Examines the reliability and validity of using a survey to gauge the percentage of time that algebra teachers use practices that are consistent with professional standards for teaching mathematics. Survey results from 28 teachers suggest that a composite of practices is quite reliable and somewhat valid but that it does not capture instructional…

This paper presents a developmental model of students' acquisition of competence in quantitative and algebraic problem solving. A key notion underlying the developmental model is a distinction between grounded and abstract representations. Grounded representations, like story problems, are more concrete and familiar, closer to physical objects and…

The purpose of this study was to find out whether students perform differently on algebra word problems that have certain key context features and entail proportional reasoning, relative to their level of logical reasoning and their degree of field dependence/independence. Field-independent students tend to restructure and break stimuli into parts…

This study identified predictors of academic performance in college algebra for postdevelopmental students at a predominantly black college. Questionnaires were randomly distributed to 175 students who were enrolled in college Algebra I and II. The sample included 142 students (classified as developmental on college entry by their own reports) who…

In fall 1991, a study was initiated at Central Florida Community College (CFCC) in Ocala to examine the effects of computer lab tutorials and cooperative learning on mathematics achievement, retention rate, mathematics anxiety, mathematical confidence, and success in future mathematics courses among 29 students in an intermediate algebra class.…

This paper presents analyses of score reliability for a mathematics placement test developed by the Mathematical Association of America in 1984 for use with undergraduate college students. Subjects included all 589 students seeking admission to the college mathematics curricula at a private university in the South during the course of the study.…

Data reduction techniques seek to combine variables that account for patterns of variation in observed dependent variables in such a way that a simpler model is available for analysis. Factor analysis is a data reduction technique that attempts to model or explain a set of variables in terms of their associations. To understand why this technique…

This paper examines the question of whether the introduction and use of the function machine representation as a scaffolding device helps undergraduates enrolled in a developmental algebra course to form a rich, foundational concept of function. It describes students' developing understanding of function as an input/output process and as an…

This study examined the generalizability and dependability of a performance-based assessment in algebra. Four forms of a five-item test were constructed using different subsets of eight items based on attributes from task analysis. Subjects included 142 "algebra 2" students from 2 high schools in the Midwestern United States and 148 11th…

The purpose of this paper is threefold. First, the description of a research plan for a large-scale computer adaptive testing program migrating from a network to Internet version is presented. The general areas needed in such a research plan include: (1) comparability studies; (2) psychometric analyses; (3) development projects; (4) validity…

This paper reviews the current theory and research on algebra/mathematics word problems. First, the major research findings are identified and summarized along with the theoretical perspectives that produced the research. The findings are then interpreted from the perspectives of traditional and wholetheme approaches. Also, a sample methodology of…

This study describes a discrete mathematics course for second year college students majoring in computer science or mathematics. Students worked in cooperative learning groups on challenging projects using the computer algebra programming language DERIVE. Results indicate that DERIVE allowed students to verify their conjectures, students generally…

A study was conducted to determine the extent to which high school graduates from Florida's Leon County needed remediation to enter college-level mathematics, reading, and writing courses. Records were examined for 2,705 high school graduates from 1992 to 1996 who were first-time college students in a Florida public community college or state…

This study examined effects of cultural and curricular variables on algebraic reasoning in early and middle adolescence. Four algebra curricula in England and Russia were included in the design. Two age groups were included in the samples: 10- to 14-year-olds, and 14- to 16-year-olds. Algebraic reasoning processes were examined using a written…

A survey of chairpersons of the Departments of Economics at 47 accredited U.S. colleges and universities collected data concerning required and recommended courses, departments in which students take the courses, satisfaction with the courses, and problems in those courses where respondents indicated dissatisfaction. Results indicated that: (1)…