# Mathematics teaching / Dave Rusin

## General comments for those interested in mathematics education

I wrote up some general pointers on communicating mathematics in email, suggesting workarounds for complex notation problems. You may also need to read this if you use the math newsgroups, or if you are retrieving mathematics information off the internet.

Students who need encouragement to wean themselves of their calculators may be interested in an assortment of calculator errors, particularly those likely to cause some confusion to students who use graphing calculators in calculus courses. Also possibly useful: a Basic TI-82 Tutorial

Students preparing to do proofs for the first time should warm up with a sampler of logic problems to get accustomed to mathematical use of "and", "or", "implies", and the use of quantifiers ("for every" and "there exists"). See also the latest in gleezip technology. Having difficulties mastering the natural-language phrasing of proofs? It's not all cut and dried. Just to sample the types of proofs you should prepare for, I've saved a sample of those too. :-)

Students who are having trouble translating a "story problem" into mathematics might want some hints about using variables. Here is a sample suggestion on how, more generally, to solve mathematics problems.

Students suffering through the Calculus might find TheCalculus.Org to be a useful site. Also related: Calculus Modules OnLine [Nova Scotia Agricultural College], Problem list at U.C.Davis, and Funnels: A More Intuitive Definition of Limit

A useful collection of common errors made by college mathematics students (along with hints about what's wrong about them and what to do instead) is available from Vanderbilt.

Can't figure out the point of mathematics education? Neither can the Car Talk guys

Students (especially first-year undergraduates) might be interested in seeing what instructors think their role is; many students seem to be missing a fundamental understanding of what college education is about. A nice study guide for understanding mathematics is perhaps useful to many students (hint: it begins with the question, "Do you feel that being lost in mathematics is the natural state of things?"). A more concise answer to the question, "How can I study for a math course?" appeared in a discussion group.

Included here is some information regarding education in general, and U.S. collegiate mathematics education in particular. A long description of the US educational system is here for foreigners trying to make some sense of our traditions. (There's plenty for natives to think about, too!) A more current (and arguably more reliable) source of eduational statistics for the U.S. is the National Center for Education Statistics; you might specifically want to consult the Digest of Education Statistics, 1999. (It's a set of long PDF files.)

An indication of the dangerous status quo in the US is in some believable remarks "made" by Senator Helms. Another illustration of the frustrating situation may perhaps suggest to students why calculus instructors sigh so often in office hours (now updated by a similar tale of woe which recently hit home.) Unfortunately, the difficulties are not limited to mathematics, as is shown by the results of a pop quiz I gave to my students.

Other pages at my own web site you may find of interest: