Rethinking the School Curriculum for a Computer Animated Medium


Mícheál Ó Dúill
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There has been a presupposition throughout the process of introducing information technology into education that IT will enhance learning. This was the motivation for the origination of Logo. The paper expands upon the thesis of the Outcome of EUROLOGO’95. In the light of the development of representation from pre-history to the present, it is suggested that we need to take more into account our media of representation. It is proposed that we divide representation into three phases: sensorimotor, formal and active. Our present educational curriculum, from school to university, focuses on formal representation. Active representation first became possible with the stored program digital computer. It is suggested that this discontinuity in our representational capability renders the curriculum obsolescent. A signpost to an active representational curriculum is erected and a potentially pivotal role in charting the route for Logo, as a computer language, is sketched.


Representation, curriculum, Logo, computer, obsolescence

1 Introduction

Within the Proceedings of EUROLOGO’95 there is an errata slip. This states that the phrase ‘embed Equation.2’ should be read as ‘® ’. The error may well have come about because the author cut out a right pointing arrow from elsewhere and pasted it into his text. On paper this would have presented no problem, however, within the computer that simple arrow came with a wholes set of relations, a field code, which emerged as the document was converted from one software format to another. This error graphically illustrates the thesis of the Outcome of EUROLOGO’95. It was asserted that IT provides us, for the first time in history, with the capability to represent time-dependent processed in writing. This paper seeks to re-evaluate the thesis of the Outcome and expand upon its consequences for Logo and the curriculum.

2 The Story of Writing

In the Outcome [1] the computer was categorised as an instrument of representation, an active-writing instrument. When provided with input/output peripherals that interface with our sensory faculties and motor capabilities, the ‘PC’ provides us with a novel epistemic communication medium. This understanding of IT hung upon the examination, from a long historical viewpoint, of two interrelated aspects of writing: the minimising of the graphic and the energising of the instrumental.

2.1 From drawing to digital

In the cuneiform writing of 3000 BC Uruk we may see, with historic hindsight the potential for binary representation. A simple wedge shape impressed into clay using a stick was first used to produce stylised pictographic forms. Some four centuries later these same spatially arranged wedge shapes began to be used for a phonetic text. Using on the rebus principle, many drawings came to represent the syllables of the Sumerian language. This system lost its rebus character when it was later used to write the successor language, the Semitic Arkkadian of the Babylonians, in which form it survived until the time of Alexander.

The simplicity of mark and space was lost with fully phonetic representation, as in the Greek alphabet. Typically, twenty five distinct characters were use to represent the meaningful sounds of a language. It was not until Leibnitz, (C1700), demonstrated that two characters alone are required to carry meaning, that this minimalism resurfaced. Its first practical application came when, in 1837, Morse developed a binary code for the telegraph. Forty-eight combinations and short and long of electric pulses represent letters, numerals, punctuation - and instructions to the human receiver. A century later patterns of timed electric pulses were employed to ‘teletype’ alphabetic characters, using what we would now call a five bit binary code.

In the mathematical culture surrounding the computer we are mistakenly conceive binary representation as the ‘numbers’ zero and one. Study the very first computer program and it is clear that these two characters may stand either for data (a number) or instruction (e.g. stop) yet are neither. These two characters the end point in the development of writing. Computer ‘multimedia’ demonstrates just how powerful binary writing as a means of representing the world. Within a single medium the sensory media of sound and vision; text and picture; speech and song are all encoded in an ever-changing quadrille for two characters.

To summarise, writing has reduced from an infinity of pictures scratched in clay to representation in patterns of two characters. To signify these characters for purposes educational it was suggested in the Outcome that we might adopt zero and zed (0 and Z); with apologies to Frank L Baum’s Wizard of OZ, better to make their post-alphabetic nature clear.

2.2 Instruments of representation

Writing instruments are an unusual form of tool. We use them to represent rather than re-form nature. Archeologically, tool using appears to have significantly predated image making. Yet at some, unidentified, stage the points and blades used to cut and scrape came to be used to incise designs and form the instruments used draw and crayon animal images on cave walls.

The characteristics of a writing instrument, in conjunction with the phonetic characteristics of a spoken language, influenced the form of writing. Brushes and soft pens facilitate a flowing right to left pushing movement, from the body’s midline outward but sharp pens tended to snag the writing medium when pushed. Over time cultures that used hard nibs, like the goose quill, developed scripts where the writer pulls the instrument left to right across the midline, favouring individually formed letters. We see this effect in the differences between the discrete letter forms of the Roman alphabet and the multiple character forms of flowing Arabic script.

The mass manufacture of steel pen nibs following the industrial revolution was perhaps the greatest facilitator of popular literacy. In the years 1820 to 1850 they fell in price from 2d each to 2d a gross (including box). That other stimulus to the democratisation of knowledge, the printed book, was similarly facilitated by the individualisation of letters in the Roman alphabet. Cast into founts, the printer had merely to select and sequence characters to a spell word or compose a formula. In turn, this fount stimulated efforts to augment the pen with a ‘type-writing’ machine. The first, a capitals only machine, appeared in September 1873. It was now possible to write by selecting, rather than forming, letters. The first instrument for binary writing was developed well before the typewriter. In 1844 a telegraph key, no more than an electric switch, was used to send a public telegram in Morse code. A century later, the teleprinter provided the first mechanical interface between the alphabet and binary coding.

On June 21st 1948, as Manchester schoolchildren were dipping steel pen nibs into inkwells, at the University we first employed a radically new instrument of representation: the first stored digital computer program was executed. At the instant the Manchester Mk.1 ran that program, it existed simultaneously in two media: in binary code in a notebook like a child’s school exercise book and as flickering dots on a Williams Tube. In the notebook form it required a comprehending mind to animate it; entered into the computer memory electric energy sufficed.

2.3 Energy and the writing instrument

Throughout the history of writing the writing instrument, be it brush, pen or Morse key, was activated by the human hand and the writing interpreted by the human brain. With the advent of a practical stored program digital computer this relationship changed.

In the newsreel covering the running of the first program on the Manchester Mk.1 the term "electronic brain" is used to describe the computer. In Victorian times such talk had been of mechanical men, of automata. Misapprehension of the nature of the medium remains evident in statements such as the following: "that kernel of knowledge needed for children to invent (and of course, build) entities with the evocatively lifelike quality of smart missiles" [2]. Let us not invest our new medium with magic. Let us avoid slippery semantics. Let the principles of physics, of consider energy conservation, entropy and information, be our guide. Our adherence will be to epistemic science rather than philosophical epistemology - noting that the difference between a computer and a typewriter is in how the energy is applied..

The computer differs in that its energy supply is directed at the contents of the record. Conversion of energy implies the capability to do work, to carry out actions. We now have an active record. Our problem is to decide precisely what variety of active record. It is obvious that the computer, like the pencil, is a means of externalising something we keep in our minds. The computer’s capacity to change the contents of its memory locations, to alter its own program as it runs, must map to some new active representation. Given that writing progressed from illustration to recording speech, let us look to the structure of spoken language for a clue. That part of speech which we associate with activity is the verb. It follows that the computer newly provides us with an enhanced capability to represent verbs, i.e. to represent their time dimension within a medium external to ourselves, in a medium unconstrained by biology.

3 Mind and medium

Before we move on to questions of curriculum we need to be clear how representational media have developed. There have been three distinct phases (fig.1).


Figure 1 Three phases of representation


We may schematically to illustrate the energy characteristics of each phase and (fig.2) loosely categorise these phases in terms of Piaget’s genetic epistemology.

Figure 2. The effect of applying energy to our representational capacity (schematic)


3.1 Sensorimotor phase

In this first phase all representation is within the mind. An apprentice stone toolmaker learns by watching a master and by being prompted physically by him. A dancer learns to move to the music and practices those movements aiming at perfection. Methodology is observation, trial, observation and improvement. Representation is within the mind. The learning style of this phase is play and practice, rehearsal without repercussion. Its proto-representational form is the ‘safe’ object with which to act realistically - the toy of childhood.

This style of learning is most obvious where a craft skill is being developed. The plasterer’s mate will be prompted to perceive the consistency for the mix, the setting characteristics of gypsum, to practice the movements of the float, through a complex of sensations. A novice welder learns to differentiate the visual pattern that is the pool of molten metal at the tip of the flame from the white noise around it and to master the wrist movements required to control it. Language plays the part of prompt to perception. All representation, as in chess, is within the mind. The culture is of finely tuned perception and bodily co-ordination, like that of bushmen.

In schools today this phase is most evident in the learning characteristics of pupils with severe learning difficulties, particularly those who have no language skills, who learn best by imitating behaviour. In mainstream education the games field evidences its enduring importance.

3.2 Formal representational phase

This second phase maps to Piaget’s pre-operational, concrete operational and formal operational stages, all of which find representation in the development of writing. In children’s learning, as in history, the two forms of language, spoken and written, initially independent, come together at rebus level quite early, whilst the full establishment of the arbitrary sign systems of alphanumeric representation take a long time to mature, because, although both speech and drawing are both formal representations of the world, only drawing has direct links with concrete representation. The emergence of the alphabet from the pictorial provides a model for the shift from concrete to formal operations. In the elementary school children learn to use language and pictures, writing and drawing, as an aid to planning, problem solving and communication. This is a complex mental process requiring the support of an institutional structure, leading to casualties, such as those termed dyslexic, who cannot ‘excel’ within it.

In the process of learning to read both text and diagrams we learn how to relate the ‘data’ we may represent externally to the ‘processing’ - the function - which must take place in our mind. Children learn that they may write down what is said but not how it is said. This is the road to Piaget’s stage of formal operations. We need to learn to relate not only the speech sound we make to the alphanumeric notation we use, but to connect this relationship back to real world referents. We may view Piaget’s operational stage as one of freeing up mental capacity better to handle processes by developing techniques of externalisation of object representation. These are the "written and part-written methods of computation" [3] taught in our schools.

In this phase externalised knowledge is rendered in an objective, nominal form. The student, by studying drawings and writings stored in libraries can stand on the shoulders of generations that have gone before. Learning is no longer ‘from scratch’ in each generation, so progress may accelerate. But the student’s mind must provide the rules that animate the relationships between objects. Those familiar with the theories relating energy, entropy and information will appreciate how the externalisation of the representation of form might enable the mind to build upon what had gone before; how effort expended on learning literacy skills facilitates a focus on process; and how, with the harnessing of fossil energy, technological progress might accelerate. We build the increasing precision of our energy-converting industrial society upon the less precise instruments of our parents, because our minds concentrate on the calculation. The computer is a person.

We may typify this phase by contrasting the engineer with the craftsman. Where the masterpiece of the craftsman is an object, the masterpiece of the engineer is a design. It is a formal representation on paper of what is to be built. The engineer does not build it and the design engineer requires very different skills from the craftsman. A steady eye and deftness of touch are superseded by a capability to relate formal representation - architectural, mechanical, electronic drawings, formulae and equations - to reality’ to break down problems into mind sized segments, and skilfully to carry out in the mind complex operations relating the parts to the action of the whole. We might cite the skills complex of Charles Babbage as an exemplar.

School and University are essential to education in the representational phase. School provides a grounding in the intellectual skill realignment required, selecting out those with the greatest capacity for mental processing. University today, as in Greek times, focuses upon honing such mental skills of distilling and relating recorded information. In their libraries lies the store of information; in the minds of their professors are found the skills of information processing.

3.3 Active representational phase

The Manchester Mk1 having successfully run its first program, we newly possessed a medium within which active relationships between the objects we can represent might be played out.

It is obvious there can be no Piagetian ‘stage’ to fit this phase, because Piaget could not use the computer as a medium of representation. He worked with only with the preceding representational systems: play, formal representation and their relation to oral interchange. He studied the genesis of precisely those mental operations that the Mk.1 externalised. It is essential that we now begin to determine precisely what this ‘post-operational’ stage entails. The first step is to give it a name; the Greek ‘logios’ [4] is a good candidate. It follows from the novelty of our new capability that there can be few examples of the manner in which logiostic learning might progress. Is it necessary to pass through the proceeding stages? To what level do children need to develop skills associated with earlier phases? At what point in education should the shift be made to logiostic learning? What pointers do we posses?

Let us gather parallels from the preceding phases. If we relate the craft-skill based blacksmith to the steam-driven manufactory and thence to manufacture of computers, we see the steady erosion of the requirement for craft skills and its replacement by those of design and machine management. We have now extend the application of energy from machines for the making of objects to those for the making of relationships. It follows that there is a range of ‘intellectual craft skills’ which are capable of being externalised. The first step in determining what we now need to teach is to identify processes that have, or are being, externalised and eliminate them.

The calculator is causing consternation, speech recognition will shortly threaten the pen nib. It is fairly clear that mathematics, which relies on high levels of cognitive facility to animate notation, will now have to redefine its educational goals. The mental skills that would seem to be required are those related to conceptualising the ramifications of the problem and thereby the reasonableness of the representation within the new medium. Similarly, written language craft skills will need reconsideration. Now that the medium itself may neatly write letters of the alphabet selected at a keyboard, transpose speech into words and words in to speech, check grammar and spelling, provide on-line dictionaries and thesauruses, and render the words of one language into another, perhaps literacy might focus sooner on expression and meaning. And, no doubt, new set of educational syndromes will be thrown up to complement dyslexia.

Of all educational institutions it is the University that will need to change most. Once we focus clearly on the processing capability the computer gives us, we see that more than mere access to information is implied. Research craft skills would appear to be as capable of external representation as mathematical craft skills are on a calculator. Our minds, relieved of aspects of sifting and processing information will have greater capacity to increment learning faster to accelerate epistemically. We may find more time to sharpen Ockham’s razor, to make actively informed decisions, and to work more at meta level. As we each use energy to supplement our own capacity perhaps we will free ourselves to think at a more strategic level. If the University is to change then so must School in its curriculum and pedagogy, if not its social organisation.

3.4 Transitional Turtling

Phase three in the development of our representational capability brings with it discontinuity.

How we might reconstruct our curriculum to cope with the computer is uncertain. We are presently in an intermediate phase, which the Turtle may be used to illustrate. Let us recall that Logo initially had no Turtle. Though specified with mathematics teaching in mind, many of the problems it enabled children to program solutions for were word oriented. This exemplified the capability of a programmer to manipulate the memory contents of a stored program digital computer. The Floor Turtle, with its commands F, B, L, R and Beep, was added around 1971. The question, "What does the Turtle do?" is answered with, "Given the two part instruction ‘forward :n’, it draws a line of length ‘n’." The relationship between a Turtle and its drawing is isomorphic with that of a CNC machine tool to a workpiece. When the Turtle left the floor and became an arrowhead on the screen it emulated the character of the pencil on paper drawing. Let us apply the model of representation developed above to Turtling (fig.3).

To square
repeat 4 [forward 50 right 90]

Figure 3. A Turtle procedure and the ‘resultant’ drawing.

When a word-processor was used to produce this figure the square had ‘ears’ which enabled its shape to be changed by dragging it with the mouse. This did not, of course, have any effect on the text of the procedure. In Turtle graphics I cannot drag out the square because it is a representation of a pencil and paper visualisation. I can draw another one by changing the parameters and re-running the procedure. Notwithstanding that all representation within the computer is of equal status, the screen drawing is as fixed as its pencil on paper precursor.

Let us, mentally, give the two representations equal status and link them so that the procedure must always be a true description of the drawing and vice-versa. Dragging out the square would result in a change in the numerical parameters in the procedure but the symmetry of a square, reflected the procedure, prohibits the square being dragged out into a rectangle. The drawing is not longer a visualisation of the procedure but a parallel description. The process of permitted transformation is represented in both the change of numerical parameter and side of square. A pupil may now address the concept of ‘square’ via interaction of text and illustration.

Couple the Turtle’s retention of the paper and pencil drawing metaphor with the expertise of teachers in that medium, contrasted this with an almost universal innocence of the nature of the new medium and it becomes clearer why the adoption of turtle geometry by mathematics teachers led to the displacement of Logo by Turtle graphics packages. Producing shapes using simple Turtle procedures relates backwards to the pencil and paper algorithms mathematics teachers traditionally employ. All they required of Logo was the capability to execute such direct sequences of instructions. This helps us comprehend why Turtle graphics came to be sold legally as Logo in the UK. Teachers had no need of the capability of a computer language.

4 Pointers to a curriculum

We noted earlier that a massive reduction in the price of steel pen nibs facilitated the development universal literacy in the mid nineteenth century. (The printing press had only reduced the cost of distributing information, democratisation of the creation of content needed a reliable and robust inexpensive writing instrument.) The cost of computing power is on a similar downward trend, making our new active representational medium available to ever more of the population. It follows that education needs to determine how best to use it.

We take from Jean Piaget a model of children as builders of their own intellectual structures. These structures relate to the three phases of representation, in the employment which children exhibit varying capabilities. Some, in common with the author, cannot co-ordinate ball and bat so do not excel in sensorimotor activities; others, defined as dyslexic, have problems perceiving notation; some have an uncanny capacity to calculate. The English academic Grammar school is quintessentially a creature of the age of formal representation. In English Primary schools children learn the mental structures of sensorimotor ‘kitchen math’ before meeting formal representational School math. In adult life much of day to day life remains sensorimotor based. Our industrial culture is founded on operational aptitude. But in commerce and industry exploitation of the capabilities of active representation is now rapidly displacing the technology of formal representation. It follows that we now need to develop active representational learning, and not only in mathematics. Our problem is that the present ‘formal representational’ school curriculum is obsolescent and yet there is massive institutional resistance to change.

4.1 A revised agenda for Logo

There is a need to recast the rationale for Logo. The original objective of contributing to mathematics learning will need putting to one side whist the mathematics curriculum is reformed. We must, for the moment, abandon all thought of Logo as a ‘learning environment’ within a sensorimotor and formal representational curriculum. The contribution of Logo should now take place in the arena for which, as a computer language, it is most suited - teaching and learning about the nature of the new medium. That is, as an aid to the understanding of IT.

In developing Logo to serve this end, we need to avoid the pitfalls of transitional objects such as the Turtle. Within the Logo community there are some pointers to the capabilities Logo will need. Through the graphic list-processing of Comenius Logo children can explore the processes of digitising continuous activity. Geomland provides a model for the symmetrical relationship between representations, in this case text and drawing, within the medium. LogoWriter, with its capability dynamically to re-write the contents of the procedures page, modelled the active nature of writing within the new medium. The relationship between computer language and the concrete world remains appropriately accessible through LEGO Dacta Control Lab. And the Turtle, with its pen stowed away, remains an attractive and accessible active entity to which, in MicroWorlds, processes may be attached. There is much potential in Logo - provided that users and developers of the language fully appreciate the nature of the medium and focus upon the new capability expressed in the command ‘forward’.

5 Conclusion

In this paper we sought to develop further the core thesis of the Outcome of EUROLOGO’95. To aid our conceptualisation, we mapped Piagetian stage theory to the genesis of writing. This served to expose the underlying structure of the school curriculum in terms of representation. It was shown that the present curriculum is founded on externalisation of objective knowledge and internalisation of operations upon that knowledge. The skills that school expects children to learn are focused towards interpreting and interrelating external representations of objective knowledge to internal relationship processing - relating nouns on paper to verbs in the head.

Given our thesis that the computer provides us newly with a capability to process information externally, it follows that our minds may begin to be freed from internal operational processing. This has consequences for the curriculum. Two linked issues need to be addressed. The first is a requirement to re-evaluate current core curricula - ‘reading, writing and ‘rithmetic’ - in the light of calculators and language processing applications. The second is to determine how best to develop the requisite new mental skills, now that we can externalise both form and process.

The change in the representational medium from passive to active has great consequences for pedagogy. Those who adhere to constructivist over S-R models of learning may delight in the conclusion that once the relationship between stimulus and response is represented within the medium S-R theory has nothing more to say about mental activity. Classic constructivism takes us a little further in that it does accept that learners construct their own learning. Unfortunately the focus is on mental operations and constructivist pedagogy entails supportive environments. So fundamental is the medium change that our vision is blurred and environmental support uncertain. We need a model of learning that encompasses the skills of mental interchange with an active medium. The Greek logios, associated with Hermes, might now appropriately carry passive logos onto the Net and help evolutionary epistemics to displace genetic epistemology.

Where might the skills in working logiostically be found? Given the nature of the change in our representational instruments, it follows that the mental structures and craft skills of the staff of our educational institutions and their academic disciplines are obsolescent. Almost by definition, the new skills we need are unlikely be found in large measure within our universities, for those who work there do so because of they are high achievers in the prior passive medium. This presents education with a fundamental problem.

The computer truly is our children’s instrument of representation and it is to them that we have no choice but look for new models of learning and pedagogy and the new curriculum. The present generation can do little more than catalyse and analyse, with an open mind, some very open learning. But two principles need apply. The first; new applications that relate to the core curriculum need to be used in school as soon as it becomes economically feasible so to do. Traditionally, this would entail researching such applications before low cost level is reached. However, because we cannot rely on researchers to apply appropriate evaluation criteria, the research stage should be positively avoided. The second; enable children to intuit the medium. Traditionally, this we would expect to train teachers to transmit. Yet, we have no appropriate pedagogy to rely on. Hence, we have no option but provide children with direct access to the activity of the medium through a powerful computer language, giving them time to experiment.

To treat Logo as a learning environment is to risk assimilation to passivity, as with the Turtle. Logo exemplifies functional activity within the representational medium. It can therefore, forward the reformation of our curriculum and pedagogy within a classroom context. In order to achieve this end, it its essential that Logo remains unambiguously active. To the ‘calculator’ capability of the earliest implementations we need to add active language and graphic capability, capability to tell a Turtle orally, for an written answer to be heard, for a graphic change to update a procedure. Let Logo be our path to logiostic thought for children.

6 References & Bibliography

  1. British Museum, Reading the Past: Ancient Writing from Cuneiform to the Alphabet, London: British Museum Press, 1990.
  2. Jackson D, The Story of Writing, Monmouth: The Calligraphy Centre, 1981.
  3. Dragoumis M, The Creative Genius of Greece, The European MagaZine, 20-26 March 1997.
  4. Ó Dúill M (Ed.) Building Logo into the School Curriculum. Proceedings and Outcome of the fifth European Logo Conference, Birmingham, 1995. Skipton: Logos. Outcome p125-136
  5. Papert S, Mindstorms, New York: Basic Books, 1979.
  6. Papert S, The Children’s Machine, New York, Basic Books, 1993. p 181.
  7. School Curriculum and Assessment Authority, The National Curriculum Orders, London: HMSO, 1995.
  8. Teacher Training Agency, Training Curriculum and Standards for New Teachers: Consultation on Primary English and Mathematics, London: HMSO, February 1997.
    Paper 4, paragraph B.4.c, p11.