Aren't you using a microcomputer to 'do' your math?

At the private Cate School in Santa Barbara, you have to keep the computer room spotless or they close it for 24 hours, and you may only play commercial games between 5 and 6 p.m. weekdays. You can play games you design yourself any time from 8 a.m. through 10:15 p.m.

At Math City in Rolling Hills, you can make up a year or two of arithmetic in a couple of months using software developed by Math City founders.

At Thatcher, a boarding school in Ojai, Calif., the computer room is open 24 hours a day and the electronics club combines microcomputer and radio technology.

At the independent day school in Flintridge, Calif., the more experienced programmers are competing in the national American Computer Science League.

And back at Cate School, some of the more advanced students may take a computer statistics course where they learn to calculate means, medians, variances, and standard deviations from lists of numerical data.

Math City is a private institution - not a school; it is a place where students of every age can get math assistance.

Do you plan on taking the GRE or SAT? Math City will give you a diagnostic test, then provide tutoring to fill in any gaps.

Blair Sullivan, co-founder of Math City, and a former teacher in Watts, explained that Math City had developed its own software to help children in grades 2-8 who were having trouble with arithmetic. By following the ''Mathware'' program on one of Math City's microcomputers, youngsters learn what they have missed.

Tutors, all with at least a B.A. in mathematics, work with high schoolers and adults. And much of what is offered is enrichment, particularly some fast-paced summer courses.

Blair Sullivan also explained that Math City gave some consideration to including a sort of arcade for computer games, but dismissed it. As she asserted , ''That would say to kids that games are some sort of reward when we want success in math to be the reward.''

Both public and private schools are struggling with the plethora of commercial computer games which are growing fast in popularity.

Most of the games are not reinforcers of program strategy, but involve random activity often involved with disaster and destruction. For example, ''Dungeons and Dragons'' is now available on disk form for use with microcomputers.

The problem of software games and school microcomputers is, teachers allege, only beginning.

The Math City software makes extensive use of branching in an effort to engage the student in building on math concepts, as well as giving users a sufficient amount of arithmetic drill.

Math City programmers have been working on an algebra course, and have the advantage of being able to ''de-bug'' as they go along by using their own tutorials as ''subjects.''

In a brief conversation with a mother who is taking a junior high student to Math City for tutoring, she admitted that the public schools in her town were doing, in her estimation, a progressively worse job of teaching math.

Math City tutors confirmed this impression as they find not only more clients among young adults but increasing confusion about how to ''do'' math on the part of younger school pupils.

Are microcomputers just another fleeting school fad? If this question is put to those who work daily with them, the answer is a resounding ''NO!'' The busy terminals in Math City and the testimonials by computer room directors emphasize this response.

Just as the word processor (on which this story has been written) has taken over the newsroom, the microcomputer is taking over the math and science classrooms.

To close this brief discussion of trends in math and microcomputers, we offer the following questions - courtesy the Cate School.

* What would one call a man who has spent the day on a sunny beach? (Answer: tangent.)

* A little boy lost his parrot; what did he tell his mother?

* What has three feet, yet can't walk?

* What do little acorns say when they realize that they are grown up?

* What should one do when it rains?

* What do you call a group that lobbies for better farm equipment?

(In reverse order the answers are: protractor; coincide; geometry; yardstick; polygon.)