We find that students in the big mathematics service courses at the Johns Hopkins University who were encouraged to use calculators in K-12 have somewhat lower grades than those who weren't.

The focus is on the metacognitive awareness of ten high-achieving high school pupils in mathematics in Denmark and England and their understanding of their cognitive learning processes and strategies. Mainly unstructured focus group interviews investigate how they explain that they learn a mathematical concept that is new to them. I develop the…

Four groups (three engineering students in each group) were videotaped while constructing concept maps in Linear Algebra. There are two aims of this study. The first is to characterize the discourse in the groups by addressing the following research questions: Do the students communicate in an "effective" way? Do the students' communications…

In the international community of mathematics and science educators the intuitive rules theory developed by the Israeli researchers Tirosh and Stavy receives much attention. According to this theory, students' responses to a variety of mathematical and scientific tasks can be explained in terms of their application of some common intuitive rules.…

In this paper, we distinguish between two ways that an individual can construct a formal proof. We define a syntactic proof production to occur when the prover draws inferences by manipulating symbolic formulae in a logically permissible way. We define a semantic proof production to occur when the prover uses instantiations of mathematical…

This paper deals with a teaching approach aimed to help students become aware of targeted techniques of significance in problem solving. The teaching approach is to present a series of tasks that all can be solved by applying the same technique. Two levels of prompting are used; first for the students to realize solutions without necessarily being…

Exercises and problems about functions found in 24 middle-school textbooks from 15 countries were analysed using an adaptation of Balacheff's theory of conceptions and Biehler's notion of the prototypical domain of application of concepts in order to describe the practices associated with the notion of function. The analysis yielded five different…

How the use of computers in mathematics classrooms was viewed by students in two middle years mathematics classrooms was the focus of the research described in this paper. The primary data sources consisted of questionnaires, classroom observations supported by videotaping of mathematics lessons, and interviews with two girls and two boys from…

The interplay among and connections between objects (structured or unstructured), images, language and symbols that lead to mathematical reasoning and the stating of mathematical propositions of very wide generality is well worth closer study. I believe that the subtle distinction between the way mathematical ideas are constructed from objects and…

The crisis in UK mathematics education, both in schools and universities, has been widely reported in the national media. A recent study shows that 26% of full-time mathematics teachers in UK schools have no qualification in the subject, and that 31% of all UK schools' mathematics teachers are now over the age of 50. The crisis in school…

This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and series made by students who have a tendency to include visual imagery in their reasoning. We explore…

The aim of the research presented in this paper is to contribute to our knowledge about problem solving in mathematics. My purpose in this paper is to compare, from this point of view, two very different institutions in the French tertiary education system, with the intention to interpret the chronic inequality of performance in problem solving…

This study explored the problem-solving schemas developed by 7th-grade pre-algebra students as they participated in a teaching experiment that was designed to help students develop effective schemas for solving algebraic problem situations involving contexts of (1) growth and change and (2) size and shape. This article describes the qualities and…

The sequential organization of actions necessary to construct a figure in a dynamic geometry environment (DGE) introduces an explicit order of construction. Such sequential organization produces what is, in effect, a hierarchy of dependences, as elements of the construction depend on something created earlier. This hierarchy of dependences is one…

A series of 13 survey questions based on a 50-50 spinner is used to explore school students' understanding of statistical variation in a chance setting. Five questions set the context by assessing the understanding of theoretical expectation and representation of repeated trials in a stacked dot (line) plot. Four questions provide opportunity to…