Investigates whether three cognitive components of language proficiency--metalinguistic awareness of symbol, syntax, and ambiguity--are associated with students' success in learning algebraic notation. Reports that very few students with low metalinguistic awareness scores achieved high algebra scores in a total sample of more than 1500 students.…

Describes a research project that examined the effects of the Computer-Intensive Algebra (CIA) and traditional algebra curricula on students' (N=802) understanding of the function concept. Results indicate that CIA students achieved a better understanding of functions and were better at the components of modeling, interpreting, and translating.…

Ninety-six eighth and ninth grade algebra students were asked to judge the equivalence of pairs of equations and to justify their responses on the basis of transformations or calculations. Students who gave justifications based upon transformation schemes had a significantly higher rate of correct responses than students who calculated solutions.…

Investigates 6th-grade students' use of equations to describe and represent problem situations prior to formal instruction in algebra. Describes students' preinstructional uses of equations to generalize problem situations and raise questions about the most appropriate curriculum for building on students' intuitive knowledge of algebra. (Contains…

This study examined the benefits to teachers who used impromptu writing prompts in first- and second-year algebra classes. Interpretive research methodology was used to collect and analyze data. Concluded that teachers' assessment of students' understanding was enhanced by reading their students' responses to impromptu writing prompts, thus…

Investigated the effect of mathematics instruction with the aid of microcomputer illustrations on the achievement of college students enrolled in an intermediate algebra course. There was a treatment effect on the comprehensive final examination. (YP)

A study compared the performance of two groups of university students. One group (n=40) was taught calculus using a computer algebra system whereas the other (n=41) used paper-and-pencil computations. The computer group scored significantly higher than their counterparts on both a conceptual knowledge test and a calculus computational exam. (JJK)

Illustrates use of rule space as a tool for cognitive analysis of students' mathematical behavior. The rule-space approach is explained and used to classify students according to two methods for solving linear algebraic equations in one unknown and diagnose their knowledge states on this topic. (Author/MDH)

Reports a case study set in the context of a "function" curriculum approach to introductory algebra. The expectation that the teacher's actions would reflect the philosophy implied in the curriculum was not supported. The teacher gave priority to curriculum content coverage, emphasized methods and procedures, and adopted teacher-focused…

Extends O'Callaghan's computer-intensive algebra study by using his component competencies and the process-object framework to investigate the effects of a graphing-approach curriculum employing the TI-82 graphing calculator. Concludes that students in the graphing-approach classes demonstrated significantly better understanding of functions on…

Students (n=105) enrolled in a college remedial mathematics course participated in a one-semester experiment to determine whether cooperative learning would help students increase their problem-solving skills in mathematics. Results indicated significant differences in favor of students using cooperative learning in solving word problems in…

Presents research in which mathematics teachers and educational researchers ordered arithmetic and algebra problems according to their predicted problem-solving difficulty for students. Analysis of students' problem-solving strategies indicates specific ways that students' algebraic reasoning differs from that predicted by most teachers and…

College students (n=32) in their first abstract algebra course were asked to list elements and find the product of 2 elements in the dihedral group D4. Most students found solutions using a combination of visual approaches and analytic strategies. Proposes an alternative model, the Visualizer/Analyzer model, which assumes visualization and…

Data from students in grades 8-10 in suburban schools were presented to show that errors in formulating algebraic equations are not primarily the result of syntactic translation, as has been assumed in the literature. A theory of cognitive models is offered as an explanation for the errors. (Contains 37 references.) (MLN)

Includes a list of research summaries and annotations of articles and dissertations listed by author within each category. Grade or age levels are indicated for each level. Articles and dissertations are indexed by mathematics education topics, and a list of the journals covered is included. Over 400 references are cited. (MDH)