One theoretical framework which addresses students' conceptions and reasoning processes in mathematics and science education is the intuitive rules theory. According to this theory, students' reasoning is affected by intuitive rules when they solve a wide variety of conceptually non-related mathematical and scientific tasks that share some common…

When we consider the gap between mathematics at elementary and secondary levels, and given the logical nature of mathematics at the latter level, it can be seen as important that the aspects of children's logical development in the upper grades in elementary school be clarified. In this study we focus on the teaching and learning of "division with…

In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations (in particular "diagrams") of mathematical problems. As a paradigmatic…

Explaining new ideas to oneself can promote transfer, but how and when such self-explanation is effective is unclear. This study evaluated whether self-explanation leads to lasting improvements in transfer success and whether it is more effective in combination with direct instruction or invention. Third- through fifth-grade children (ages 8-11;…

For good reason, many believe that class teachers should make a significant contribution to the music education of young children. In practice, these teachers are often unenthusiastic about the task, feeling that they lack the knowledge and skills to teach music with confidence. Could elementary music textbooks intended for children serve as…

Science, technology, engineering, and math (STEM) fields, including cell biology, are characterized by the "leaky pipeline" syndrome in which, over time, women leave the discipline. The pipeline itself and the pond into which it empties may not be neutral. Explicating invisible norms, attitudes, and practices by integrating social…

This article explores the factors that contributed to personal learning and development as a result of being a member of a collaborative action research project group. The project took place in a university School of Education, and involved five lecturers and the students they were supervising for their dissertations. Data were collected by…

Chemistry is commonly portrayed at three different levels of representation--macroscopic, submicroscopic and symbolic--that combine to enrich the explanations of chemical concepts. In this article, we examine the use of submicroscopic and symbolic representations in chemical explanations and ascertain how they provide meaning. Of specific interest…

In preparing to teach speed to a Y10 intermediate class in a multicultural secondary modern, the author was aware of the difficulty in getting students not only to follow a complex logical argument, but also to be able to reproduce it in a variety of different problem situations. Normally one would set out the working out of the problem as a…

The great interest aroused by the incorporation of Statistics and Probability into curricular projects has been accompanied by considerable evidence of significant difficulties in the meaningful learning and application of the concepts. These difficulties have been the subject of many studies, mostly concerning secondary school students. This…

This article reports findings from formative assessments of one state's administrator mentoring and induction program during two years of program piloting in 2002/03 and 2003/04. The purpose of this evaluation research was to establish baseline data and to detect problem areas, so that changes could be made in subsequent years. More broadly, the…

The article contends that previous scholars have misread George Pierce Baker's efforts by focusing primarily on "The Principles of Argumentation" and the role of logic. Baker's view of logic was more complex than scholars have claimed. He challenged traditional concepts of formal logic, highlighting only those aspects that would help students…

In this classic essay, first published by the "Harvard Educational Review" in 1986, Vivian Gussin Paley details the beginnings of her career as a teacher and author. The article describes her methods of tape-recording and analyzing her students' daily engagement in the "three Fs: fantasy, fairness, and friendship." Her careful analysis provides…

The likelihood that students will make a successful transition to the college environment is often a function of their readiness--the degree to which previous educational and personal experiences have equipped them for the expectations and demands they will encounter in college. A key problem is that the current measures of college preparation are…

Students begin their college studies with a set of epistemological beliefs about what they think knowledge is and how they think it is learned; for most students, the experience of college alters these beliefs in fundamental, transformative ways. This study explores the relation between epistemological beliefs, motivation, and cognition in two…