Proving that a given set is indeed a subgroup, one needs to show that it is non-empty, and closed under operation and inverses. This study focuses on the first condition, analysing students' responses to this task. Results suggest that there are three distinct problematic responses: the total absence of proving this condition, the problematic…

Prospective teachers (PTs), enrolled in a mathematics methods course, were asked to analyze children's mathematical thinking by viewing videotaped clinical interviews over the course of an entire semester. They were also asked to conduct two of their own interviews with children as the semester progressed. While the type of analysis varied, all of…

In this study we set out to investigate the errors made by students in logarithms. A test with 16 items was administered to 89 Secondary three students (Year 9). The errors made by the students were categorized using four categories from a framework by Movshovitz-Hadar, Zaslavsky, and Inbar (1987). It was found that students in the top third were…

The use of online translation (OT) is increasing as more pupils receive laptops from their schools. This study investigates OT use in two groups of Swedish pupils (ages 17-18) studying Spanish as an L3: one group (A) having free Internet access and the spelling and grammar checker of Microsoft Word, the other group (B) using printed dictionaries…

This paper reports on the first stage of a research project still in progress aiming at identifying undergraduate students' difficulties and errors in solving linear algebra problems. Some students' difficulties related to very basic notions of vector space theory are shown and discussed with respect to both Balacheff's theory of conceptions and…

Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…

This research is aimed at diagnosing the problem-solving skill of elementary school children and subsequently improving their competence in early mathematics. To reach this goal, a computer assisted instruction (CAI) program on open sentences, incorporating knowledge about students' problem solving strategies and misconceptions, was constructed.…

The projection of shadows task developed by Inhelder and Piaget was used to identify error patterns and solution strategies used by diverse populations in a sequence of proportion tasks. In Study A, two group tests were administered to 607 students from science and mathematics classes in grades 9 and 10. A sub-sample of 69 students was involved in…

It was found that the seemingly greatly increased oral fluency of Middlebury College seniors who had studied in college-sponsored junior year abroad programs did not carry over to written skills or to comprehensive grammatical knowledge. In the oral proficiency interview for Spanish, many returning students had no control of the subjunctive, a key…