Function Probe is a multi-representational software for Apple Macintosh computers. It was designed to allow students to approach problems in different ways and/or use different representations. This case study describes a 16-year-old student as he creates a path among a variety of representations of transformations of functions while using the…

This study investigated the development of students' abilities to see connections between algebraic equations and life-situated relationships during an extended problem solving experience. The design problem required students to analyze some aspect of their socio-physical environment for cause and effect and to generate a dynamic model using the…

This study examines teachers' mathematical understanding of various representations of slope and their knowledge for teaching the concept of slope. Specifically examined in this research are the concept images and concept definitions of slope held by both preservice (N=18) and inservice (N=21) secondary mathematics teachers. Data collected include…

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,…

The focus of this paper is to further understanding of the distribution and the effects of an expanded conception of opportunity to learn on student mathematics achievement. In addition to descriptive statistics, a set of two-level hierarchical linear models was employed to analyze a subset of the restricted-use National Education Longitudinal…

Six classroom research-based instructional projects funded under Chapter 2 are described, and their outcomes are summarized. The projects each used computer hardware and software in the classroom setting. The projects and their salient points include: (1) the Science Technology Project, in which 48 teachers and 2,847 students in 18 schools used…