International Electronic Journal of Mathematics Education

International Electronic Journal of Mathematics Education
Computer Graphics as an Instructional Aid in an Introductory Differential Calculus Course
APA
In-text citation: (Tiwari, 2007)
Reference: Tiwari, T. K. (2007). Computer Graphics as an Instructional Aid in an Introductory Differential Calculus Course. International Electronic Journal of Mathematics Education, 2(1), 32-48. https://doi.org/10.29333/iejme/174
AMA
In-text citation: (1), (2), (3), etc.
Reference: Tiwari TK. Computer Graphics as an Instructional Aid in an Introductory Differential Calculus Course. INT ELECT J MATH ED. 2007;2(1), 32-48. https://doi.org/10.29333/iejme/174
Chicago
In-text citation: (Tiwari, 2007)
Reference: Tiwari, Tapan Kumar. "Computer Graphics as an Instructional Aid in an Introductory Differential Calculus Course". International Electronic Journal of Mathematics Education 2007 2 no. 1 (2007): 32-48. https://doi.org/10.29333/iejme/174
Harvard
In-text citation: (Tiwari, 2007)
Reference: Tiwari, T. K. (2007). Computer Graphics as an Instructional Aid in an Introductory Differential Calculus Course. International Electronic Journal of Mathematics Education, 2(1), pp. 32-48. https://doi.org/10.29333/iejme/174
MLA
In-text citation: (Tiwari, 2007)
Reference: Tiwari, Tapan Kumar "Computer Graphics as an Instructional Aid in an Introductory Differential Calculus Course". International Electronic Journal of Mathematics Education, vol. 2, no. 1, 2007, pp. 32-48. https://doi.org/10.29333/iejme/174
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Tiwari TK. Computer Graphics as an Instructional Aid in an Introductory Differential Calculus Course. INT ELECT J MATH ED. 2007;2(1):32-48. https://doi.org/10.29333/iejme/174

Abstract

Mathematicians in general claim that the Computer Algebra Systems (CAS) provide an excellent tool for illustrating calculus concepts. They caution, however, against heavy dependency on the CAS for all computational purposes without the mastery of the procedures involved. This study examined the effect of using the graphical and numerical capabilities of Mathematica as a supplemental instructional tool in enhancing the conceptual knowledge and problem solving abilities of students in a differential calculus course. Topics of differential calculus were introduced by the traditional lecture method to both the control and experimental groups comprised of students enrolled in two sections of the Business and Life Sciences I course. Mathematica was used only by the students of the experimental group to reinforce and illustrate the concepts developed by the traditional method. A content analysis was conducted using the qualitative data obtained from students’ explanations of the derivative of a function. The quantitative data, the students’ test scores, were analyzed using ANCOVA. The results showed that students in the experimental group scored higher than students in the control group on both the conceptual and the computational parts of the examination. The qualitative analysis results revealed that, compared to the control group, a higher percentage of students in the experimental group had a better understanding of the derivative. 

References

  • Armstrong, G., Garner, L., & Wynn, J. (1994). Our experience with two reformed calculus programs. Primus, 4 (4), 301 - 311.
  • Bennett, R. E., & Whittington, B. R. (1986). Implications of new technology for mathematics and science testing. Princeton, NJ: Educational Testing service.
  • Boyce, W. E., & Ecker, J. G. (1995). The computer - oriented calculus course at Rensselaer Polytechnic Institute. The College Mathematics Journal, 26 (1), 45 - 50.
  • Cipra, B. A. (1988a). Calculus: Crisis looms in mathematic’s future. Science, 239, 1491-1492.
  • Cipra, B. A. (1988b). Calculus for a new century: A pump not a filter. (MAA Notes No. 8) Washington, DC.: Mathematical Association of America.
  • Douglas, R. (1986). Report of the conference/workshop to develop curriculum and teaching methods for calculus at the college level. (MAA Notes NO. 6). Washington, DC.: Mathematical Association of America.
  • Dreyfus, T., & Eisenberg, T. (1982). Intuitive functional concepts: A baseline study on intuitions. Journal for Research in Mathematics Education, 13, 360 - 380.
  • Dubinsky, E. (1992). A learning theory approach to calculus. In Z. A. Karian (Ed.), Symbolic computation in undergraduate mathematics education (pp. 43-55). Washington, DC.: Mathematical Association of America.
  • Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24, 94 - 116.
  • Francis, E. J. (1993). The concept of limit in college calculus: Assessing student understanding and teacher beliefs (Doctoral dissertation, University of Maryland College Park, 1992). Dissertation Abstracts International, 53, 3465 A.
  • Fredenberg, V. G. (1993). Supplemental visual computer-assisted instruction and student achievement in freshman college calculus (Doctoral dissertation, Montana State University, 1993). Dissertation Abstracts International, 55, 59 A.
  • Gordon, S. P. (1993). Calculus must evolve. Primus, 3 (1), 11 - 17.
  • Heid, M. K. (1988). Resequencing skills and concepts in applied calculus using the computer as a tool. Journal for Research in Mathematics Education, 19, 3 - 25.
  • Hundhausen, J. R. (1992). Some uses of symbolic computation in calculus instruction: Experiences and reflections. In Z. A. Karian (Ed.), Symbolic computation in undergraduate mathematics education (pp. 75 - 81). Washington, DC.: Mathematical Association of America.
  • Judson, P. (1988). Effects of modified sequencing of skills and applications in introductory calculus (Doctoral dissertation, University of Texas at Austin, 1988). Dissertation Abstracts International, 49, 1397 A.
  • Judson, P. (1992). Antidifferentiation and the definite integral: Using computer algebra to make a difference. In Z. A. Karian (Ed. ), Symbolic computation in undergraduate mathematics education (pp. 91 - 94). Washington, DC.: Mathematical Association of America.
  • Kolata, G. B. (1988). Calculus Reform: Is it needed? Is it possible? (MAA Notes No. 8). Washington, DC.: Mathematical Association of America.
  • Kowalczyk, R. E., & Hausknecht, A. O. (1994, November). Our experiences with using visualization tools in teaching calculus. Paper presented at the Annual Conference of the American Mathematical Association of Two - Year Colleges, Tulsa, OK.
  • Larson, R. E., Hostetler, R. P., & Edwards, B. H. (1995). Brief calculus with applications (alternate 4th ed.). Lexington: D. C. Heath and Company.
  • Lefton, L. E., & Steinbart, E. M. (1995). Calculus & Mathematica: An end-user’s point of view. Primus, 5(1), 80-96.
  • Leinbach, L. C. (1992). Using a symbolic computation system in a laboratory calculus course. In Z. A. Karian (Ed.), Symbolic computation in undergraduate mathematics education (pp. 69 - 74). Washington, DC.: Mathematical Association of America.
  • National Research Council. (1989). Everybody counts: A report to the nation on the future of mathematics education, Washington, DC.: National Academy Press.
  • Nowakowski, A. J. (1992). Computer analysis systems in mathematics education: A case study examining the introduction of computer algebra systems to secondary mathematics teachers (Doctoral dissertation, State University of New York at Buffalo, 1992). Dissertation Abstracts International, 53, 1435 A.
  • Orton, A. (1984). Understanding rate of change. Mathematics in School, 13 (5), 23 - 26.
  • Park, K. (1993). A comparative study of the traditional calculus course vs the Calculus & Mathematica course (Doctoral dissertation, University at Urbana-Champaign, 1993). Dissetation Abstracts International, 54, 119 A.
  • Park, K., & Travers, K. (1998, January 25). Study by the College of Education, University of Illinois. [On - line], http://www-cm.uiuc.edu/compare/study.html. Web site dealing with the evaluation of the computer - based course Calculus & Mathematica.
  • Porzio, D. T. (1995, October). Effects of differing technological approaches on students’ use of numerical, graphical and symbolic representations and their understanding of calculus. Paper presented at the Annual Meeting of the NorthAmerican Chapter of the International Group for the Psychology of Mathematics Education, Columbus, OH.
  • Ralston, A. (1991). Calculators for teaching testing mathematics: A mathematician’s view. College Board Review, 160, 81 - 26.
  • Rochowicz, J. A., Jr. (1996). The impact of using computers and calculators on calculus instruction: Various perceptions. Journal of Computers in Mathematics and Science Teaching, 15 (4), 423 - 435.
  • Schoenfeld, A. H. (1992). On calculus and computers: Thoughts about technologically based calculus curricula that might make sence. In Z. A. Karian (Ed.), Symbolic computation in undergraduate mathematics education (pp. 7- 15). Washington, DC.: Mathematical Association of America.
  • Smith, D. A. (1992). Question for the future: What about the horse? In Z. A. Karian (Ed.), Symbolic computation in undergraduate mathematics education (pp. 1 - 5). Washington, DC. : Mathematical Association of America.
  • Solow, A. E. (1991). Learning by discovery and weekly problems: Two methods of calculus reform. Primus, 1 (2), 183 - 197.
  • Steen, L. A. (1988). Calculus for a new century: A pump not a filter. (MAA Notes No. 8). Washington, DC.: Mathematical Association of America.
  • Tall, D. O. (1987). Whither calculus? Mathematics Teaching, 11, 50 - 54.
  • Tall, D. O., & Vinner, S. (1981). Concept image and concept definition in mathematics, with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151 - 169.
  • White, P. (1990). Is calculus in trouble? Australian Senior Mathematics Journal, 4, 105 - 110.
  • Zorn, P. (1992). Symbolic Computing in Undergraduate Mathematics: Symbols, pictures, numbers, and insight. In Z.A. Karian (Ed.), Symbolic Computation in Undergraduate Mathematics Education (pp. 17 - 29) Washington, DC.: Mathematical Association of America.

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