Science Education in California

Transcribed from the printed issue; not yet reviewed. Read it in the PDF of the issue, page 22

The Chevron Corporation in La Habra has a programme of science instruction to 5th grade students. The programme, called Adopt-a-School is currently available to three grade schools in the La Habra (Southern California) area.

Volunteers are mostly employees of the Chevron research facility in La Habra, but there are also several of us who have retired in recent years. Under the programme, one day a week is devoted to one of the schools. The volunteer in charge for that particular day spends one period (about 45 minutes) with each of four or five classes, mostly 11 to 12 year olds. The subject of study is generally some aspect of science. Examples include the study of fossils, simple experiments in physics, and construction of simple objects.

At the time I found out about this program, I was involved in writing lessons for I-APL. It seemed a good idea to try to extend my work by volunteering in this project.

Clearly, 45 minutes (or as someone pointed out, one micro century) is too short a time to teach APL, but it may be sufficient, I thought, to create a favourable impression that could in time motivate some of the students to pursue a career in maths and science.

Right away, I bumped into a road block, when I discovered that the only personal computers available for instruction were the Apple IIe’s. I proposed to give a lesson in elementary maths instead, but I-APL came to the rescue with the announcement of a version for the Apple IIe. Mr Rolf Levenbach was kind enough to send me an early copy of the version.

I was able to access the Apple IIe about one week before the sessions were to be started. The time allotted was much too short (about 5 hours), and my total unfamiliarity with the Apple operating system was a great handicap. Fortunately I had prepared a session in advance using I-APL on my IBM PC/XT. At first, my approach kept changing from session to session as I was getting feedback from students’ reactions and from the extremely slow response of the computer.

On a typical day I have 4 to 5 classes (each class with different students). The room facilities include 12 to 15 computers, and a blackboard. This year two of the schools also had facilities to project the monitor display on the screen. I have an assistant volunteer from Chevron to help me, and there is usually, but not always a teacher or a teacher’s aide with each class. The size of the class is determined by the number of computers in the room. There can be no more than two students sitting at each keyboard. To complicate the problem, one of the schools has a group of students who do not speak English. This class requires an interpreter, and I must say that this particular session is somewhat discouraging.

Clearly 45 minutes is totally inadequate for an extensive training in APL. However, I have gradually developed an approach that seems to give the students some idea of the excitement that APL users have when exploring the power of this language.

When the class enters the room, I request that the students sit in front of me and the blackboard. Then I explain that computers are quite "dumb". They do only what they are told to do. To illustrate this, I pretend to be a computer, and ask them to tell me to draw a square on the blackboard.

The first class in the morning usually has a hard time figuring out that the first instruction to me should be to pick up the chalk. By the time I get to the last class of the day this exercise goes pretty fast.

My next step is to write on the board the number 2, and ask: "What is the square of 2?" We then discuss the graph of a square and the number square. Once the students accept the concept that squares are obtained by multiplying a number by itself, I ask whether it may be possible to get squares by adding numbers instead. Using graphs again, I show that the first N odd numbers add to N squared.

At this point I mention an 11 year old boy named Karl who lived about 200 years ago. (Of course I refer to Karl Friedrich Gauss.) Karl’s teacher asked his class to add the numbers 1 to 100 (actually this is a simplification), and was astounded when Karl came up with the answer in seconds.

I tell the class that we will next go to the Apple keyboards and do some exercises. At the end of these, if the students pay attention, they will not only be able to solve Karl’s problem, but some may even figure out how Karl did it.

In the I-APL session, the students are asked to enter their names. The names are reversed, and the students are given some problems in arithmetic. For example they are asked to add two numbers. If they do it correctly, they see a "happy face", and if they make a mistake they see a "sad face". Some students never get past this stage.

The next problem is to add a sequence of three numbers using reduction (+/). If they get past that they see exercises in multiplication. First two numbers followed by a product with (×/). About half of the students get this far. In the next exercise they learn how to store a numeric vector and how to rotate it. They also learn to use the index generator (iota). Some students get trapped here spending the rest of the time displaying ⍳X where X is some large number. When ⍳5 is added to its reverse, they see a vector of constants. Very few students recognize this as an important clue in the solution of Karl’s problem.

A few students with some help end the session understanding the expression +/⍳100. So far (after instructing over 600 students) no students discovered on their own Karl’s solution of adding the vector to its reverse, reducing the result and dividing by 2. (Several got there with a little help.)

Invariably there are some students who finish the lesson early, but show no interest in arithmetic. These usually ask me for some other "game". I do have a second exercise which shows manipulation of character strings. An array of words is generated, and the students learn how to rotate it, transpose it, and are challenged to find a pattern that will produce valid words no matter how this array is displayed.

From my experience so far, the fifth grade (ages 11 and 12) seems ideal for the introduction of concepts in science and mathematics by individuals from outside of the school. I believe that even a short exposure, if it demonstrates the beauty and challenge of maths and science, will have a significant effect in later years of the individuals.

CPCUG APL Lessons Available for Several Interpreters¶

A series of 26 interactive self-teaching on-disk lessons is now available for TryAPL2, IBM APL2, STSC APL*PLUS and Pocket, Sharp, and I-APL. Based on the work of Z.V. Jizba, these lessons were transferred to multiple APL formats by the APLSIG of the Capital PC User Group (CPCUG) for use in their 1991 APL classes. Lessons were edited to make them more generic, and to incorporate classroom experience.

CPCUG lessons are downloadable free from the BBS\APL: 301-384-3672, 300/1200/2400 baud, N-8-1, 24 hrs. See File menu Y. Lessons may be ordered by mail from HRH Systems, Box 4496, Silver Spring MD 20914 USA, for $US19, postage paid worldwide. Mail orders should specify disk size and APL version (.TRY, .ATF, .AWS, .SAW, or .IWS). Cheques accepted in any national currency. Lessons will be sent free upon request to Eastern Europe and the Soviet Union.

Dick Holt, HRH Systems, Box 4496,
Silver Spring MD 20914 USA.