In this theoretical essay, I build on complexity theory and commognition to theorize the ways in which failure to teach/learn mathematics (FTLM) emerges through the dynamic interactions among teacher, learner, and curriculum demands. I focus on two main concepts of complexity theory: emergence in dynamic systems and attractor states (stable,…

Many students are finishing secondary school without the essential mathematical skills needed to participate in social activities. Research in mathematics education has been investigating the phenomenon of persistent low achievement in mathematics learning from various perspectives, including cognitive, affective, and social ones. Each perspective…

Mathematics-specific learning difficulties and disabilities (MLD) have received increasing attention in scholarly research. In this study, we place MLD research in its wider context of risk societies by discussing the manufacturing of MLD as "a risk." This framing of MLD builds on a certain idea of "hope" in how research could…

Problematic learning situations (PLS) arise when students encounter learning difficulties and their teacher encounters difficulties assisting them. The current study looks at student and teacher difficulties revealed during PLS, in the course of instruction of basic geometrical concepts for average and below-average junior high school students,…

This article addresses one way in which decades of mathematics education research results can inform practice, by offering a framework for designing and implementing an in-service teacher education programme for upper secondary mathematics teachers in Denmark. The programme aims to educate a "task force" of so-called "maths…

Various studies suggest that French students (grades 7 to 10) may solve geometric problems within a paradigmatic framework that differs from that assumed by teachers, a situation prone to misunderstandings. In this paper, we study the extent to which secondary school teachers recognise the conflicting paradigms and how they handle the geometric…

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…

Responds to F. Uhlig's article on linear algebra that appeared in an earlier edition of this journal. (KHR)

The concept of equivalence is shown to be an elusive one that provides difficulty for preschoolers through college students. The idea persists that the equal sign is a "do something," or operator symbol, rather than a symbol for an equivalence relation. (MP)

To understand the difficulties that many students have with comprehension of mathematics, we must determine the cognitive functioning underlying the diversity of mathematical processes. What are the cognitive systems that are required to give access to mathematical objects? Are these systems common to all processes of knowledge or, on the…

This study covers 11-year-olds, school leavers, student nursery nurses, and bus conductor trainees, and their understanding of subtraction, and whether shortcomings in understanding and performance that occurred at ages six or seven would continue in later years and affect feelings toward the subject. (MP)

This paper is a translation of a report on two Swedish investigations concerning children's lack of understanding of the quantitative value of numbers (specifically, decimals and fractions). (MN)

This study attempts to explain certain difficulties which ninth grade students face in tackling geometrical "problems to prove," by relating them to general and to specific rigidity and cognitive style variables. The results confirm the conceptual analysis of Geometric Rigidity (GR). (MP)

Items from mathematics tests developed for Concepts in Secondary School Mathematics and Science (CSMS) program are examined for general dimensions to explain differences and similarities in facility within and across tests. (MP)

The insufficiency of the standard psychological concepts of instrumental and relational understanding to interpret learning in an educational context is indicated. (MP)