The Education VECTOR
Vector 3:2, page 37
Transcribed from the printed issue; not yet reviewed. Read it in the PDF of the issue, page 37
Welcome to a new feature of VECTOR. In it we shall report developments in the progress of APL in the world of education. And what richer source of material for the opening column than the Education Day organised by Sylvia Camacho as a curtain-raiser to APL86. This event attracted over 100 of those most intimately connected with the combination of APL and education. The attendance included educators of APL, educators with APL, educators without APL, educators of educators, educational researchers, educational marketers. With twelve formal speakers covering such a spectrum, plus a discussion forum, it wasn't surprising that every aspect of education and APL (and its competitors) was touched on at some time, and quotable sayings abounded:
"APL is easy, fun and of great practical use" (Romilly Cocking)
"APL helped me to see the problem, and not only that, it worked!" (Bernadette McAlinden)
"APL is part of the continuing evolution of symbolic notation, and thus of the evolution of scientific thought" (Ray Polivka)
"Students accept it, staff do not" (Bob Spence)
"The biggest constraint to the growth of APL is the people who know APL" (Romilly Cocking)
"APL removes the computer barrier" (Norman Thomson)
"Computer people are learning to be baffled by parallel thinking" (Anthony Camacho)
"The language for problems – pure and symbol"
The opening address on "Executable Analytic Notation in Teaching Mathematics and Programming" was delivered with typical Iverson flair. Attempts to integrate other programming languages with mathematical instruction have failed – only APL has been able to combine executability with analytic power. Its real rival is CMN (i.e. Conventional Mathematical Notation – please memorise new acronym!). There are no courses given in CMN – likewise APL can be introduced "in passing" in a wide range of contexts, given the right concomitants of a dictionary, and a computer to experiment with.
This view of APL as an "emergent" language was reinforced by the talks of Professors Hawkes and Spence, who separately related the naturalness with which APL emerges as the instructional medium for their respective courses with a minimum of initial formal instruction.
Roger Knott from the Centre for Mathematical Educational Technology at Loughborough University also sang the virtues of an emergent language. The emphasis of his Institute is on mathematical investigation, an area in which candidate languages, e.g. LISP, APL, LOGO, must compete on the grounds of power, expandability, good support features and the capability to add excitement. In spite of the clear advantages of a computer as a super-calculator and as a calm, uncriticising "student's friend", there remained a residual, irrational hostility of teachers towards it.
Further sound advice in this direction came from Roy Atherton of Bulmershe College of Education, Reading. The promotion of APL in schools has to be supported by an honest case and good materials.Explicit thought should be given to the target audience – is it the brightest pupils or all pupils; have pilot projects been considered; and is there a realistic view of the time frame for success. Taking structured programming and modern mathematics as analogues, a decade seemed about par for introducing something new, surely a sobering corrective to the impulsive energy and impatience of APLers who above all think in terms of making things happen now!
Romilly Cocking aired his concern at the failure to produce new APLers at the level of secondary and tertiary education, and added advice as to why APL has not taken off as it should. Avoid the dangers of oversell, he advised, and the temptation to over-reach the audience. Occasionally the APL message gets through quickly, but more often hostility, conservatism and indifference result in scepticism (APL too good for its own good!), horror stories, or "reasoned" objection, handed down and absorbed in lieu of knowledge.
These experiences found echoes in Ken Johnson's talk. Ken is from the Artificial Intelligence Unit at Edinburgh University, where he has promoted the introduction of LOGO into the Scottish secondary school curriculum, the rationale for which is similar to that for introducing APL. Where officialdom does not understand, its response is to ignore – note the total absence of LEA representatives and maths advisors present, in spite of an intensive mailing and advertising campaign. Ken's talk led to an interesting discussion about the break-off point between "easy" LOGO (accessible to 8-year olds), and "difficult" LOGO (beyond school level). There is a similar break-point in APL, but surely this comes at a much later stage making APL a much more suitable language for backing the secondary curriculum. It was good to have the two foremost promoters of APL in American public education present, namely Linda Alvord and Howard Peelle, and some comfort to know that the Americans have similar problems at this level.
Anthony Camacho put forward a view of programming, in which the power of forthcoming parallel processors will be unusable except in APL because of the inability of traditionally educated programmers to think in parallel. The theme of parallelism was also taken up by Dr. Frank Evans of South Bank Polytechnic in examples of how multi-dimensional arrays and other APL features naturally match problems arising in the chemical and oil industries. APL produces a unique programming environment, he concluded. It was interesting to hear this academic view balanced a short while later by Bernadette McAlinden's admission that in the real world of Tesco Stores (18,000 product lines!), the purity of multidimensional arrays with 525 planes was sometimes tempered with a "scissors and Sellotape" approach!
One fact that nobody could doubt by the end of the day was that shortage of money is the biggest barrier to the progress of APL in Education. In the concluding talk, Ray Polivka declared starkly that money is in Industry, and it thus behoves us all to increase APL's exposure by writing letters to the technical press in order to stamp out misconceptions and to let the Captains of Industry be in no doubt that APL is a language of industrial strength.
The above were just some of the riches to which I added my plea as Education Officer for action to get something moving in British schools to make the APL terminal an unobtrusive presence in the classroom and thus realise some of its great possibilities. This, I said in apology to overseas visitors, was a U.K. concern – how wrong I was! The events of the ensuing week winkled out the parallel concerns of our American cousins, and led to the formation of a group dedicated to the publication of a Public Domain APL for small machines, e.g. the BBC Micro, on both sides of the Atlantic. The joint Chairmen are Anthony Camacho (UK) and Ed Cherlin (USA). British members are Dave Ziemann, of Cocking and Drury, Sylvia Camacho and myself; US members are Howard Peelle and Linda Alvord. We hope to raise sufficient funds to have Paul Chapman implement the portable product. Meanwhile Inner Product have announced that they are putting the VIZ::APL product into the public domain with immediate effect to the benefit of those with 8-bit CP/M machines.
I shall be happy to hear from anyone in the educational world about positive things that they are doing with APL, which I may not already know about; please write to me at:
[address omitted]
Roy Sykes said in his closing address at APL86 that the next phase for APL was not more technical progress, but wider dissemination. The most important aspect of this is Education, through which, given the medium of public domain APL, we shall in time address an audience not of thousands, but of millions!
Teaching Statistics through APL¶
APL is alive and in action at Swansea University Statistics Department – that was the message of Alan Hawkes' tutorial, and to prove it Richard Green's fingers roamed nimbly over Barco-connected keyboard, illustrating the words of his professor as he talked through an outline of the APL-based course given to all first-year statistics students. There is no formal APL instruction at this stage – APL is learnt in the context of statistics by having the students use a workspace of utility functions which enable them to draw histograms, obtain standard descriptive statistics, calculate expected values, produce binomial distributions, and construct Operational Characteristic Curves for acceptance sampling.
In the second year, there is an optional course on Statistical Computing, which includes a more comprehensive study of APL. In the third year, projects can be based on APL, and at this point Richard took the floor to talk about the influence of APL on the project he has just completed on nesting sets of rectangles within each other.
Alan then talked through a first-year case-study involving the analysis of predicted birth dates of Glamorgan babies based on ultra-sonic scanning as one method, and mothers' forecasts as another.
In all, this turned out to be a convincing demonstration that APL in education works!
Topics for a second course in APL¶
In Mobil Labs, APL is the medium for numerical literacy of the research scientists. Following a basic course and a little experience, upgrade skills are necessary and Stephen provides these through a series of three lectures on advanced APL, given at weekly intervals. The first is on controlling multi-dimensional arrays; the second on special uses of grade and scan; and the third on building interfaces from APL to other parts of the system.
This tutorial was a compressed version of these three lectures, emphasising how real-life examples from the Labs are used to illustrate and motivate. Those who have taught advanced APL must have picked up many echoes from their own experience, e.g. the difficulty of explaining in English why double grade-up produces rank in the combinatorial sense! Stephen's informal rules for handling multi-dimensional arrays, and his practical tips for juggling with axis lengths, are part and parcel of the business of teaching APL. Although this material could have been written ten years ago, this is the first explicit statement of such pedagogic considerations, and the accompanying paper in the Proceedings should be a valuable source for APL teachers.