! Much of the research focused on the first three stages (J.M. Francisco and C.A. Maher, "Conditions for promoting reasoning in problem solving: Insights from a longitudinal…