PART D: Philosophical Theories of the Problems which Trigger Children's Inquiries
IX.
Although many philosophies of education are not in total agreement with Dewey's arguments that children learn through active inquiry, the starting point of which is subjectively felt problems, nevertheless it is interesting to extract (or reconstruct) implicit views about the logical types of problems which children face and the factors which make problems important.
Not surprisingly, philosophers of education who were influenced by Bacon or Locke present an inductivist justificationist theory of learning. For Rousseau, the primary job of the tutor is to shelter the young pupil from the beliefs, tastes and judgments of others so that he can grow up with "no mistaken ideas and no vices." Emile will have limited knowledge, but everything he knows he will have learned for himself. (The censoring tasks of the tutor range from not letting Emile form the habit of using one hand more than the other to cutting out the moral conclusions of La Fontaine's fables!).
Although trial-and-error learning is involved, one gets the impression that Emile never faces any problems based on deep inconsistencies. Rather the problems dealt with are primarily ones of random curiosity (what I have called problems of filling in blanks) plus the search for explanations of how things work or stories or where they came from. ("When he sees a spring made, he will want to know how the steel was got from the mine.")
On Rousseau's account, it should be possible (in the ideal case) for children to accumulate knowledge both about the natural and the social world steadily and without major revision. At fifteen, Emile will have "a true mind free from prejudice" and is presumably well-equipped to extend his knowledge in the same easy, infallible manner.
Piaget's theory of cognitive development, on the other hand, presents quite a different view. First of all, Piaget stresses that at all stages the child's knowledge system is organized into fairly abstract schemata. Secondly, the concepts and theories which the child uses in order to understand and interact with the world frequently have to be adapted in order to accommodate new experiences. Some of these revisions are smooth extensions of the conceptual schema, but often the scheme has to be altered in fundamental ways. Thus, the thirsty child soon learns that the height of a column of lemonade is not always a good predictor of how much liquid it contains. And the child who is confronted with an intriguing array of objects only some of which float in water will probably wrestle with a variety of explanations before eventually accounting for all the observed phenomena by using the notion of specific gravity.
Piaget's theory emphasizes the role of problems of systematicity. Like the scientist, the child wants theories of different phenomena to fit smoothly together. And although the rather bland terms "accommodation" and "adaptation" tend to obscure the logic of the situation somewhat, analysis reveals that problems of inconsistency furnish a major impetus towards inquiry in Piaget's account.
So far, our account of the structure of students' problems neatly parallels the account of scientists' problems. All three logical types are encountered - problems generated by gaps, inconsistencies and systemic flaws. And for most philosophers the problem of inconsistencies is viewed with some embarrassment which is partially covered by using euphemisms such as "anomaly," "accommodation," "adjustment," "recalcitrant phenomena," etc. I will return to this custom of covering up the fact that inconsistencies are a major motivation for inquiry later. But first, let us look at what on the surface appear to be enormous differences in the problem-situations of students and scientists. When the scientist asks why-p or whether-p or how to resolve the inconsistency between p and q, it is generally assumed that no one knows the answer or has ever solved the problem. This assumption is not always correct - the temporary eclipse of Mendel's work is a striking counter example. But even with the historian's delight in searching for precursors, very few such examples have turned up. Cases such as the following are more typical; Anaxagoras certainly had the idea of putting the sun in the center; yet he hardly could have been said to have had the full solution to Copernicus' problem because none of the quantitative details or implications, such as the expected phase behavior of Venus, were worked out.
Students' problems on the other hand are almost always ones in which the answers are already known - sometimes they can even be found in the back of a textbook! I deliberately spoke of students, not children. Many children, as any psychologist or social worker can report, face terrible problems for which no adult has a cut-and-dried solution: What should a little girl do if she is sexually molested by her father, but her mother says to overlook it because the authorities will break up the home if she tells? What should a little boy do if each of his divorcing parents say they can't live without him and so he must tell the judge which he wants to live with, mother or father? How can a child decide whether a younger sibling is being battered or merely severely disciplined? What if a child is sincerely convinced that if s/he doesn't believe the Bible s/he will go to hell, but also loves science and is persuaded that the theory of evolution is true?
Adults, including teachers, may be able to help children solve such problems, but they certainly don't have the answers. However, at least in the traditional curriculum, a principle of selection for the appropriateness of a problem for inclusion was the fact that it had an answer, and that the answer was relatively easy for the student to find and comprehend. And even in less orthodox school settings, the environment is structured in a way not only to excite the curiosity of the child, but also to prompt questions which the child may well be able to answer through investigation. Granted children may make new discoveries about hamsters and that scientists often solve quite routine problems; the typical situations are quite different. Scientists work on problems for which there is no known answer and no guarantee that a solution is even obtainable. Students work on problems the solution of which is known - often it is even known by the teacher!
This introduces a certain complexity into both the dynamics of student inquiry and the evaluation of problems for students. Suppose a scientist is genuinely puzzled by why-p and is trying to "extort the answer from Nature" as Bacon would describe it. Suppose you now point out to the scientist that a "resource person" over in the corner knows the answer and that the solution has been independently tested a thousand times before. Surely the scientist would stop work and just go ask the resource person for the answer.
Yet most inquiry in the classroom would be useless if the child behaved in this manner! If we try to make the child genuinely puzzled in why-p, but then refuse to let it find out the answer in what appears to be the most direct efficient fashion (namely, by asking us) we're introducing a lot of frustration into the situation. How can this paradox be resolved? Various solutions have been adopted.
1. One can didactically furnish the solution to why-p, without even bothering to make the student aware of the problem it solves.
2. One can present the problem, arouse interest in it, but then quickly provide the solution.
3. As in (2), except that one dialectically presents a variety of solutions (starting with the weakest first), criticizes them in turn, and finally arrives at the preferred solution.
4. One presents the problem and then plays a game with the students in which they provide the dialectic of conjectures and criticisms until the preferred solution is generated.
None of these solutions is totally satisfactory. (I will offer a better one below.) Of course, the whole tension can be avoided by sticking to inquiry in which the teacher either does not know the answer or is unable to communicate it. Examples of the first kind of problem would include "How much water per day does our hamster drink?" (assuming the class didn't have hamsters last year), and "What is the average shoe size of third graders in Booneville?" Examples of the second kind would be problems involving motor skills, such as how to ride a bicycle. Although the teacher can coach the child, it is impossible to communicate completely this kind of knowledge.
I have no objections to motor skills or to children and teachers working together to answer questions. However, it would seem terrible to restrict classroom inquiry to matters of which the teacher was either ignorant or unable to describe! (An argument seems to be lurking that the less the teacher knows, the easier it will be for his/her students to engage in authentic inquiry!)
I propose the following solution to the problem. Let us assume that the student is already genuinely interested in answering the question why-p (or any other problem). (We will deal with problems about motivating students later.) Let us also assume that there is a standard, non-controversial answer to the student's question which the teacher knows. How then should the interaction between student and teacher proceed? I suggest the following paradigm.
Student: I am wondering why wood floats while iron sinks. Can you help me? [Note that the student initiates the interaction, not the teacher.]
Teacher: Yes, I can help in three possible ways. Tell me which you prefer. 1) The phenomenon you describe was discussed by Archimedes. You will find accounts under "Archimedes Principle" in the library. I could give you more detailed references if you wish. 2) I also remember the Principle and so could explain it to you right now. Or, as a third alternative, 3) I could help you as you make your own inquiry into this matter. [The student is offered a choice of instructional techniques.]
Student (1): I like reading things on my own - guess I'll go to the library. Thanks.
[OR]
Student (2): My interest in the problem is really technological, not theoretical - I'm trying to design a floating cover to keep my bees from drowning in the horse trough, and I'm trying to figure out what material to use - wood floats too high. I have a list of specs on various plastics here, but I've forgotten what is relevant. Is it just density or does thickness count? If you could please just tell me quickly what the Principle says...
[OR]
Student (3): I would like to try to figure it out myself, but wouldn't that be an inefficient way to learn? After all, Archimedes lived a long time after Adam and Eve. Why will I be able to do it faster than Adam/Eve?
Teacher: Very good questions. I will try to answer each of them. In response to your questions about efficiency, I have several points:
(1) If you solve your problem through a process of inquiry, you will not only be learning about floating bodies, you will also be learning methods of problem solving, so you will learn more.
(2) By actively entering into the solution process yourself, you will remember the solution longer - or be able to reason your way to it on another occasion.
(3) In the process of arriving at a satisfactory solution, you will probably consider theories about floating bodies which don't work and discover why they don't work. You will thereby gain deeper understanding of the preferred answer. To appreciate a theory fully, we need to know both what problems it solves and also how well it solves them compared to other theories. About the Adam and Eve point: By working with a teacher who knows Archimedes Principle, your inquiry will go faster than that of a Cain or Abel or even Archimedes. If you ask me to, I will suggest experiments to test the conjecture we are working on. Or if you get stuck and cannot come up with a suitable conjecture, you may wish to request me to try to think of one.
Student: So I can control exactly when and how much you contribute to the inquiry?
Teacher: Exactly. I am at your service.
Student: That's wonderful, but I don't know how to begin.
Teacher: Suppose you restate the problem and explain as best you can exactly why it seems puzzling.
Student: Well, when we were hauling in firewood, an enormous log fell off the truck and rolled down into the river - and it floated even though it was very heavy. But no matter how much water you have, it won't hold up even a tiny thumbtack.
Teacher: So you have already discovered that the theory which says "big, heavy objects sink and light objects float" is false?
Student: Yes, you are right. I have learned that much. I guess now I better look for another theory. Maybe it has something to do with the surface area...
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The pedagogical problem we started with was this: If the student is genuinely puzzled about a matter, and if the teacher knows the answer, why should the teacher frustrate the student by being coy and making her/him go through certain teacher-set hoops before the answer is revealed? The following solution tries to eliminate paternalism:
(5) The student is put in control over the kind of assistance which the teacher provides. In our example, the teacher is to volunteer no information concerning floating bodies unless specifically asked. However, if asked, the teacher may deliver a traditional lecture on the topic.
Of course, there are limits to the extent to which teachers should acquiesce to student requests. Nuclear engineering teachers need not hand plans for atom bombs over to the students who are would-be terrorists. Teachers are paid to provide certain intellectual services for students, but they are not required to answer requests which are frivolous or rude. There may be extraordinary situations (perhaps cases involving catatonics) in which the teacher should plan an initiating role, but a special argument must be made whenever the teacher is tempted to subvert the student's autonomy over the pedagogical procedures. [Notice that the student has no control over what the teacher says when asked, only over the occasions on which the teacher contributes to the inquiry.]
To summarize the discussion so far: A typical student's problem differs from a typical scientific problem in that an acceptable solution to the former is already known (a fortiori their expected degree of solubility is one) while in the latter case, it is not even known whether the problem has a solution.
I now turn to another difference. In science since the solution to our problem is unknown, our estimates of how valuable it will turn out to be are often very rough. Here are two examples where the solution turned out to be much more valuable than expected: (1) In attempting to derive the continuum hypothesis from set-theory (a project of moderate interest), Cohen invented the method of "forcing" which has turned out to be a very valuable proof technique. (2) In the process of exploring apparently routine consequences of his 1905 relativity paper, Einstein derived E = mc2, an unexpected result of obvious theoretical and practical importance. Sometimes we are surprised in the other direction. For example, early eugenicists believed that once we had solved the problems of which traits were inherited, it would be easy, in theory at least, to eliminate undesirable characteristics. As it turned out, many of the traits of interest are polygenic and the genes in question govern other traits as well, so even if selective breeding were socially acceptable, it would not be practical in many cases.
In education, by contrast, we not only know what the answers to the problems are, we also known which ones are more valuable. This then brings up the pedagogical problem of motivation: Given that some problem-solutions are more important than others and assuming that one job of the teacher is to ensure that students learn valuable things, how can the teacher get children interested in/puzzled by/motivated to inquire into the right topics?
I will begin with a radical response to the motivation question, one which challenges its presuppositions. First, it might be argued that it is very difficult to assess today what it will be important for the child to know tomorrow - how much time should be spent on the details of spelling when word processors have built-in dictionaries? What use is it to sweat over English units if we will soon switch to metric? Who needs to know how to extract square roots by hand, or even by logarithms, in an era in which inexpensive calculators adorn every wrist or checkbook?
Secondly, those skills and subject matters which are universally useful, e.g., reading, modes of critical thinking, basic science, are ones which the child will inevitably be led to, no matter which problems they pick for inquiry. Problems in cooking may well lead to an interest in chemistry which quickly necessitates one to learn some mathematics which can lead to set theory, then to logic, then to philosophy which involves ethics, etc. A serious interest in firetrucks leads to architectural engineering, or perhaps thermodynamics and the Doppler effect, or questions about differing quality of community services in poor neighborhoods, then to political theory, etc.
So, the argument continues, contrary to the assumptions of the question about motivation, the teacher need not worry about trying to select valuable problems for the kids - valuable inquiry can begin anywhere. And since kids are naturally curious, they are self-starters as long as we don't squelch them. There is no selection or motivation problem - children do not need to be seduced in order to learn.
I am in basic sympathy with the above position insofar as it stresses once more the child's ability to and right to assume responsibility for what s/he learns. But I want to consider two criticisms of the radical child autonomy proposal which may lead us to modify it. One concerns practicality; the other its assumptions about the human condition.
First, the practical objection which goes as follows: Inquiry of the child-controlled dialectic variety described in (5) above often requires materials. In the example taken from Piaget concerning floating bodies, one may need water, scales, rules, chunks of wood, balloons. If one teacher is trying to deal with thirty students, each passionately puzzled about a different problem, either mayhem or frustration seems inevitable.
I can think of two solutions - each has both advantages and disadvantages.
(1) One can set up "problem rich environments" around the room, perhaps a poster saying "Why does wood float?" accompanied by tubs, scales, etc. The children can either wander around and either choose a work station or work on a problem of their own devising, knowing they will get only occasional help from the teacher.
Structured problem set-ups function like the teacher somewhat in that they help keep the children from getting stuck -if a graduated cylinder is sitting there, it probably means volume is important! However, it also tends to limit the range of hypotheses a child will consider ("if no thermometer is present, temperature can be ruled out") and may turn into a sterile guessing game ("wonder what the string is for?").
On the other hand, the problem set-ups allow the child to work in privacy and at his/her own rate.
(2) Another possibility is for the group to discuss and vote on which problem they will communally investigate. Group investigation should speed up the dialectical process (more people to generate both hypotheses and criticisms), but it's very hard to keep the discussion from turning into a teacher-controlled dialectic. (After all, it's cumbersome to keep on asking the group to vote on whether they want a teacher intervention or not.) One solution is to have one of the children moderate the dialectic, by reminding the group which hypotheses are under discussion etc. The teacher then will only speak when called upon.
Let us now turn to a second objection to the radical child autonomy proposal - one which challenges the view of the typical child's mind as a tabula rasa has been decisively criticized by both Dewey and Popper (among others). But we must be careful not to put in its place a conception of the child as possessing an indefatigable curiosity. At all ages of life our inquisitiveness is bounded. Tiny babies have an innate fear of falling and are reluctant to crawl out onto a transparent glass surface. Many young children have quite conservative tastes in food and refuse to try unfamiliar dishes. (Whether this is largely learned or a biologic stage does not affect my point.) Many American teenagers are very conformist in their taste in pop music, dress, and have styles and show little interest in exploring alternatives.
So for certain periods of their lives, at least, there are definite constraints on the areas of inquiry which children will consider. More important are the processes which teach children that certain questions are taboo or that certain cognitive activities are unsuitable for them. I am not concerned here with the child who has a burning question about sex or Communism, but dares not make inquiries. Its curiosity is unimpaired - all it needs is an opportunity to express it.
Instead, what I am thinking about are the subtle cues which operate - cues which convince fat kids that they aren't interested in sports, or little girls that they don't like math, or little boys that art is boring, or little black kids that Shakespeare is less fun than typing.
Obviously, we each have intellectual preferences - and what we are most curious about is shaped in part by how satisfactory our previous inquiries in related areas have been. The child will inevitably form tastes. But we don't want their preferences to be coerced. If the bullying is overt, it is sometimes easier to combat. If girls were not allowed into advanced math classes, there would probably be an outcry (although for years no one complained about sex-segregation in shop and home economics or the inferior programs in athletics for girls) just as it took a long time before the "separate but equal" defense of segregated schools was struck down).
When we are unaware of the coercions and perhaps even internalize them, they are much harder to resist. They are also harder for the outsider to identify.
Let us assume that children are frequently bullied (unbeknownst to themselves) into avoiding certain areas of inquiry. Let us also assume that the teacher has reason to believe that those areas would be valuable to the child. Given our presumption that children should be free to choose their own research problems, what, if anything, should the teacher do? First, it is worth noting that the child may actually invite the teacher's intervention. A little girl may say, "I have a problem. I love animals and would love to go to vet school, but I'm afraid I won't be able to get in because I hate math. What shall I do?" At this point, the teacher may discuss various theories about why people hate math or various techniques for getting over it. Or a little fat kid may say, "I feel unhappy today." At which point the teacher may ask if s/he wishes to discuss possible reasons for the feeling and if so, the discussion may turn to missing out on the fun of sports, etc. If no such occasions arise and if the teacher judges that the child's curiosity has been seriously damaged, direct intervention may be called for, but it should be done with full recognition that the normal "etiquette" of the classroom has been violated.
To summarize then: It might at first appear that there are fewer uncertainties in evaluating problems which children might solve as compared to scientists' problems. And one might be tempted to conclude from this that children's inquiry should be more structured and less pluralistic than scientific inquiry. On closer examination, however, this turns out not to be the case.
If children generally learn best when they are genuinely interested in a topic and if children generally learn best when they have input on the teaching method which is utilized, then one should allow for the possibility in the curriculum for a great diversity of problems and modes of inquiry. Unless we make it so, there is no reason why schooling should be any more cut-and-dried (or more predictable) than scientific research.