Great scholar Herbert Simon: kritiek op contextuele en constructivistische aanpak wiskunde-onderwijs
- net als onze kritiek in Onderwijskrant vanaf 1986 en onze recente kritiek op in ZILL-leerplan-visie op wiskunde-onderwijs
Simon criticises authentic, real-world learning tasks.
Contrary to the contention that knowledge can always be communicated best in complex learning situations, the evidence shows that: A learner who is having difficulty with components can easily be overwhelmed by the processing demands of a complex task. Further, to the extent that many components are well mastered, the student wastes much time repeating these mastered components to get an opportunity to practice the few components that need additional effort. There are reasons sometimes to practice skills in their complex setting. Some of the reasons are motivational and some reflect the skills that are unique to the complex situation. While it seems important both to motivation and to learning to practice skills from time to time in full context, this is not a reason to make this the principal mechanism of learning.
He defends drill, in the face of criticisms that it drives out understanding
This criticism of practice (called drill and kill, as if this phrase constituted empirical evaluation) is prominent in constructivist writings. Nothing flies more in the face of the last 20 years of research than the assertion that practice is bad.
All evidence, from the laboratory and from extensive case studies of professionals, indicates that real competence only comes with extensive practice.
He rejects discovery learning, and praises teacher instruction
When, for whatever reason, students cannot construct the knowledge for themselves, they need some instruction.
The argument that knowledge must be constructed is very similar to the earlier arguments that discovery learning is superior to direct instruction. In point of fact, there is very little positive evidence for discovery learning and it is often inferior (e.g., Charney, Reder & Kusbit, 1990). Discovery learning, even when successful in acquiring the desired construct, may take a great deal of valuable time that could have been spent practicing this construct if it had been instructed. Because most of the learning in discovery learning only takes place after the construct has been found, when the search is lengthy or unsuccessful, motivation commonly flags.
Bijlage van dezelfde auteur
False dichotomies, begging the question and the knowledge-skills debate
A lot of the time, I hear people say that the tired old knowledge-skills debate is a false dichotomy. This is of course true. Knowledge and skills are not polar opposites. But a lot of people who say that its a false dichotomy go on to make what I think is a further misconception. They say we should teach both or that we should have a balance lets make sure we dont get too knowledge heavy/too skills heavy. Knowledge and skills are definitely a false dichotomy, but to say that we should teach both does not necessarily follow.
Skill is a very useful descriptive term. If I say of someone hes a highly skilled footballer, I dont mean that he knows a lot about football. I mean that he is excellent at playing football. If I say someone is a highly skilled maths problem-solver, I dont mean that they are good at solving a lot of routine textbook tasks. I mean that they can be confronted with a completely new and unexpected maths problem and they can solve it.
But whilst the word skill is very useful at describing a reality, Im not sure it is so useful at providing us with analysis of that reality. Here is what Herbert Simon says about the ability of words to confuse rather than explain.
The magic of words is such that, when we are unable to explain a phenomenon, we sometimes find a name for it as Molières physician explained the effects of opium by its dormitive property. So we explain superior problem-solving skill by calling it talent, intuition, judgment and imagination.[i]
This Molière reference is an example of circular reasoning, or of begging the question. You hear politicians do this a lot. I heard a politician on Radio 5 a few months ago respond to the question what makes a good teacher? with the answer someone who is very very skilled at being in the classroom. I dont begrudge politicians their use of this tactic: theyre put on the spot a lot, they dont want to necessarily commit to something that they regret later, so they simply answer a question by restating the question. Fair enough. But if we want to find out the root causes of a phenomenon, we have to go beyond this.
In the play which Simon refers to, Molière is deliberately satirising the way that language allows you to beg the question. The original quotation is actually in a kind of pig Latin, designed to mock medical pomposity. It goes like this.
Mihi a docto doctore
Demandatur causam et rationem quare
Opium facit dormire.
A quoi respondeo,
Quia est in eo
This is particularly effective as a parody because of the similarity of the words dormire and dormitiva. In the unlikely event that anyone ever asks me for my advice on the translation of this line into English prose, I would recommend that for maximum comic effect you want something like this:
Why does opium make you sleepy? Well, its because of its sleep-inducing properties!
I think this works because the similarity of sleepy and sleep-inducing highlight the circular reasoning and hence the absurdity. Much less effective as a joke but more effective as an obfuscating tactic would be the following:
Why does opium make you sleepy? Its its dormitive properties.
This is less effective because sleepy and dormitive dont sound the same, so the reasoning doesnt sound as circular. The reasoning is just as circular, but it doesnt seem to be. You could well imagine a confident and forthright doctor bamboozling an uncertain patient with just such a choice of words. It helps that dormitive is a Latinate word and sleep is Anglo-Saxon, because Latinate words tend to sound much more impressive and professional than their Anglo-Saxon synonyms.[ii] A number of logicians have noted that the number of synonyms in English make it easy to beg the question.
In The Problem of Logic, Gibson and Klein write that a Sophist may bring forth a proposition expressed in words of Saxon origin, and give as a reason for it the very same proposition stated in words of classical origin. They then quote an example of this from Whateleys Elements of Logic: To allow every man an unbounded freedom of speech must always be, on the whole, advantageous to the State, for it is highly conducive to the interests of the community that each individual should enjoy a liberty perfectly unlimited of expressing his sentiments.
Let me make one thing clear. Describing opium as having dormitive properties is very useful. The word dormitive does help us to understand an important feature of opium. But it doesnt help us to explain why opium has this property. Its a descriptive word, not one that explains.
As Simon goes on to say:
Behind such words, however, there usually lies a reality we must discover if we are to understand expert performance. One label often applied to persons skilful in solving physics and engineering problems is physical intuition. A person with good physical intuition can often solve difficult problems rapidly and without much conscious deliberation about a plan of attack. It just occurs to him (or her) that applying the principle of conservation of momentum will cause the answer to fall out, or that a term in kinetic energy can be ignored because it will be small in comparison with other terms in an equation. But admitting the reality of physical intuition is simply the prelude to demanding an explanation for it. How does it operate, and how can it be acquired?
The same is true of the word skill. It is excellent at describing a phenomenon we all recognize. But it is less good at explaining how we have acquired or can acquire that property. To describe someone as a good solver of maths problems may be true, and useful. But to attempt to explain that she is good at maths problems because of her high levels of mathematical skill is less useful.
So, what does cause high levels of mathematical skill, or any other skill? This is the question Simon concerns himself with in the rest of his article. You can read his conclusions in the article, but I will quote briefly.
In every domain that has been explored, considerable knowledge has been found to be an essential prerequisite to expert skill. Our growing understanding of an experts knowledge and the kinds of processes an expert uses when solving problems enables us to begin to explore the learning processes needed to acquire suitable knowledge and problem-solving processes. We have no reason to suppose, however, that one day people will be able to become painlessly and instantly expert. The extent of the knowledge an expert must be able to call upon is demonstrably large, and everything we know about human learning processes suggests that, even at their most efficient, those processes must be long exercised. Although we have a reasonable basis for hope that we may find ways to make learning processes more efficient, we should not expect to produce the miracle of effortless learning.
A quotation from another Simon essay, this time about chess expertise, is also relevant:
The question is: how does one become a master in the first place? The answer is practice-thousands of hours of practice. This is implicit in the EPAM theory; what is needed is to build up in long-term memory a vast repertoire of patterns and associated plausible moves. Early in practice, these move sequences are arrived at by slow, conscious heuristic search -If I take that piece, then he takes this piece . . .-but with practice, the initial condition is seen as a pattern, quickly and unconsciously, and the plausible move comes almost automatically. Such a learning process takes time years to build the thousands of familiar chunks needed for master level chess. Clearly, practice also interacts with talent, and certain combinations of basic cognitive capacities may have special relevance for chess. But there is no evidence that masters demonstrate more than above-average competence on basic intellectual factors; their talents are chess specific (although World Champion caliber grandmasters may possess truly exceptional talents along certain dimensions). The acquisition of chess skill depends, in large part, on building up recognition memory.[iii]
Anderson says something similar.
All that there is to intelligence is the simple accrual and tuning of many small units of knowledge that in total produce complex cognition. The whole is no more than the sum of its parts, but it has a lot of parts.[iv]
What we see, therefore, is that the phenomenon of skill which we observe all the time is explained by the knowledge we have in long-term memory and the practice we have at retrieving that specific knowledge from memory.
Therefore, to say that knowledge and skills are a false dichotomy: we should teach both skills and knowledge is slightly flawed. What Simon shows us is that it isnt really possible to teach skills in this abstract fashion. We achieve skilled performance through committing knowledge to long-term memory and practising using it.
So more accurate would be knowledge and skills is a false dichotomy: if pupils commit knowledge to memory and practise retrieving it from memory, that will cause skilled performance.
It may be argued that I am splitting hairs here and this is a minor semantic point. And it is indeed true that there are doubtless many people who talk about teaching skills who nevertheless are in fact teaching the building blocks of knowledge that will cause skilled performance. But the reason why I think its worthwhile dwelling on this is that too often that is not the case.
Too often, this semantic point is the root of actual bad practice. If you think that your teaching time should be divided equally or in some kind of proportion between teaching knowledge and teaching skills, the time that is given over to teaching skills will very likely be devoted to practice that wont actually improve skills. For example, you might spend time teaching generic reading skill by getting pupils to skim texts, scan them and find the main idea. But these tactics have a very limited benefit because reading is not a generic skill. Reading depends on knowledge, so if you want to improve your pupils reading skill, you would be better off spending your time on vocabulary acquisition or indeed teaching pupils knowledge from other subjects.
Its for this reason that each chapter of my book begins with an analysis of a common education theory, and then an analysis of the practice that theory gives rise to. If the only problem here was one of confused terms, then there wouldnt really be much of a problem. But in this case, and indeed many others, when we confuse the words we use to describe and explain reality, it often leads to our actions becoming confused too. I began this post with a quotation from Tennyson about how words can mislead; Confucius understood this problem too.
If language is not correct, then what is said is not what is meant; if what is said is not what is meant, then what must be done remains undone; if this remains undone, morals and art will deteriorate; if justice goes astray, the people will stand about in helpless confusion. Hence there must be no arbitrariness in what is said. This matters above everything.[v]
The other semantic problem this gives rise to is that when I talk about teaching knowledge, a lot of people worry that I am not concerned about skills. I am absolutely concerned with skills. The end point of education should be to produce skilled individuals. My point is that the best way to achieve that aim is not to teach skills; its to teach knowledge.
[i] Larkin, Jill, et al. Expert and novice performance in solving physics problems. Science 208.4450 (1980): 1335-1342.
[ii] And, of course, in the famous case of pig/pork and cow/beef this Anglo-Saxon/Latinate class divide is built into the very meaning of the words the Anglo-Saxon word is used for the animal and the Latinate word for the meat you eat.
[iii] Simon H. and Chase W. Skill in chess. American Scientist 1973; 61: 394403
[iv] Anderson J.R. ACT: A simple theory of complex cognition. American Psychologist 1996; 51: 355365.
[v] I know that Andrew Old will point out that we dont have any good record that Confucius actually said this. Thats true, but this quotation is taken from the Arthur Waley edition of Confuciuss Analects, which is at least a reliable edition of what people think Confucius might have said. Arthur Waley, The Analects of Confucius, New York: Alfred Knopf , 2000, p.161.