A cognitive demands analysis of a learning technology, a term that includes the hardware and the computer software products that form learning environments, attempts to describe the types of cognitive learning expected of the individual by the technology. This paper explores the context of cognitive learning, suggesting five families of cognitive…

Northwest Guilford High School, Guilford County (North Carolina), is an essentially rural, largely white school that serves about 1,200 students from all socioeconomic levels. An evaluation was conducted of a heterogeneous grouping project involving students in a 2-year sequence of algebra for those who scored below the 40th percentile on a…

The degree of gender differences in mathematics and science appears to vary with the content subdomain. Differences also appear to be greater on items assessing content knowledge than with items measuring reasoning about scientific processes. Many studies of gender differences have involved fairly select populations. This study focuses instead on…

This paper focuses on student understanding and learning of the algebraic concept--rate of change. Teachers' knowledge about their students and current literature on students' understanding is used to design and assess the instruments. Data were obtained as part of two-year research program that focused on how the study of students' understanding…

As part of the Electrical Engineering program at the Univesity of Southern Maine, students are typically introduced to Two's Complement algebra and representation, a method to include negative numbers in the binary representation of integers that is widely used in microprocessors and related digital systems. The traditional, procedural method to…

D. B. Bailey and S. A. Palsha (1992) proposed two modified versions of the Stages of Concern Questionnaire for measuring teacher concerns during a reform effort. Their analysis suggested the use of a 5-factor model with 35 items or 15 items rather than the original 7-stage, 35-item Concerns Based Adoption Model (CBAM). The present study was…

An approach to teaching problem-solving based on using the computer software Mathematica is applied to the study of electrostatics and is compared with the normal approach to the module. Learning outcomes for both approaches were not significantly different. The experimental course successfully addressed a number of misconceptions. Students in the…

This paper reviews an approach for finding optimal solutions to the traveling salesman problem, a well-known problem in combinational optimization, and describes implementing the approach using the MAPLE computer algebra system. The method employed in this approach to the problem is similar to the way ant colonies manage to establish shortest…

A pentagonal model, based on the star model of function understanding of C. Janvier (1987), is presented as a framework for the design and interpretation of research in the area of learning the concept of mathematical function. The five vertices of the pentagon correspond to five common representations of mathematical function: (1) graph; (2)…

Evidence is presented from an ethnographic study of an eighth grade pre-algebra teacher's classroom in support of the idea that teachers' beliefs about the ontology and epistemology of math profoundly influence how they teach and thus what students learn. Specifically, beliefs based on a traditional view of mathematics as procedurally-based are…

This paper describes the use of radical constructivism as a basis for curriculum reform in university mathematics courses and reports on research conducted on two of the courses developed, one in geometry and one in problem solving. The theoretical underpinnings of the project are described along with the implications for course design and…

This study examined the problem-solving behaviors, strategies, and achievement of college students enrolled in a one-semester college algebra and statistics course, with respect to the content areas of quantitative literacy, connections between algebraic and graphical representations, and mathematical modeling. Four instructional units of this…

The relationship between college students' preferred mode of processing mathematical information--visual or nonvisual--and their performance in calculus classes with and without technology was investigated. Students elected one of three different versions of an introductory differential calculus course: using graphing calculators, using the…

This paper presents the results from a paper-and-pencil instrument designed to elicit students' thinking about the rate of change in particular situations. A scoring rubric was designed to classify students' solution strategies to algebra problems. The purpose of the study was to validate the results in different ways. First, the results from this…

In the last few years educational researchers have become increasingly aware of the need to examine interaction among students to understand the impact of cooperative small groups on learning. For this study 26 students in an 11th-grade Algebra II/Trigonometry class were trained to use a didactic cooperative learning technique called scripted…