Scientific studies
of the use of computer algebra systems
in calculus instruction

by Lisa Denise Murphy

Beckmann, C. E. (1988). Effect of computer graphics use on student understanding of calculus concepts. (Doctoral dissertation, Western Michigan University, 1988). Dissertation Abstracts International, 50, 1974B.
Charlene Beckmann (1988), evaluating four different first semester calculus courses at Western Michigan University, discovered that students in courses using a graphical approach had greater understanding of calculus concepts than students in the traditional course based on a symbolic approach, with no loss in skill levels. The sections using a graphically-developed conceptual approach also had much higher retention rates. This study is unusual in that it involves four different types of instruction. Most studies involve only two.

Bookman, J. & Friedman, C. P. (1994). Final Report: Evaluation of Project CALC 1989 - 1993. (mimeo).
Jack Bookman and Charles Friedman, evaluating Project CALC at Duke University, used a retention study, an attitude survey and problem solving test given to selected students in both the experimental and control groups during the second semester of the calculus sequence, and a study of students' performance in later courses where calculus skills and concepts are used. In addition, matched pairs of students in seven majors were interviewed after completing the sequence. Students in a course using MathCAD and Derive were found to be significantly better at problem-solving than students in the traditional course, and had more positive attitudes toward mathematics and their own abilities.

Crocker, D. A. (1991). A qualitative study of interactions, concept development and problem-solving in a calculus class immersed in the computer algebra system Mathematica. (Doctoral dissertation, Ohio State University, 1991). Dissertation Abstracts International, 52, 2850A.
Deborah Ann Crocker studied two sections of introductory calculus using Calculus&Mathematica at Ohio State. I found this study frustrating due to the lack of a control group. The paper didn't tell me whether these students were learning more or less than they would have in a traditional course. The conclusions she reached, such as the fact that the students' concepts of a derivative gradually developed and became stronger as the course progressed, seemed fairly obvious to me. One conclusion that was surprising was that high achieving students were less likely to try multiple approaches to a problem or to experiment with a problem. This suggests that students who have been successful in situations where passive absorption was the accepted mode of learning are reluctant to try a different approach, while students who have been less successful with previous methods are more willing to try new ones.

Hamm, D. M. (1989). The association between computer-oriented and noncomputer-oriented mathematics instruction, student achievement, and attitude towards mathematics in introductory calculus. (Doctoral dissertation, University of North Texas, 1989). Dissertation Abstracts International, 50, 2817A.
Don Hamm compared the achievement and attitude of two sections of introductory calculus students, one taught with computers and one taught with traditional methods. He found no significant differences between the two groups.

Hawker, C. M. (1986). The effects of replacing some manual skills with computer algebra manipulations on student performance in business calculus. (Doctoral dissertation, Illinois State University, 1986). Dissertation Abstracts International, 47, 2934A.
Cheryl Hawker noted that achievement levels of the two groups in her study were similar, but the group using muMATH had scored significantly lower on the algebra pre-test than the students in the standard course. Since poor algebra skills would be expected to lead to lower performance in calculus, the fact that the two groups performed at the same level in the calculus course could be taken to mean that the use of muMATH helped the students to compensate for their lack of algebraic skills. This study is one of the earliest of its kind.

Heid, M. K. (1984). An exploratory study to examine the effects of resequencing skills and concepts in an applied calculus curriculum through the use of the microcomputer. (Doctoral dissertation, University of Maryland, 1984). Dissertation Abstracts International, 46, 1548A.
Heid's work was profound. She designed and taught a computer-based calculus course that was substantially different from the traditional course, rather than being simply a traditional course with computerized work tacked on. She demonstrated that her students were as good at algebraic manipulations as the control group, and had a better understanding of the concepts of the course. Several similar projects have been done since, but I think hers was the first. (If you find a reference to an earlier project, please email it to me.)

Heid, M. K. (1988). Resequencing skills and concepts in applied calculus using the computer as a tool. Journal for Research in Mathematics Education, 19 (1), 3-25.
This is a shorter description of Kathleen Heid's work than is found in her dissertation, and probably easier to find. If you are interested in the use of computer algebra systems in calculus instruction, you should read this paper.

Judson, P. T. (1988). Effects of modified sequencing of skills and applications in introductory calculus. (Doctoral dissertation, The University of Texas at Austin, 1988). Dissertation Abstracts International, 49, 1397A.
Phoebe Judson studied two sections of business calculus, one using computers and the other using traditional methods. The computer section learned concepts and applications before manipulative skills. No significant achievement differences were found, although some affective differences were noted.

Palmiter, J. R. (1986). The impact of a computer algebra system on college calculus. (Doctoral dissertation, The Ohio State University, 1986). Dissertation Abstracts International, 47, 1640A.
Talk about control groups! Jeanette Palmiter started with 120 students who signed up for second quarter calculus, randomly divided them into two groups of 60 students each, and taught one group with MACSYMA (a computer algebra system) while the other was taught a traditional course. The MACSYMA course was similar in spirit to Kathleen Heid's work, with concepts covered first and skills left to the end. Palmiter followed the students' achievement in mathematics for two semesters after they left her course. Fewer students from the experimental group went on to the next two semesters of calculus, although this seems to have been dictated by the requirements of their majors rather than their preparation in this course. For the ones that did go on, the experimental group did better than the traditional group in the following quarter and much better in the quarter after that.

Park, K. (1993). A comparative study of the traditional calculus course vs. the Calculus & Mathematica course. (Doctoral dissertation, University of Illinois at Urbana-Champaign, 1993).
Kyungmee Park, evaluating Calculus&Mathematica at the University of Illinois, assessed students' conceptual understanding by means of classroom observations, attitude surveys, interviews, pre- and post-tests, and concept maps drawn by the students. She developed an elaborate scoring system for the concept maps. Park was able to give both pre- and post-tests to all students during class, although the lengths of the tests were limited by time constraints. She found that Calculus&Mathematica students showed greater understanding of the relationships between graphical and symbolic representations that did students in the traditional course. The C&M students also developed significantly more positive attitudes toward cooperative learning, while students in the traditional sections showed only slight changes in this area. If you are interested in concept maps, read this.

Park, K. & Travers, K. J. (1996). A comparative study of a computer-based and a standard college first-year calculus course. CBMS Issues in Mathematics Education, 6, 155-176.
This is a shorter description of Kyungmee Park's work than is found in her dissertation, and probably easier to find. The dissertation has much more material on the concept maps, and references to literature on concept maps, than this paper has. It is also the most recent paper in my list, and has 20 references, so it will be useful to anyone trying to start a literature review in this area.

Porzio, D. T. (1994). The effects of differing technological approaches to calculus on students' use and understanding of multiple representations when solving problems. (Doctoral dissertation, Ohio State University, 1994).
Donald Porzio used classroom observations, interviews, and written tests to assess students' preferences for numerical, graphical, or analytical representations and their ability to make connections between types of representations when solving problems. He found that students using Mathematica were better able to use different forms of representations (symbolic, numerical, and graphical), particularly ones involving combinations of different representations, and were better able to make connections between representations than either of the other two groups in his study. The other two groups, a traditional calculus class and a class using graphics calculators, were not significantly different from one another in this regard.

Porzio, D. T. (1994). Investigating how differing technological approaches to calculus impact students' use and understanding of multiple representations when solving calculus problems. Presented at NCTM meeting in Indianapolis.
I would like a copy of this, if anyone has one.

Schrock, C. S. (1989). Calculus and computing: An exploratory study to examine the effectiveness of using a computer algebra system to develop increased conceptual understanding in a first-semester calculus course. (Doctoral dissertation, Kansas State University, 1989).
Connie Sue Schrock found that a calculus class using Maple were more confident, had better attitudes, and had better understanding of the concepts than the control classes using traditional methods, without loss of computational ability.

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This page last revised February 3, 1999.