Catálogo de publicaciones - libros

Many challenges face those of us for whom mathematics education research is our life’s work. In some countries where significant attempts are continually being made to reform mathematics teaching, it is often a highly politicised field. While rational arguments and relevant data-gathering are valid parts of a democratic research process, awareness of the broad cultural context is paramount. Despite the challenges that adopting a new cultural perspective brings, episodes and analyses from our sociocultural research field do demonstrate much promise for advancing mathematics educational practices. In particular the relatively new ideas of values and valuing show much research promise. In this paper, referencing Felix Klein’s fundamental ideas, I will analyse the twin pluralised notions of ‘elementary mathematicians’ and ‘advanced standpoints’. In addition research focussed on a third key notion, ‘pedagogical practices’ will be discussed. Finally some of the implications of this three dimensional and culturally oriented research will be presented.

This chapter describes the Shell Centre team’s “engineering research” approach to the improvement of practice through researched-based design and development of tools for teaching and learning mathematics, for professional development and for supporting large-scale change. The contributions of projects over the past 35 years to the development of design principles and tactics are outlined and illustrated. The roles of tasks of different kinds in learning and assessment are explained, with particular reference to the design of tests, and of formative assessment lessons for concept-development and problem solving. The chapter concludes with a look at the barriers to turning success at classroom level into large-scale change—and how this challenge can be tackled.

East Asian students have persistently performed well in recent international comparative studies of mathematics achievement, and I have been offering explanations from the perspective of the influence of the Confucian Heritage Culture (CHC), which is shared by these high performing East Asian countries. In this paper, two challenges to this cultural explanation will be dealt with: whether these East Asian countries really form a group and whether there is a more direct way to study the influence of culture on mathematics achievement. Three studies on secondary analyses of the TIMSS and PISA datasets are presented to support the assertion that the East Asian countries do form a cultural cluster, and preliminary results of a study that looks into the influence of the English and Chinese languages on students’ assessment in mathematics are reported.

In this survey paper we focus on identifying recent advances in research on digital technology in the field of mathematics education. We have used Internet search engines with keywords related to mathematics education and digital technology and have reviewed some of the main international journals. We identify five sub-areas of research, important trends of development, and illustrate them using case studies: and These exemplary case studies may help the reader to understand how recent developments in this area of research have evolved in the last few years. We conclude the report discussing some of the implications that these digital technologies may have for mathematics education research and practice as well as making some recommendations for future research in this area.

This paper surveys the notions, conceptualisations and roles of mathematical competencies and their relatives in research, development and practice from an international perspective. After outlining the questions giving rise to this survey, the paper first takes a brief look at the genesis of competency-oriented ideas as a prelude to identifying and analysing recent trends. The relationships between different notions and terms concerning competencies and their relatives are discussed, and their roles in the 2015 PISA framework are presented. Two kinds of research, on and by means of mathematical competencies, are surveyed. The impact of competency-oriented notions and ideas on curriculum frameworks and documents in a number of countries is being charted, before challenges to the implementation of such notions in actual teaching practice are identified. Finally the paper takes stock of the international state-of-the-art of competencies and similar notions, with a focus on the need for further research.

When looking at teaching and learning processes in mathematics education students with mathematical learning difficulties or disabilities are of great interest. To approach the question of how research can support practice, an important step is to clarify the group or groups of students that we are talking about. The following contribution firstly concentrates on the problem of labelling the group of students having mathematical difficulties as there does not exist a single definition. This problem might be put down to the different roots of mathematics education on the one hand and special education on the other hand. Research results with respect to concepts and models for instruction are multifaceted and related to specific content and mathematical topics as well as underlying views of mathematics. Taking into account inclusive education, a closer orientation to mathematical education can be identified and the potential of selected teaching and learning concepts can be illustrated. Beyond this, the role of the teacher and the corresponding teacher education programs are discussed.

The authors of this paper were tasked by ICME-13 organisers with conducting a survey on the topic “Mathematics Teachers Working and Learning through Collaboration”. Four research questions guided the survey, concerned with: the of collaborative working; the who engage collaboratively; the and used; what could be observed and how it related to collaboration? The resulting survey drew from a wide range of sources, identifying papers relevant to the topic—316 papers were identified, analysed against a set of criteria and organised into three major themes, each relating to one or more of our research questions: ; . In addition to the papers revealed by the survey, the team sought contributions from projects around the world which are not represented in the published literature. Members from these projects offered ‘narratives’ from the work of teachers in the projects. This paper reports on the nature of the projects revealed by the survey and the narratives, their theoretical and methodological focuses, and the range of findings they expressed. While we offer a significant range of factors and findings, resulting from a very considerable work, we are aware of limitations in our study: we missed relevant papers in journals outside our range; papers reviewed were usually not authored by teachers so the teachers’ voice was often missing; narratives came from projects with which we were familiar, so we missed others. The survey team is in the process of initiating an ICMI study which can take this work into these missing areas. This paper follows closely the presentation made by the survey team at the ICME-13 congress. In presenting findings from the survey, we have tried to provide examples from and make reference to the survey papers. Because the set of references would be too large to fit within our word limit, we have had to reduce the number of references made. However, readers can find a full set of references in a more detailed paper, Robutti et al. in (ZDM Mathematics Education, 48(5), 651–690, ).

This is a summary report of the ICME-13 survey on the theme of recent research in geometry education. Based on an analysis of the research literature published since 2008, the survey focuses on seven major research threads. These are the use of theories in geometry education research, the nature of visuospatial reasoning, the role of diagrams and gestures, the role of digital technologies, the teaching and learning of definitions, the teaching and learning of the proving process, and moves beyond traditional Euclidean approaches. Within each theme, there is commentary on promising future directions for research.

In this paper, we report on the presentations and activities from the strand on “European Didactic Traditions” during the Thematic Afternoon at ICME-13. The focal point of the first hour of this afternoon were four key features that were identified as common in all European traditions and the second and third hours were devoted to the presentation of concrete examples from four specific traditions, organised in four parallel sessions.

This paper describes and analyzes developments that have taken place in German mathematics education research during the last 40 years. Which developments and ideas were characteristic for the discussion and how was Germany influenced by and how did it interact with the international community? The themes range from subject matter didactics to large-scale studies.