Calculus Quest is a complete online tutorial for Calculus I (Differential Calculus); this is the content part of an online course (Mth251) offered by the Mathematics Department of Oregon State University. (Registration for the course is not necessary to use the tutorial, but is required to access any components on the Blackboard server, such as graded quizzes or discussion boards.)
Type of Material:
Calculus Quest could serve as an online text for self-paced learning, or as a source of individual learning modules for inclusion in courses uses other texts and materials.
Computer with browser.
Identify Major Learning Goals:
Proficiency in Differential Calculus, from limits to related rates and linear approximation.
Target Student Population:
College students or High School students who have mastered pre-calculus.
Prerequisite Knowledge or Skills:
Familiarity with the content and skills of pre-calculus.
Evaluation and Observation
This is a complete online course in differential calculus. Each of the 10 ``stages'' has a hub from which the various sections are accessed, and a valuable list of local objectives. Each section has a quiz for student self-evaluation. The organization and structure of the site are superb. The introductory remarks for each stage are well thought out and engaging.
The quizzes are good tests of understanding of the topics covered. The authors have done a good job of trying to predict and minimize student difficulties in using the site: detailed site-navigation instructions are included, as well as a trouble-shooting page.
The material needs a careful proofreading by an outside reader. Besides one or 2 typos (usually minor) per page there are some careless mathematical misstatements that can be very confusing for students. (These were in the ``Field Guide to Functions'' section which may have been written separately).
Every ``Stage'' could do with more exercises, including more elementary exercises. The jump from the material presented to the understanding required to do the exercises sometimes seemed quite large, especially for an independent reader. (Of course, it must be remembered that the site is designed to be used for an online course, and registered students can discuss problems with the instructor or their classmates.)
The material is presented largely from a `reform' viewpoint, as in Stewart's Calculus: Early Transcendentals, a book which is in fact recommended as a supplementary text. The rigorous definition of limit, and rigorous proofs of limit theorems, are present but definitely not emphasized. Depending on one's personal preference, this may be either a point of concern, or a feature of excellence.
Potential Effectiveness as a Teaching Tool
A good student could learn differential calculus just from this site. It could also be useful for students in conventional calculus courses who need extra explanation and drill on a specific topic. The lessons include interactive applets that are fun to use and excellent at illustrating the phenomena being considered. See, for example, the "mystery function" on the Limits Need Not Exist page.
As mentioned above, an independent reader may very well have some difficulty with the exercises if her only preparation is reading the material on the website. There are also a few places where natural connections do not seem to be made. For example:
In the discussion of limits and continuity in ``Stage 2'', the notion of a removable discontinuity is introduced. Later, in the ``Stage 5'' practice section, there is a discussion of continuous extensions of functions, but there is no explicit mention at this point of removable discontinuities.
It is never explained why the rule for differentiating inverse functions follows, at least formally, from the Chain Rule, so the student is faced with one more unconnected formula to memorize. (Later on, the derivative of the logarithm function is computed twice, once with the inverse formula and once with the chain rule, but even here the connection between the two approaches is not made explicit.)
Ease of Use for Both Students and Faculty
The organization and connectivity of the site make it transparent to navigate. The applets providing interactivity and solutions to exercises do so smoothly.