This article is concerned with "commonsense science knowledge", the informally gained knowledge of the natural world that students possess prior to formal instruction in a scientific discipline. Although commonsense science has been the focus of substantial study for more than two decades, there are still profound disagreements about its nature…

This study investigated middle school students' conceptual understanding of algebraic equations. Participants in the study--257 sixth- and seventh-grade students--were asked to solve one set of algebraic equations and to generate story problems corresponding with another set of equations. Structural aspects of the equations, including the number…

Dividing by zero can be confusing for students at all levels. If teachers are to provide clear and understandable explanations of this topic, they must possess a strong conceptual understanding of it themselves. In this article, the authors present qualitative data on fourth- through eighth-grade teachers' perceptions of division by zero. They…

Encouraging students to share and compare solution methods is a key component of reform efforts in mathematics, and comparison is emerging as a fundamental learning mechanism. To experimentally evaluate the effects of comparison for mathematics learning, the authors randomly assigned 70 seventh-grade students to learn about algebra equation…

This study investigated children's knowledge of division and its relationship to their teacher's conceptual understanding of division following Professional Development. A paper and pencil test was administered to 47 year 7 students and 2 teachers over 2 phases. Following the testing, six students and the teacher from each phase were interviewed.…

This study investigated the differential effects of two modes of instructional program (conceptual change oriented and traditionally designed) and gender difference on students' understanding of heat and temperature concepts, and their attitudes toward science as a school subject. The subjects of this study consisted of 72 seventh grade students…

Using Freudenthal's method of historical phenomenology, the history of statistics was investigated as a source of inspiration for instructional design. Based on systematically selected historical examples, hypotheses were formulated about how students could be supported in learning to reason with particular statistical concepts and graphs. Such a…

The aims of this study were considered under three headings. The first was to elicit misconceptions that students had about the terms "solute", "solvent" and "solution." The second was to understand how students' prior learning affected their misconceptions. The third was to determine if students were able to make a…