"Logo" in Curricula - Logo85

Logo 85 Cambridge, Mass

Some suggested issues for consideration if Logo is to be integrated into formal curricula

Liddy Nevile, Barson Research, Melbourne, Australia.

Many schools are seriously considering the implications of including Logo within the curricula. This becomes an issue at two levels; what should the children do and when is a major question; but so is the question of what underlies what they should be doing, and what lasting effects are hoped for if Logo is a part of the curriculum.

I suggest that the latter question should be answered satisfactorily before we even consider the tasks, exercises, activities which will engage the children. We should know why they are using Logo. Once we do have a reason, there is a much greater chance that we will be able to apply the right evaluation criteria to what is chosen and done.

The first question is: Why Logo? •

A number of very different answers are given to this question. Some categories might be:

• to teach procedurality;
• to teach programming — the language of the future;
• to teach programming in a structured way as a means for teaching something else, eg problem—solving;
• to teach Logo as a language for expression, particularly of mathematical ideas;
• to teach Logo as an explicit discipline of thinking; and so on.

Papert, in Mindstorms, described a gap in the developmental stages of children. He identified it as the gaining of the concept of procedurality, and argued that if children knew what it was, many of the tasks which presently elude them could be handled. It was not having the skills to write correct Logo procedures which he saw as the cure for this, but rather that if children became familiar with procedures as entities, perhaps by using Logo procedures, they would have a conceptual framework into which they could tap when confronted by many other "procedural" activities at school. The learning of procedurality is the goal in this case, not what the procedure does.

If Papert's hypothesis is accepted, and one could suspect that many Logo users will believe anything if Papert said it, there are implications for curriculum design. The content of the procedures is irrelevant, and so, presumably, the context. Manipulation of procedures, editing of procedures, development of procedures from other procedures, etc, take precedence.

In real terms, the difference is that instead of encouraging children to make more and more procedures, to gain greater competence in achieving aims with procedures, teachers might be helping children gain competence in making the connections between procedures, in editing procedures, in understanding the status of procedures, etc.

The act of processing a procedure involves a different perspective of procedures. Once this understanding is achieved, it is a short step to being able to write procedures which themselves manipulate other procedures, and the concept of a procedure as a entity can develop.

While many Logo texts aim to promote the ideas of Papert, I find that very few have given this sort of emphasis to the concept of procedures. If Papert is right, and Logo does provide a tool for filling this gap in children's learning, then the benefits in other recognized subject areas, such as math, surely warrant this approach to using Logo in schools. But for this to happen, the topic "procedurality" needs to be added to the syllabus formally. Then more teachers would feel justified in letting the children learn to write Logo procedures, and be freed from the need to always camouflage their Logo activities in 'math' or some other clothing.

For those teachers who wish to teach Logo primarily as a programming language there are some questions to answer.

Alan Kay described the problem of designing a language for the people at the Institute of Advanced Study at Princeton. He said:

"I realized that if I was going to design a good system for them, I would not be able to anticipate very many of their needs at all. What I really wanted was a kind of kit that they could use to tailor their own information resources and tools." (i)

Like the designers of Logo, he wanted to provide the users with a non—prescriptive language.

Kay continued:

"A good programming language is something that can be evaluated not by how it does when its features are working but how it does when it has no features for you."

These words apply so aptly to Logo. Logo is such a good programming language, in Kay's terms, that it is very easily stylized. This is a difficulty with Logo. It is well-recognized that stylized languages "lead" users to particular developments, and that the higher the level of the language, the more likely this is to happen. As Hofstatder wrote:

the programmer "is not forced by the language into writing programs of any particular type, but the language makes it easy for him to do certain kinds of things. Proximity to a concept, and a gentle shove are often all that is needed for a major discovery — and that is the reason for the drive towards languages of even higher levels." (ii)

Logo is not a stylized language and yet its flexibilty makes it vulnerable to conversion. Inadvertently, many teachers take  advantage of this. Therefore, I suggest that if Logo is to be used as a programming language, teachers need to make rational and informed judgements about how this is to be undertaken, and what values are to be associated with the language as a result of the teaching.

In fact, there are a number of teachers who have, thoughtfully, chosen to encourage particular programming styles. For instance, there are many teachers who believe using Logo will develop problem—solving skills, and they have some concept of these which they cannot fail to encourage in the children. Many other teachers can be seen rewarding modularity of one sort or another in the programming of graphic images.

Although the teachers in this group have good motivations, the real success of their efforts is still being questioned. This does not necessarily mean that stylized languages should be condemned, but that the problem is complex, and still not solved. Perhaps simple answers will be uncovered in time, as was the notion that programming a certain way would make non—planners into planners. "Model" problem—solving still challenges the greatest minds, and the virtues associated with holistic as opposed to modular thinking are not defined.

In no sense then, should the efforts of those involved be discouraged, but it is realistic to keep in mind that rigorous and constant re—evaluation is still needed while we lack a means for assessing these approaches.

Perhaps a different approach to using Logo is to focus very closely on the features of the language. Papert advocates using procedurality to teach procedurality. Abelson and diSessa in another way, seem to use the procedurality of Logo as a tool for making Logo a declarative language. Descriptive statements made in a procedural language appear to combine the best of both worlds. I would like to suggest that less substantial thinkers can use Logo's features beneficially too.

The artificial intelligence of Logo is more than a convenience for the user.

When people are operating in a world where they have an incomplete understanding of the descriptions and relationships of objects, they are likely to mis-interpret results. In particular, they are likely to explain a perceived error with what is in fact another error, a modified theory which is generally only consistent with what they know up to that point in time.

Using Logo to model concepts, and the invalid model to generate a more correct one, is an activity which uses Logo power significantly. But this is not always easy to achieve, and often because the teacher for one reason or another doesn't know what guidance to give.

In "Thinking about (TLC) Logo" (iii), John Allen praised Logo bugs for the fact that they could be located. Margaret Donaldson (iv) argues that if errors are to be instructive they should be recognizable. Absence of these features of errors presents great difficulty to learners normally, but using Logo the bugs can become helpful.

List-processing is one of the great features of Logo because it makes everything so easy. Instead of having to worry about a collection of things and what is to be done to them, the list processing facility allows the user to concentrate on what is to be done, and the user can leave all the doing to the computer. One suspects that this is not the common view of list-processing in Logo. "Learning list processing" is seen by many as a great achievement, and the majority of modest Logo users struggle to avoid it.

But those who do master list processing find that being able to put the emphasis where it belongs, on the rule for the processing operation, makes Logo a very good language for describing and identifying classificatory principles, and can help develop a greater facility for the same thing in natural languages. I suggest that if list-processing is seen in this light, its benefits can be enjoyed by far more users.

Recursion is another scary feature of Logo. Many Logo users do not persevere beyond the simplest uses of tail recursion. It is too hard. That seems extraordinary when by its very nature recursive definitions are (recursively) simplifications of themselves. Perhaps there is a fear of 'the hard questions', the ones which cut through to the essence of the issue, whic pervades peoples' use of even Logo.

The notions of micro-worl and de-composition are familiar with many teachers; yet these same people have often not realized that the most powerful de-composition aid provided by Logo depends on the recursive facility, and its relationship with Logo list-processing.

More generally, many teachers may benefit from attempting to replace their own strictly algorithmic approach to complex tasks by more generalized ones which include recursive operations, declarative and procedural thinking, and fondness for errors. And then Logo's qualities will be more widely appreciated. If teachers do try to broaden their perspective, they may well need help: they will be learning to understand the culture of tomorrow, and the children they teach.

References

(i) Alan Kay, The A.I. Business, p 172.

(ii) Douglas Hofstatder, Godel, Esher and Bach, p 200.

(iii) John Allen', Thinking About (TLC) Logo.

(iv) Margaret Donaldson, Children's Minds,