Analyzes student construction of function-based problem solving methods in introductory algebra. Describes longitudinal observation of a pair of students that studied algebra for three years using the function approach including intensive use of graphing technology. Offers terms for describing and explaining what and how do learners appreciate and…

Presents a problem included on the 1992 National Assessment of Educational Progress in mathematics at grade eight in the content area of algebra and functions. Collects and examines a set of responses to this problem and discusses some examples of strategies that students used to determine the answer to the problem. (ASK)

Discussed is an approach in which algebra and geometry are interwoven in a series of problems that develop one from another. The two main concepts are the algebraic concept of function and the geometric concept of the "family of quadrilaterals." (MNS)

Uses the notion of focusing phenomena to explain how a teacher's actions were connected to her students' interpretations of a linear equation. Conducts interviews and analyzes a high-school classroom that emphasized dependency relationships in real-world situations. Describes how the teacher directed attention away from functional relationships…

An application of functions and their inverses is described--the coding and decoding of messages, or cryptographs. The helpfulness of computers is noted, with two programs listed. (MNS)

This book features a set of problems assembled to reflect the criteria of the mathematics portion of the North Carolina High School Comprehensive Test. The problems are not necessarily suited to timed situations but rather are intended for classroom use by teachers to review high school mathematics and build upon concepts and skills developed in…

A method is described for representing quadratic functions by three-dimensional wire models. This enables one to form a simple geometric concept of the location of imaginary zeros. (MNS)

This document is concerned with developing an understanding of problem solving by providing tasks to help students with their problem solving strategies. These tasks were used by Vermont teachers during the pilot years of the High School Mathematics Assessment and were selected by attendees of the June, 1995 Research Scoring meeting. Tasks are…

Describes the successful use of a computer algebra system (CAS) with a student as he worked on a problem involving functions far more difficult than he had previously encountered. (Author/NB)

Discusses the implications of a research study of more than 2000 students aged 11 to 15 that explored why the students interpret algebra in certain ways. Recommends strategies that can help teachers deal with prior knowledge that students may bring to their study of algebra. (DDR)

Proposes activities that promote students' awareness of the structure of the information involved in their everyday activities, and builds the concept of function from students' mental representations of phenomena. Recommends the use of spreadsheets to provide external representations of these functions. (DDR)

Discussed are the idea, examples, problems, and applications of convexity. Topics include historical examples, definitions, the John-Loewner ellipsoid, convex functions, polytopes, the algebraic operation of duality and addition, and topology of convex bodies. (KR)

This paper has two goals. The first is to present a model of the acquisition of a concept image of function. Theories describing the objectification of function are outlined through two different but related paths, and both stem from the conception of function as a process. The first path to objectification involves the generalization of the…

This book was developed for teachers, youth group leaders, after-school child care providers, and parents, who may not have the time or the expertise to develop strategies for preparing students to be effective problem solvers. The content is organized in a pyramid style to make it easy to locate and grasp the information provided. Information on…

Discusses the interconnection among the various modes of the TI-92 calculator (geometry, data graphing, function graphing, and algebra) and how the power of visualization is extended to provide multiple approaches to complex problem situations. Provides a graphing problem with illustrations and results. (AIM)