Proyecto Tesis (Disertación)



Submitted in partial fulfillment of the requirements

for the degree of Doctor of Education in Education

in the Graduate College of the 

University of Illinois at Urbana-Champaign, 2001


Edgardo José Avilés-Garay

B.S., Inter American University of Puerto Rico, San Juan, 1994

M.E., Pontifical Catholic University of Puerto Rico, 1996

Urbana, Illinois




    The purpose of this study was to investigate possible effects on lower division undergraduate mathematics achievement of instructional uses of multiple representations.  Four weeks of lessons on linear functions were developed, based on multiple representations supported by the use of electronic spreadsheets.  The participants in this project were 52 students enrolled in a college level algebra course.  Two groups of students, experimental and control were randomly chosen as intact classes.  The control group (23 students) received instruction strictly limited to the textbook and aligned with the course syllabus.  The experimental group (29 students) received an intensive treatment based on the use of spreadsheets and multiple representations, also parallel with the course content.  The researcher was the instructor of both groups.  The research took place during the fall semester of the academic year 2000-2001 at a private university in Ponce, Puerto Rico.

            Three main variables were investigated in this study: prior achievement of mathematics (based on reported high school grades), achievement in mathematics, and attitudes toward mathematics.  Achievement in mathematics, particularly in linear functions, was examined through content areas taught in the course (Cartesian coordinates, graphs, and slope) and using multiple representations of linear functions (symbolic, graphical, tabular, and verbal).  Attitudes toward mathematics were explored in two areas: technology and its uses, and feelings about mathematics.  The data on high school grades, and other information concerning student prior experience (such as use of graphing calculators) were collected through a student profile administered at the beginning of the study.  The remaining data were obtained using an attitude scale and an achievement test on linear functions, administered both at the beginning and at the end of the project.

            The results on this study indicate that the experimental group had higher performance in achievement on linear functions than did the control group at the end of the study (p < .05).  On various achievement sub-scores (content areas and multiple representations), the experimental group scored higher (p < .05) than did the control group.  Similarly, more positive attitudes toward mathematics (p < .05), particularly in technology were observed in the experimental group at the end of the treatment.  Furthermore, using analysis of variance, significant (p < .05) interaction effects (conditions X occasions) for certain achievement sub-scores were found.  For example, for the topic of slope, the amount of gain in achievement was greater for the experimental group than for the control group.  Similar effects were found for the representation sub-scores of verbal and graphical.

            It was concluded that emphasizing multiple representations of linear functions using spreadsheets enhanced achievement in mathematics (linear functions) in the course where this study was carried out.  This was further documented by significant interaction effects for selected achievement sub-scores.  It was also found that more positive attitudes toward certain aspects of mathematics could be expected as a result of using multiple representations for selected topics dealing with linear functions.  It was recommended that more research be carried out along the lines pursued in this thesis, exploring more topics, over a greater period of time, with students having a wide range of academic background.
 ©Copyright by Edgardo José Avilés-Garay, 2001

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