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…

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,…

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…

Investigates students' abilities to draw inferences. Introduces cognitive conflict in the form of video clips of reasoning expressed by students. Documents change with regard to the levels of observed response for the protocol and the use of displayed variation in the graphs. Analyzes change associated with the presentation of cognitive conflict.…

Common mathematical errors of pupils as identified by the Concepts in Secondary Mathematics and Science Project are identified and traced to the use of methods invented by students rather than formally taught methods. (MP)