Drawing on the commognitive framework, we construe the secondary-tertiary transition (STT) as a distinctive element in the pedagogical discourses of various communities. Our interest rests with university tutors in light of the emergent recognition of their impact on undergraduates' mathematics learning in many tertiary contexts worldwide. We aim…

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…

In 1968, Hans Freudenthal launched the journal "Educational Studies in Mathematics." This paper describes the events leading to the foundation of this journal. It turns out that his wife, Suus Freudenthal, deserves more credit for her husband's interest and achievements in mathematics education. The couple was interested in education…

This article addresses the issue of transition from secondary to post-secondary education through collaborative research with teachers from both levels. It takes into account implicit elements in this transition. Research on the transition in mathematics education tends to focus more on the tertiary level, studying difficulties encountered by…

This paper presents findings from a comparative analysis of three similar secondary geometry texts, one critical unit, one standards-based reform unit, and one specialist chapter. I developed the critical unit as I took the tenets of critical mathematics (CM) and substantiated them in printed curricular materials in which to teach as part of a…

This article discusses an empirical study on the use of history as a goal. A historical module is designed and implemented in a Danish upper secondary class in order to study the students' capabilities at engaging in meta-issue discussions and reflections on mathematics and its history. Based on videos of the implementation, students' hand-in…

We examine teachers' classroom activities with the spreadsheet, focusing especially on episodes marked by improvisation and uncertainty. The framework is based on Saxe's cultural approach to cognitive development. The study considers two teachers, one positively disposed towards classroom use of technology, and the other not, both of them…

The secondary-tertiary transition has been studied in a great amount of research in mathematics education, adopting different focuses and theoretical approaches. I present here how these focuses led the authors to identify and study different students' difficulties and to develop different means of didactical action. Individual, social, but also…

The paper discusses findings of a study that investigated Malawian students' meanings for some probability vocabulary. The study explores the meanings that, prior to instruction, students assign to some words that are commonly used in teaching probability. The aim is to have some insight into the meanings that students bring to the classroom. The…

Recent research suggests that the examination of students' work may lead to changes in teaching practice that are more effective in terms of students' mathematical learning. However, the link between the examination of students' work and the teachers' actions in the classroom is largely unexamined, particularly at the secondary level. In this…

Using Freudenthal's method of historical phenomenology, the history of statistics was investigated as a source of inspiration for instructional design. Based on systematically selected historical examples, hypotheses were formulated about how students could be supported in learning to reason with particular statistical concepts and graphs. Such a…

Two approaches to teaching number concepts and operations are discussed. Their relationships to the foundations of mathematics as well as to the characteristics of the learner are explored. On the basis of this discussion the implicit approach is advocated over the definitial approach. (SD)

The hypotheses, methods, and results of the mathematics portion of the International Project for the Evaluation of Educational Achievement are discussed. Several issues are raised in this critical review of the project and its findings. (SD)

The Czechoslovakian Academy of Sciences is sponsoring an experimental approach to the modernization of the geometry curriculum. Geometry is viewed as ancillary to other parts of the curriculum and is taught as appropriate to other subjects (e.g., algebra). Combinatorial geometry is taught formally. (SD)

The author describes by examples the type of coordination between mathematics and physics instruction that he feels must take place to enhance the learning of both subjects. (JP)