The Math Forum: 1998 Summer Institute - sum98

July 6-11, 1998 - Swarthmore, Pennsylvania

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Ginny Renzi
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Who Died and Made Calculus King?

Ginny Renzi, M.Ed.

Many students experience some difficulty in attaining proficiency with the conceptually difficult and rigorous mathematics adventure that is calculus. As I contemplate the problems they face, both individually and collectively, I am left with many questions, together with some answers. My thoughts reinforce a long-held belief that there are issues that need to be considered when counseling students regarding appropriate courses, and that these issues should also be addressed in future examinations of curricular design and teaching methods for the various calculus options.

There are implied assumptions concerning the teaching and learning of calculus that are not borne out in the experience of all calculus students or in all calculus classrooms. Calculus students are often expected to learn by the "intuitive approach," which demands certain competencies and learning styles, but who is to determine what these competencies are and whether they exist within an individual student? If math students have not experienced this pedagogical methodology in their previous courses, will a magic switch turn on within them, simply because they have walked through the door of the calculus classroom?

My own experiences in learning calculus, along with those of my students, demonstrate the problems inherent in this approach. I have considered the following questions at length:

What are some of the implied assumptions of calculus instruction?

In reality, which students take calculus?

What should college counselors, students, and parents consider when making the decision for math placement following pre-calculus? What are some other options that should be considered by students who have successfully completed pre-calculus?

  1. Non-advanced placement calculus courses that place an emphasis on how to learn calculus along with the expected course content. Because such courses are not taught to the AP test, teachers can have the luxury of slowing down when needed.

  2. Statistics, either the traditional or the new AP course, can be an equally rigorous mathematical expedition. Unlike calculus, which has little apparent connection to everyday life, statistics proficiency is essential to becoming an educated consumer in today's society. Unfortunately, statistics is not always looked upon with the same favor by the aforementioned college counselors and admissions officers.

  3. Discrete math is the course that is generally recommended to students who need to fulfill their math requirement, who realize that it is not a good idea to take their senior year off from math, or who recognize that calculus is not their best option. The content of this course varies tremendously from school to school but is often not considered by students or counselors to be rigorous enough to warrant consideration for better math students. Whereas calculus builds upon itself continuously, discrete math, as the name implies, includes self-contained units. Consequently, it can be an excellent choice for overly committed seniors.

What causes students to experience difficulty once they are taking calculus?

How can teachers help all students learn calculus?

Finally, I am not arguing that students should not take calculus; indeed, I am convinced that most students can succeed in this rigorous course of study if their learning is properly structured. Even more important, I truly believe that students can enhance their mathematical self-esteem while recognizing the value of their efforts. I wish, however, that I were convinced that this is the case for most high school seniors who take calculus. It would be interesting indeed to see how many of these students continue along the path to higher-level math courses in college.

Ginny Renzi, M.Ed.
Mathematics and Learning Specialist
November, 1997

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The Math Forum
12 June 1998