It is difficult for mathematics teachers to find and utilize relevant historical content for their students. In this study, we aimed to examine how prospective mathematics teachers (PMTs) evaluate the history of mathematics (HM) in curriculum resources and how they integrate the HM into lesson plans. We collected data through PMTs' evaluation…

We present evidence of a secondary school teacher's Knowledge of Mathematics Teaching when she teaches linear equations in a word problem setting. We focus on analyzing the examples and mathematics support that she provides her students with during two classes. When faced with contingencies, she takes decisions whereby she adapts or creates…

Diagrams and in general the use of visualization and manipulative material play an important role in mathematics teaching and learning processes. Although several authors warn that mathematics objects should be distinguished from their possible material representations, the relations between these objects are still conflictive both from an…

In this article, a theoretically derived grid is presented combining Pólya's phases of the problem-solving process with the way in which teachers emphasize their students' strategic diversity in problem solving. It is used to categorize previous results from the literature. In an empirical part, the grid is also used to describe mathematics…

Attention to mathematical reasoning in curriculum standards is part of an international trend, but identifying and understanding reasoning continues to challenge teachers. We report on one component of an Australia-wide initiative supporting teachers to implement innovative pedagogies. This paper contains insights from design research that focused…

We recognise that though teachers may participate in various forms of professional development (PD) programmes, learning that they may have gained in the PD may not always lead to corresponding perceivable changes in their classroom teaching. We offer a theoretical re-orientation towards this issue by introducing a construct we term…

This paper presents the analysis of two teaching experiments carried out in the context of the mathematics laboratory in a primary school (grades 3 and 4) with the use of the pascaline Zero + 1, an arithmetical machine. The teaching experiments are analysed by coordinating two theoretical frameworks, i.e. the instrumental approach and the Theory…

This paper aims to contribute to discussions on the multimodal nature of cognition through an elaboration of the ways multimodal aspects of thinking are exploited by learners doing mathematics. Moving beyond the fact "that" multimodality occurs, this paper focuses on "how" it occurs, with particular attention drawn to the…

This paper discusses different conceptual frameworks for measuring mathematics pedagogical content knowledge (MPCK) in international comparison studies. Two large-scale international comparative studies, "Mathematics Teaching in the Twenty-First Century" (MT21; Schmidt et al., 2011) and the "Teacher Education and Development Study…

The purpose of this article was to describe the task design and implementation of cultural artefacts in a mathematics lesson based on the integration of modelling and conjecturing perspectives. The conceived process of integrating a soccer ball into mathematics lessons via modelling- and conjecturing-based instruction was first detailed. Next, the…

There is mounting research evidence that contests the metaphysical perspective of knowing as mental process detached from the physical world. Yet education, especially in its teaching and learning practices, continues to treat knowledge as something that is necessarily and solely expressed in ideal verbal form. This study is part of a funded…

This paper explores the nature and source of mathematics homework and teachers' and students' perspectives about the role of mathematics homework. The subjects of the study are three grade 8 mathematics teachers and 115 of their students. Data from field notes, teacher interviews and student questionnaire are analysed using qualitative methods.…

The professional literature in mathematics education is replete with calls to use tasks that are "authentic", "relevant" and related to "real life" and the "real world". Such activities are frequently advocated for their potential to motivate and engage students, but evidence of their ability to do so is rarely presented. This paper examines…

This paper explores the potential impact of a national pilot initiative in England aimed at increasing and widening participation in advanced mathematical study through the creation of a new qualification for 16- to 18-year-olds. This proposed qualification pathway--"Use of Mathematics"--sits in parallel with long-established,…

This study investigates the effect on student performance in drawing their attention to relevant task variables, focusing on accuracy of responses and reaction times. We chose this methodology in order to better understand how such interventions affect the reasoning process. The study employs a geometry task in which the irrelevant salient…