ON UNDERSTANDING OF TRANSFORMATIONS,

DOMAIN, AND RANGE OF FUNCTIONS

Bernadette Baker

Drake University

Bernadette.Baker@drake.edu

Clare Hemenway

University of Wisconsin Marathon County

Maria Trigueros

Instituto Tecnológico Autónomo de México

There has been considerable research in students' understanding of functions (Dubinsky & Harel, 1992). As a result, there have been many suggestions of working with multiple representations of functions and transformations of basic functions such as quadratic, rational, exponential, etc. to help students increase their understanding of functions and their properties.

This research project focuses precisely on this question by examining students' interview responses to questions about domain, range, and transformations. Twenty four students were interviewed at the end of a college algebra course where the emphasis was on studying families of functions, their graphs, and other properties. The research questions addressed in this study examined the effects of student understanding of graphical transformations on students' construction of function concepts.

This project uses APOS (Action, Process, Object, Schema) theory (Asiala, et al., 1996) to analyze student responses. The theory is used to measure the level of understanding a student exhibits when identifying domain and range for functions represented either algebraically or graphically. Secondly, the student is asked to sketch a graph of a quadratic on which some transformations have occurred. Finally, there is a comparison question concerning a different function having the same transformations. The results are interesting. While it seemed that the use of multiple representations was accessible to the students during the course, it did not appear to help them as much as expected in constructing a rich function concept but did show that most students expressed a clear preference for the graphical context.

References

Asiala, M., Brown, A., DeVries, D., Dubinsky, E., Mathews, D., Thomas, K. (1996) A framework for research and curriculum development in undergraduate mathematics education. Research in Collegiate Mathematics Education II, 3, 1 - 32.

Dubinsky, E & Harel, G. (Eds.). (1992). The concept of function: Aspects of epistomology and pedagogy. MAA Notes 25, Washington, DC: Mathematical Association of America.