This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying particular conceptions of each construct. Through analyses of classroom practice across grade levels using different lenses -…

Logical reasoning as part of critical thinking is becoming more and more important to prepare students for their future life in society, work, and study. This article presents the results of a quasi-experimental study with a pre-test-post-test control group design focusing on the effective use of formalisations to support logical reasoning. The…

This paper reports on a teaching experiment on mathematical modelling in an upper secondary school class that investigates how the constructs of "model eliciting" and "emergent modelling" may be brought together to inform teaching and learning. A prominent role is covered by the process of task design, seen as a complex process…

In this paper we interpret pervasive difficulties with second degree inequalities as a macro-phenomenon emerging from Large Scale Assessment. In line with the theory of reification, we link common students' difficulties to approaches they use that undermine the intertwining of processes and the ensuing emergent mathematical objects. To frame the…

Teaching simulations such as scriptwriting tasks offer a novel way to support pre-service teachers in gaining diagnostic competencies and in guiding students to work through difficulties. We first report on the theory-driven development of a scriptwriting task, specifically the theoretically-founded language- and accompanying content-related…

This paper presents a research framework for investigating the role of language use in mathematics learning. The paper draws on the wider M[superscript 2]EID study, which explores whether differences in languages (English and Irish) and their use by bilingual mathematical students have a differential impact on their mathematics meta-level…

Although it is assumed that parents influence their children's lives, little is known about how students navigate between their own expectations and their parents' views of mathematics and how this navigation affects mathematical learning. Using an exemplary case of Philip, we illustrate how he made sense of his father's high expectations related…

Continuing to study mathematics throughout schooling is considered important in most developed countries, where mathematics is incorporated within the curriculum until school-leaving age. By comparison, in England, relatively few post-16 (upper secondary) students study mathematics once it becomes optional. Core Maths qualifications, introduced in…

The comparison of different languages in terms of specific mathematical ideas can provide insights into the nature of mathematics and into the learning and teaching of mathematics in both languages. This paper uses a typological perspective to contrast the language of comparison of isiXhosa and English, specifically when comparing countable…

We present a case study of an elementary teacher, Jen, who transformed her mathematics teaching practice and deepened her conception of angle measure. Employing Teacher Development Experiment methodology, rooted in a constructivist perspective of learning, we analysed sets of pre/post interviews and classroom observations, for two lessons on angle…

This article aims to develop a framework for the characterisation of problem-posing activities. The framework links three theoretical constructs from research on problem posing, problem solving, and psychology: (1) problem posing as an activity of generating new or reformulating given problems, (2) emerging tasks on the spectrum between routine…

We report our progress on the "River Memorial Museum" didactic intervention project developed with schools, in the basin of the Atoyac River in Mexico, that are significantly impacted by the pollution produced through industrialisation. The teachers of the elementary schools in these communities, environmental scientists, educators, and…

We report on an action research study conducted by two mathematics teacher educators in the United Kingdom and Hong Kong. The project consisted of three phases, the first two taking place in our respective teacher education courses and a final phase in which prospective mathematics teachers from both locations engaged in dialogue through a…

The paper reports on updating and integrating two reformed curricula designed in an era of national crises in Greece. In particular, the curriculum design activity of the Leading Coordinators (LCs) is studied under the lenses of Activity Theory and Positioning Theory. Sixteen transcribed videotaped meetings over a period of ten months are analysed…

In New Zealand and internationally, diverse groups of people are under-represented in mathematics. Disrupting deficit discourses requires educators to recognise the funds of knowledge of learners. This article focuses on stories of mathematics at home and in the community of Pacific learners to highlight what we can learn from the voices of…