Tasks play an important role in mathematics education, as they provide opportunities for students to develop their competencies and to cognitively engage with the mathematical content. The potential for cognitive activation as a central feature of a mathematical task has been considered in numerous studies, mostly as a didactical analysis by means…

Repeating patterning proficiency predicts students' later mathematical proficiency. A comparative multi-case design enabled the present study to compare patterning success and strategy use for repeating patterns of 75 Norwegian 6-year-old grade 1 students. We provided the students with duplicate, extend, transfer, and unit isolation activities in…

The literature reports that students have difficulties connecting different meanings, multiple representations of the derivative, and performing reversibility processes between representations of f and f'. The research goal is to analyze the mathematical connections that university students establish when solving tasks that involve the graphs of f…

In university mathematics education, students do not simply learn mathematics but are shaped and shape themselves into someone new - mathematicians. In this study, we focus on the becoming of "dis"abled mathematical subjects. We explore the importance of abilities in the processes of being and becoming in university mathematics. Our…

Curricular implementations are unlikely to deliver the anticipated benefits for mathematics learners if written guidance to teachers is interpreted and enacted differently from the ways that policymakers and curriculum designers intend. One way in which this could happen is in relation to the mathematics tasks that teachers deploy in the…

This paper focuses on kindergarten teachers' interactions with young children during mathematical learning activities involving the use of digital tools. We aim to characterise the teachers' roles and actions in these activities and extend considerations of teachers' orchestrations current in the research literature with regard to agency and…

Students' seatwork plays an important part in their learning in their lessons, and very often, students record their private work in the notebooks during seatwork. The students' private work in their notebooks reflects students' learning and thinking, representing explicit learning outcomes. The students' private work in their notebooks of 14…

The purpose of this study is to investigate the ways in which Swedish seventh grade students (12 and 13 years old) handle chance encounters. Four groups of students working in pairs participated in the study. In the group discussions, which were tape-recorded and fully transcribed, the students were encouraged to explore strategies for winning a…

Recent changes in mathematics curricula, both in South Africa and elsewhere, have begun to change the overwhelmingly symbolic nature of mathematics in schools (in the sense of use of mathematical symbolism), promoting more use of the oral and written language. Engaging students in "Writing-to-Learn" activities in mathematics classrooms…

From time to time, the International Commission on Mathematical Instruction (ICMI) mounts studies to investigate in depth and detail particular fields of interest in mathematics education. This paper is the Discussion Document of the forthcoming ICMI Study 16, "Challenging Mathematics in and beyond the Classroom."

The Anthropological Theory of Didactics describes mathematical activity in terms of "mathematical organisations" or "praxeologies" and considers the teacher as the "director of the didactic process" the students carry out, a process that is structured along six dimensions or "didactic moments." This paper…

The aim of the research presented in this paper is to contribute to our knowledge about problem solving in mathematics. My purpose in this paper is to compare, from this point of view, two very different institutions in the French tertiary education system, with the intention to interpret the chronic inequality of performance in problem solving…

Investigates proficiencies when students work on mathematics problems and the extent captured by knowledge categories. Explores competency that goes beyond knowledge to include mathematical 'dispositions' and 'practices' in which students engage. Considers ways in which research knowledge is conceived and developed, reflecting upon the role of…

The purpose of this paper is to contribute to the debate about how to tackle the issue of "the teacher in the teaching/learning process", and to propose a methodology for analysing the teacher's activity in the classroom, based on concepts used in the fields of the didactics of mathematics as well as in cognitive ergonomics. This…