1. Home
  2. Peer Review: COW -- Calculus on the Web

Peer Review

COW -- Calculus on the Web

Reviewed:
Jun 29, 2005 by Mathematics
Bookmark

Ratings

Overall Rating: 4.0 stars
Content Quality: 5.0 stars
Effectiveness: 4.0 stars
Ease of Use: 5.0 stars
Overview:
This site is devoted to learning mathematics through practice. Many dozens of
practice problems are provided in Precalculus, Calculus I - III, Linear Algebra,
Number Theory, and Abstract Algebra. The last two subject areas -- referred to
as "books" on the site -- are under construction. To each topic within a book
(for example, Epsilon and Delta within Calculus I) there is a "module" of
approximately 20 to 30 problems. Each module also includes a help page of
background material. The modules are interactive to some extent and often
provide suggestions when wrong answers are entered.
Type of Material:
Drill and Practice.
Recommended Uses:
Student practice.
Technical Requirements:
A JavaScript enabled browser.
Identify Major Learning Goals:
To promote the learning of mathematics through practice.
Target Student Population:
Students who are studying Precalculus, Calculus I - III, Linear Algebra, Number
Theory, or Abstract Algebra.
Prerequisite Knowledge or Skills:
Since the learning material presented here is devoted to practice rather than
instruction, students should be familiar with the concepts and methodologies in
the stated subject areas.

Content Quality

Rating:
Strengths:
Just the sheer quantity of practice material here is impressive. It is enough
to keep students busy -- and profitably so -- for many hours. The problems are
clearly stated, nicely rendered graphics complement many of the problems, and
encouraging, often humorous, comments are provided throughout. The practice
problems within a given module (topic) are not automatically generated; while
this limits the number of practice problems, the authors take good advantage of
this “limitation” by providing many different kinds of problems instead of
near-replications of the same problem. The coverage of topics within the
calculus books is quite thorough, and the range of difficulty in the problem
sets is adequate for the purposes of a drill and practice learning site.
Concerns:
None

Potential Effectiveness as a Teaching Tool

Rating:
Strengths:
Even though this is a “practice” site, every module (or topic) has a help page
which contains basic explanations of concepts, tables of formulas, and worked
out examples. Also, wrong answers always result in some kind of interactive
comment and graphic aimed at setting the student on the right course – and often
humorously, at that. Some of the more difficult modules use the first problem
in the practice set as a worked-out example. Several modules are designated
“hands-on” and use JavaScript to allow students to experiment with concepts by
changing the values of certain parameters and immediately seeing the graphical
consequences. Clearly, any student wanting additional practice in one of the
areas covered on this site will benefit from her/his time spent here.
Concerns:
Practice on basic trigonometry is sketchy, both in the Precalculus book and the
Calculus I book. This is not a big concern, since the major emphasis of this
site is on the calculus. A somewhat more serious concern is that the modules on
limits, derivatives as slope, some applications of derivatives, and several
other topics with strong graphical consequences have few or no problems
involving actual graphs. The methodology in these modules is exclusively
algebraic, whereas these topics lend themselves so naturally to graphical
approaches. For example, the modules on Graph Sketching under Applications of
the Derivative have not a single graph represented among the problem sets. It
would have strengthened these modules to have considered this and to have
included more graphs and maybe even more of the hands-on modules that are
employed elsewhere on the site.

Ease of Use for Both Students and Faculty

Rating:
Strengths:
Indices to the modules (topics) within each book (subject area) provide easy and
convenient navigation. The site provides a wonderfully thorough introduction
on how to use its features. Buttons that link to additional help or site
guidance are almost always available. Also, the pages involving JavaScript
worked flawlessly.
Concerns:
None
Other Issues and Comments:
This review does not evaluate the “recording/grading” feature of this site.
That feature is exclusive to students with logins and passwords.
Creative Commons:
creative-commonscreative-commons by