ZDM

Representations are an account of reality. Their construction involves several choices: what to represent, how to represent, from which point of view. Here, we introduce tools to represent mathematics teaching through the study of sign exchanges. We first emphasize how signs are tightly related to different shares of knowledge of sign users. In the regular case, sign exchanges are considered to rest on a kind of shared obviousness. The knowledge imbalance between actors of the didactical situation renders this shared obviousness minimal, and therefore requires distinguishing different kinds of sign exchange processes. From the notion of semiosis, we define the processes of tacitation and implicitation. We present a field study from these theoretical concepts and discuss some implications for future research.

Research literature on the role of mathematics teachers during the COVID-19 crisis shows that teacher preparation for emergency situations is required. In reporting on this exploratory study, we present and analyse lesson plans created by seven future teachers for mathematics classes during the pandemic. Data were collected between April and October 2021 from 16 four-hour class sessions in a Mathematics Degree Program at a public university in Medellín, Colombia. The notion of Humans-with-Media and the Learning by Expanding theory were used as frameworks to understand what roles prospective mathematics teacher (PMTs) assign to technologies for teaching in pandemic conditions. The PMTs’ uses of technology for teaching mathematics during a pandemic were categorized. The results show that technology was used to reorganize and reproduce mathematics teaching practices. This report addresses the impact of technology on the activity system, and we conclude with a discussion of opportunities and limitations of students’ conceptions about teaching and technology during a pandemic.

The problem of adverse effects of prior knowledge in mathematics learning has been amply documented and theorized by mathematics educators as well as cognitive/developmental psychologists. This problem emerges when students’ prior knowledge about a mathematical notion comes in contrast with new information coming from instruction, giving rise to systematic errors. Conceptual change perspectives on mathematics learning suggest that in such cases reorganization of students’ prior knowledge is necessary. Analogical reasoning, in particular cross-domain mapping, is considered an important mechanism for conceptual restructuring. However, the use of analogies in instruction is often found ineffective, mainly because the structural similarity between two domains is obscure for students. To deal with this problem, John Clement and his colleagues developed the bridging strategy that uses multiple analogies to bring students to pay attention to the structural similarity that often goes unnoticed. This paper focuses on the cross-domain mapping between number and the (geometrical) line that has been instrumental in the development of the number concept. I summarize findings of a series of studies that investigated students’ understandings of density in arithmetical and geometrical contexts from a conceptual change perspective; and I discuss how this research-based evidence was used to design an intervention study that used the analogy “numbers are points on the number line”, and a bridging analogy (“the number line is like an imaginary rubber band that never breaks, no matter how much it is stressed”) with the aim of bringing the notion of density within the grasp of secondary students.

This article presents one approach to addressing the important issue of interdisciplinarity in the primary school mathematics curriculum, namely, through realistic mathematical modelling problems. Such problems draw upon other disciplines for their contexts and data. The article initially considers the nature of modelling with complex systems and discusses how such experiences differ from existing problem-solving activities in the primary mathematics curriculum. Principles for designing interdisciplinary modelling problems are then addressed, with reference to two mathematical modelling problems—one based in the scientific domain and the other in the literary domain. Examples of the models children have created in solving these problems follow. A reflection on the differences in the diversity and sophistication of these models raises issues regarding the design of interdisciplinary modelling problems. The article concludes with suggested opportunities for generating multidisciplinary projects within the regular mathematics curriculum.

Students’ mathematical achievement in Iceland, as reported in PISA 2003, showed significant and (by comparison) unusual gender differences in mathematics: Iceland was the only country in which the mathematics gender gap favored girls. When data were broken down and analyzed, the Icelandic gender gap appeared statistically significant only in the rural areas of Iceland, suggesting a question about differences in rural and urban educational communities. In the 2007 qualitative research study reported in this paper, the authors interviewed 19 students from rural and urban Iceland who participated in PISA 2003 in order to investigate these differences and to identify factors that contributed to gender differences in mathematics learning. Students were asked to talk about their mathematical experiences, their thoughts about the PISA results, and their ideas about the reasons behind the PISA 2003 results. The data were transcribed, coded, and analyzed using techniques from analytic induction in order to build themes and to present both male and female student perspectives on the Icelandic anomaly. Strikingly, youth in the interviews focused on social and societal factors concerning education in general rather then on their mathematics education.