Creativity and giftedness in mathematics education research are topics of an increased interest in the education community during recent years. This introductory paper to the special issue on Mathematical Creativity and Giftedness in Mathematics Education has a twofold purpose: to offer a brief historical perspective on the study of creativity and…

According to our approach to mathematics education, the optimal aim of the teaching of mathematics is to assist students in achieving efficient mathematical work. But, what does efficient exactly mean in that case? And how can teachers reach this objective? The model of Mathematical Working Spaces with its three dimensions--semiotic, instrumental,…

Blended learning, which combines face-to-face workshops with self-directed online learning, is becoming a good alternative in designing and deploying professional development programs. The online component adapts to teachers' time constraints, requires fewer trained professionals for its implementation, and enhances participants' opportunities to…

This paper provides a survey of the research on the relationship between teachers' professional knowledge and their instructional quality in the domain of mathematics education. First, an overview is provided of the way in which mathematics professional knowledge has been conceptualized. Second, the relation between mathematics teachers'…

Mathematical argumentation is generally thought to be the paradigm of cogent reasoning. The concept of mathematical proof thus seems to be associated with necessity and enforcement, but not with freedom; however, in various ways a reference to freedom is also needed to understand the phenomenon of mathematical proof, for example, to distinguish it…

The cognitive relationship between intuition and proof is complex and often students struggle when they need to find mathematical justifications to explain what appears as self-evident. In this paper, we address this complexity in the specific case of open geometrical problems that ask for a conjecture and its proof. We analyze four meaningful…

Teachers are increasingly being called upon to teach in ways that develop 21st century learning skills in their students. Various frameworks for 21st century learning have been proposed and while they differ, all agree on four components for development--creativity, collaboration, communication and critical thinking. Both individually and…

In this survey paper, we describe the state of the field on linear algebra research. We synthesize themes, questions, results, and perspectives emphasized in the papers that appear in this issue, as well as a selection of those published between 2008 and 2017. We highlight the extensive base of empirical research detailing how students reason…

This paper makes a proposal, from the perspective of a research mathematician interested in mathematics education, for broadening and deepening whole number arithmetic instruction, to make it more relevant for the twenty-first century, in particular, to enable students to deal with large numbers, arguably an essential skill for modern citizenship.…

Statistical modeling is emerging as a fertile research environment in which to promote and learn about student statistical reasoning processes. We outline a paradigm shift toward a modeling perspective that is occurring in statistics education research and how statistical modeling processes involve connecting data, chance and context. The…

Practical instructional approaches are often criticized for focusing too exclusively on vocabulary work whereas research has revealed rich insights into the role of language on the discursive level. On the other hand, the mathematics education research community focusing on language has not yet filled the gap between research and classroom…

How might teachers transform routine tasks into non-routine ones? The purpose of this article is to address this question. The article opens with a discussion of why non-routine problems require creative and original thought. Specifically, I discuss how non-routine problems require students to confront uncertainty and how uncertainty can serve as…

A number of myths about mathematically gifted students, mathematics itself, and programs designed to serve these students tend to inhibit educators, parents and students themselves from developing students' mathematical creativity, expertise and enjoyment. This paper discusses some of the myths that can discourage students' mathematical…

This papers comments on the contributions of "ZDM Mathematics Education" dedicated to the theme "Perception, interpretation and decision making: understanding the missing link between competence and performance". The papers within this issue are brought together under the perspective of the stated aims of this issue, and then…

This paper comments on the theoretical formulations and usage of the construct of teacher noticing in a selection of the papers in this special issue of "ZDM Mathematics Education." The analysis of how the notion of teacher noticing is used in the papers suggests that it draws attention to several interdependencies involved that have not…