Undergraduate students are expected to produce and comprehend constructive existence proofs; yet, these proofs are notoriously difficult for students. This study investigates students' thinking about these proofs by asking students to validate two arguments for the existence of a mathematical object. The first argument featured a common structural…

This study illustrates how two secondary mathematics teachers used students' incorrect answers as they supported students' engagement in collective argumentation. Three ways of supporting argumentation when students contributed incorrect answers are exemplified, and the structures of these arguments are investigated. Then, by focusing on the…

Thinking is a tool to construct knowledge in learning mathematics. However, some college students have not been fully aware of the importance of constructing their knowledge. Therefore, this study aims to explore students' thinking processes in completing mathematical proofs through assimilation and accommodation schemes. This research was…

Research in psychology and in mathematics education has documented the ubiquity of "intuition traps" -- tasks that elicit non-normative responses from most people. Researchers in cognitive psychology often view these responses negatively, as a sign of irrational behaviour. Others, notably mathematics educators, view them as necessary…

We explore the transition from school to university through a commognitive (Sfard 2008) analysis of twenty-two students' examination scripts from the end of year examination of a first year, year-long module on Sets, Numbers, Proofs and Probability in a UK mathematics department. Our analysis of the scripts relies on a preliminary analysis of the…

This study designed and developed a Chinese character handwriting diagnosis and remedial instruction (CHDRI) system to improve Chinese as a foreign language (CFL) learners' ability to write Chinese characters. The CFL learners were given two tests based on the CHDRI system. One test focused on Chinese character handwriting to diagnose the CFL…

The purposes of this study were to (1) compare peer and self-video modeling in terms of effectiveness and efficiency in teaching first aid skills to children with intellectual disability and (2) analyze the error patterns made in probe sessions to determine whether the children who took the role of sufferers during the first aid skill sessions…

In recent years, an increasing number of analyses in Learning Analytics and Educational Data Mining (EDM) have adopted a "Discovery with Models" approach, where an existing model is used as a key component in a new EDM/analytics analysis. This article presents a theoretical discussion on the emergence of discovery with models, its…

The objective of this paper is to explain the need for and defend the sufficiency of the child's-play method of teaching the place value notation concept to preschool and elementary school children. Discussion first illustrates error patterns of school children in the use and interpretation of place value notation, arguing that the errors reflect…