Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

Summarizes theoretical and empirical aspects of research that is investigating how best to support conceptual learning and the critical role that representations have in complex scientific and mathematical domains. Explains Law Encoding Diagrams (LEDs) and considers how computers may further enhance the potential benefit of LEDs for conceptual…

This paper reports on a study of seventh grade students (N=4) who attend a rural K-12 school. Students participated in a 5-week teaching experiment designed to build on their existing knowledge of the unit concept and extend it to the rational number operations of multiplication and division. Data collected comes in the form of videotapes,…

This research focuses on the graphics calculator in calculus and its impact on students' abilities to work with graphical, numerical, and symbolic representations. Three courses are compared, two of which are taught with less emphasis on the use of graphing calculators. The format of the course emphasizing calculator use is more traditional than…

This paper explores a framework for research on the development of the angle concept based on theories of abstraction. The framework suggests that children initially acquire a body of disconnected angle knowledge situated in everyday experiences, group the situations to form angle contexts, and then form an abstract angle concept. The framework is…

This paper describes how a target group of seven students in a combined fourth and fifth grade mathematics class used structured representations to solve fraction problems situated within various realistic contexts. Emphasis is given to the ways in which students' thinking about rational number concepts influences and is influenced by the…

This paper addresses dilemmas in the practices of six teachers from the perspective of alternate paradigms of knowledge growth, particularly constructivism. The dilemmas focus on the relationships between theory and practice in the growth of knowledge in learning and teaching mathematics. The data for this study are drawn from a four-year…

This study explores seventh- and eighth-grade students' thinking about mathematical patterns. Interviews were conducted in which students solved problems about sequential perimeter and area problems modeled with pattern blocks and tiles, generalized the relationships related to the patterns and represented the relationships symbolically,…

This study explores the combined use of concept maps and interpretive essays as a method of assessment in three mathematics courses. The primary objectives were to describe and document: (1) the use of concept maps and written essays to assess the connectedness of students' knowledge; (2) the correlation between students' scores on the concept…

This paper examines students' mathematics learning in a social context as two versions of an instructional sequence designed to facilitate students' development of a conceptual foundation for place-value numeration are enacted in two third grade classrooms. The same instructional sequence is used in each classroom with the regular classroom…