This paper explores how college students understand ideas of functions, and which representations are productive for them in promoting their ability to work flexibly across representations. The study used pre- and post-test scores, and triangulations via student self evaluations, to generate a hypothesis related to flexible thinking and success in…

Discussion of the nature of the algebraic and graphical representations of functions focuses on a study integrating cognitive research and the development of an intelligent tutoring system (ITS), the Function Characteristics Tutor, to evaluate the effects of pairing representations of mathematical functions on high school students. (Author/LRW)

The typical path of instruction in high school algebra courses for the study of polynomial functions has been from linear functions, to quadratic functions, to polynomial functions of degree greater than two. This paper reports results of clinical interviews with an Algebra II student. The interviews were used to probe into the student's…

In posttest results, 76 prealgebra students who learned about functions in a unit emphasizing multiple formats, anchoring learning in a thematic context, and problem solving in cooperative groups were more successful at problem solving and problem representation than were 56 comparison students conventionally taught. Similar results were found for…

Examines how components of the concept of function (variable, domain, and range) and the process-object duality in its nature emerge as highly relevant to student learning in various mathematical contexts related to linear and abstract algebra. (Contains 22 references.) (ASK)

Reports the results of an investigation designed to help algebra teachers and curriculum developers by providing insights into how high-performing college algebra students (N=30) develop an understanding of major aspects of the concept of function. Results revealed that these high-performing students actually possessed weak understanding. Contains…

Researchers and educators are calling for increased use of technology and attention to function concepts in school mathematics. Students often have considerable difficulty gleaning pointwise and global information from Cartesian (R squared) representations of functions, whether they are hand- or machine-produced. Described here is an interactive…

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…

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…

The purpose of this study was to determine the effect of the TI-81 Graphics Calculator as an instructional tool on college algebra students' conceptual and procedural achievements involving functions and graphs and on the students' attitudes toward mathematics. The study was a posttest-only, equivalent control group design conducted with students…

This paper describes student difficulties in first-year calculus classes and suggests some instructional strategies to address these difficulties. Participants in this study were 200 low socio-economic background freshmen majoring in business in Brazil. Results show that the main difficulties are related to lack of understanding of algebraic…

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…

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…

Algebra students typically pay little attention to choosing appropriate domains, ranges and scales of axes for graphing functions. The purpose of this study was to investigate the effect of introducing an assignment and employing the graphing calculator to examine and alleviate students' difficulties regarding the selection of appropriate domains,…

Reports on a case study of a 16-year-old student working on transformations of functions in a computer-based, multirepresentational environment. Presents an analysis of the work during the transition from the use of visualization and analysis of discrete points to the use of algebraic symbolism. (AIM)