On the screen in front of me is a peculiar squiggle called, for reasons best known to its maker, a Turtle. Beside me sits Barbara Hilberg, cofounder of Electronic Learning Facilitators (ELF) in Bethesda, Md., a woman of extraordinary patience. She wants me to make a triangle.
''You can make a line by telling it to go forward and then giving it a number - no, not 'forward.' Type FD. Good. Now a space. Now give it a number of steps to take. Forty? Good.''
The squiggle has moved up the screen, leaving a line behind it. ''Now turn - how many degrees?'' Memories of my geometry class, from which I emerged with less than a brilliant record, plod back to my mind. Triangles, triangles - aren't they 90-degree turns? I type: R (for right) 90 FD 40.
''You're doing the inside angle of a triangle; you need the outside angle,'' Ms. Hilberg says, cheerfully. ''We always have to show this to adults; kids don't know anything about geometry, so they figure it out for themselves.''
''Remember the Total Turtle Trip Theorem - if you're going to make a closed figure, your turns must add up to 360,'' she says.
Do I really want to participate in a Total Turtle Trip Theorem? And what is 360 divided by 3 anyway? I try: R 120 FD 40. It works!
''Good,'' says Ms. Hilberg in a practiced voice. ''Now finish it.'' OK. ''Now try a square.'' Oh, no!
After some stumbling, we find that the turn is 90 degrees for a square - FD 40 R 90, FD 40 R 90, FD 40 R 90, FD 40 R 90. . . . Isn't this a little tedious? ''Sure it is. How can you make it easier?'' she asks. Well, you could ask it to do the same thing four times - 4 (FD 40 R 90).
''Great. You've just written your first program,'' she announces.
''We can teach this to kids as young as three or four, but six-year-olds do it best,'' she says, calmly.
Does she mean that my son - the one who forgets his mittens and loses his lunch money - could do this? ''Sure,'' she says. ''LOGO was invented just for young children.''
LOGO, a deceptively simple computer language used on some Apple, Texas Instruments, and Radio Shack computers, was invented in the late 1970s by Massachusetts Institute of Technology's Seymour Papert to teach pure mathematics to young children on at least an intuitive level. It gives them all the tools with which to plot out basic geometry: angles and velocity; and addition, subtraction, and multiplication.
Using the turtle, youngsters learn to draw pictures by inventing programs for different shapes - like the square - and plotting them around the screen. With LOGO, the student learns - by himself, or with his teacher when he gets stuck, Ms. Hilberg says - to break problems down into their component parts, apply logical solutions, and build on past mistakes and successes.
Ms. Hilberg is convinced it will develop ''wonderful problem solvers among our youth - something we're weak on right now in education.'' But in a controversial book Dr. Papert wrote describing the system and his work with it (''Mindstorms,'' Basic Books), he claims more than that. By using computers with LOGO, he believes, children will teach themselves mathematics as easily and naturally as they would learn to speak French by living in France. Experiments with LOGO in New York and Texas schools have given some cautious confirmation to his claims, and the language is beginning to catch on in other areas of the country.
''We've been teaching LOGO since last spring,'' says Deborah Blank, also of ELF, ''and I have to say that we've found most of Dr. Papert's claims to be true.'' Children in the 6- to 12-year-old range do seem to pick up the concept of LOGO and the math it illustrates very easily, she says.
But the ELF instructors aren't sure about Dr. Papert's idea of giving LOGO to three- and four-year-olds. ''They come in and push buttons, and something happens on the screen, but what does that mean to them?'' says Ms. Blank.
Mary Jane Bullen, who teaches LOGO to four-year-olds at a Montessori school in Annandale, Va., echoes this thought. ''They can do it, with some adjustment to the program,'' she explains (her version of LOGO has ''Instant,'' single-key commands, and is presented along with a mechanical turtle who crawls around to commands on the classroom floor). ''They even learn to program a few simple ideas. But it's two-dimensional - by the time you get to the computer in math, you've lost a dimension.'' She still prefers teaching very young children with the hands-on, three-dimensional rods and cubes developed by Maria Montessori.
Ms. Bullen also points out that ''for many of our tasks, the computer will be a wonderful tool, but (working with it) does not give children the experience they need with other people.'' She has found that putting two children on one computer adds greatly to the learning - something other teachers of LOGO confirm. ''It's not the end-all (of learning mathematics),'' she says, ''but it does add speed to the process.''