More and more things that humans used to do can be automated on computer. In each case, complex tasks have been automated -- not to the extent that they can be done as well as humans, but better. I will draw and develop parallels to education -- showing how and why advances in the Structural Learning Theory (SLT) and the AuthorIT development and…

Instructional resources that employ multiple representations have become commonplace in mathematics classrooms. This study will present computer software, LaborScale which was designed to improve seventh grade students' word problem-solving skills through computer-based multiple representations including graphic, symbolic, and audio…

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 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 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 presents a new model for simulating procedural knowledge in the problem solving process with our ontological system, InfoMap. The method divides procedural knowledge into two parts: process control and action performer. By adopting InfoMap, we hope to help teachers construct curricula (declarative knowledge) and teaching strategies by…

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…