Investigates the cognitive and linguistic demands of learning algebra and explores students' understanding of algebraic notation. Findings indicate specific origins of misinterpretation that include intuitive assumptions and pragmatic reasoning about a new notation, analogies with familiar symbol systems, interference from new learning in…

An algebra test was constructed within a Piagetian framework. Results of a selection of the test items are given and discussed. (MP)

This research study shows that it is possible to advance the use of proportional reasoning of many secondary school students by means of a well-designed teaching program. (MP)

Presents a theory of the development of algebraic abstraction that extends Sfard's and Mason's ideas on learners' progress from operational or process-oriented thinking to the abstract or structural perspective. Analyzes secondary school students' approaches to classifying a set of complex equations. (Author/MKR)

Analyzes the nature and growth of students' algebraic knowledge and thinking from an epistemological perspective supported by historical observations. Focuses on two crucial transitions: from the purely operational algebra to the structural algebra of a fixed value of an unknown and then to the functional algebra of a variable. (Contains 58…

This study related high-inference teacher behaviors to measures of pupil achievement and attitude in ninth-grade algebra classes. A sample of 50 classes came from 13 suburban high schools. The most consistent results showed that pupil and observer assessments of clarity, enthusiasm, and task orientation were important for attitudes toward…

In the attempt to improve the quality of geometry instruction in schools, researchers and teachers alike have given considerable attention to the van Hiele theory of geometry learning and development, which proposes a series of cognitive levels through which every geometry student passes. This paper reports a study to determine the extent to which…

Reviews the history of the concept of function, looks at its relationship with other sciences, and discusses its use in the study of real world situations. Discusses the process of constructing mathematical models of function and emphasizes the importance of the roles of the numerical, graphical, and algebraic representational forms. (MDH)

The focus of this paper is on the use of frames in achieving understanding of learning and problem solving in school mathematics. The paper seeks to illustrate the use that has been made of frames and frame-like conceptions and to add to the case for the usefulness of such conceptions. Results reported are: (1) those related to more sequential…

The author defines and discusses the cognitive theory of constructivism as it relates to teaching mathematics. It is suggested that the philosophical and theoretical view of knowledge and learning embodied in constructivism offers hope that educational processes will be discovered enabling students to acquire deep understanding rather than…

Discussed are the philosophy and procedures behind the introduction of algebra to students in grade 7 in Australia. Included are the importance of concrete experiences, language development, and the consequences involved in this procedure. (CW)

Discusses research findings related to students' ability to make connections between analytical (symbolic) and graphical representations of functions in calculus. Describes graphing tasks and typical student interpretations. Implications for teaching are suggested. (Contains 17 references.) (MKR)

Discussed is the use of a program called MathCAD which allows students to solve higher order polynomial equations and geometry problems. The use of cooperative learning is emphasized. Included are graphs and part of a printout generated while solving problems with MathCAD. (KR)

Presents computer approach formulated within a framework of versatile thinking designed to overcome obstacles to understanding algebra. Results from related studies comparing the computer and traditional approaches taught to 11, 12, and 13 year olds showed that the computer approach significantly improved the understanding of higher order concepts…

Describes and illustrates the Monomial Sums Approach, a graphical learning strategy, facilitated by microcomputer capabilities that allow easy manipulation and exploration of graphical representations of polynomial functions. Reduces emphasis on memorized rules in favor of qualitative understanding of functional behavior, visualization of…