Higher Mathematics

Paper Summary:

This paper recognizes the the growing importance of higher mathematics for young people today. The paper explains its use in the modern technological arena. It claims that there have been a number of studies in recent years that have focused on how to best communicate the concepts of limit and continuity in higher mathematics. The author explores how to help young learners make the leap of intellect required to master these concepts. The paper uses schematic representation to qualify points made.

Table of Contents:
Background and Overview
Studies in the Concept of Limit and Continuity in High School and Early College-Level Calculus Courses
Interactions of Methods and Questions for Further Study.
Real-World Applications of Limit and Continuity Theory.
References

From the Paper:

"Clearly, then, helping high school and early college students achieve mastery of complex subject matter such as calculus frequently requires more than a cursory understanding of how young learners acquire and retain knowledge and what processes serve to facilitate this acquisition and retention. For instance, in their study, "Conceptual knowledge of introductory calculus," White and Mitchelmore (1996) point out that, "Research into the understanding of calculus has shown a whole spectrum of concepts that cause problems for students. In particular, student difficulties with the abstract concepts of rate of change and function are well documented. These concepts involve mathematical objects or processes specific to calculus. Another aspect that needs to be considered is the question of what other concepts are involved in applying calculus knowledge" (p. 79)."

Sample of Sources Used:

• Bezuidenhout, J. (2001). Limits and continuity: some conceptions of first-year students. International Journal of Mathematics Education and Science Technology, 32(4), 487- 500.
• Cipra, B. A. (1988). Calculus: crisis looms in mathematics' future. Science, 239(4847), 1491(2).
• Conaway, B. J., & Reynolds, N. G. (2003). Factors affecting mathematically talented females' enrollment in high school calculus. Journal of Secondary Gifted Education, 14(4), 218.
• Dosemagen, D. M., & Schwalbach, E. M. (2000). Developing student understanding: Contextualizing calculus concepts. School Science and Mathematics, 100(2), 90.
• Ferrini-Mundy, J., & Graham, K. G. (1991, August-September). An overview of the calculus reform effort: Issues for learning, teaching, and curriculum development. The American Mathematical Monthly, 98(7), 627-35.

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