The Problem
It has been said that it is better to argue an issue without settling it than to settle an issue without arguing it. I believe that this must have been said by philosophers with educational issues in mind. This paper will present some ideas of modern philosophy of science in hope that debate will continue concerning the issue of "theoretical versus descriptive chemistry: Should one or the other prevail?"
The tack I shall take was suggested by a juxtaposition of T. S. Kuhn's claim (I ) that practicing scientists must use concrete "exemplars" to communicate science, with the claim by modern Piagetians (2) that the large fraction of college freshmen operating on the concete level is an impediment to science education today. We can only hope, I presume, that the Piagetians will continue to apply the category "concrete operational" to underprepared freshman while ignoring our own references to "particles in boxes." 2
The science philosopher/historian T. S. Kuhn suggests that even at the frontier of science, scientists frequently must communicate by the use of concrete "exemplars" (a term whose meaning and application will be further explained below). This claim contrasts with much of what teachers are predisposed to believe, for example, that the use of pure theory is equivalent to sophistication in science, and only unsophisticated students should deal in concretes. This notion is perhaps reinforced by interpretations of Piaget, which suggest that use of concretes comes psychologically before, rather than developing with, use of abstracts. I believe that the contrast of the Piagetian description with the Kuhnian one will suggest the pedagogically important idea that theoretical and concrete elements which constitute a science do not serve mutually exclusive functions. On the contrary, neither is fully intelligible in the absence of the other, and each contributes to the understanding of the other (3).
I suggest that the distinction indicated by the terms "theoretical" and "concrete" (as opposed to "theoretical" and descriptive") is the pedagogically useful and descriptively accurate one. Furthermore, the conceptual distinction does not imply a dichotomy in scientific practice, where, I will argue, theoretical and concrete elements are more inseparable in function than previously suspected. The physical experience of riding a trolley away from the Berne clocktower and theoretical insight were probably both necessary to Einstein's development of special relativity. Why, then, do we separate theory and concrete so strongly in science education?
"Descriptive chemistry" has not yet been well defined. It may have two connotations. First, it may connote topics that are rendered essentially concrete, in the Piagetian sense, by our efforts to relate them to the everyday life of the student (e.g., the chemistry of vinegar and baking soda). If we construe "descriptive chemistry" this way, we must guard against opposing it to (or teaching it to the exclusion of) theoretical chemistry, thereby violating the epistemological inseparability of theory and concrete example. All facts contain theory implicitly. To use Whewell's words, "a fact is a familiar theory",3 and it is better to recognize the development of the theoretical operations that occur through the interplay of descriptive facts and the generalizations that make them intelligible. The qualitative analysis scheme for cations teaches as much (presented correctly) about theory as theory (presented correctly) teaches about the concrete tests.
"Descriptive chemistry" in the second sense, however, connotes topics like industrial chemistry or environmental chemistry which must be recognized as containing both concrete elements and explicit formal (theoretical) elements. Construed this way, "descriptive chemistry" certainly cannot be opposed to theoretical chemistry, and the fact that we may attempt to do so indicates insensitivity to the degree to which formal operations are demanded of our students.
My intention has been to blur the theory/exemplar dichotomy. Only the chemistry of the reaction "A + B -> C + D" is purely theoretical, and only memorizing the symbols for the elements approaches the purely concrete. Both of these approaches should be avoided, if one wishes to teach science, which blends the theoretical and concrete. The interplay of the theoretical and the concrete in science is perhaps the topic of greatest concern for modern philosophers of science, and I hope the following explication of some of their work, in light of Piaget's description of learning, will support the arguments of the first few paragraphs and perhaps lead to new insights in science pedagogy.
Thomas Kuhn's influential book, "The Structure of Scientific Revolutions," should not be read in isolation by the philosophically naive. Critical or qualifying essays abound (5-12) that suggest a number of weaknesses. But Kuhn's description of science leads to pedagogically sound and important results (13). Kuhn's central claim is that contrary to received dogma among both scientists and philosophers of science, theory is not the exclusive locus of cognitive content in science. Kuhn suggests that a "disciplinary matrix," consisting of symbolic generalizations, metaphysical beliefs, values, models, and "exemplars," must be proposed as the complex medium by which scientific knowledge is transmitted, to make the history of science, and indeed its current practice, intelligible. Kuhn claims that theoretical formalisms like "f = ma" are meaningless in themselves without further information about how they attach to natured This information must enter "at the top," (l, 14) or theoretically, whereby the "generalization sketch" is tailored to the particular application (f = ma might become mg = d2s/dt2 for freefall or f = mx2r for rotation). More central to the present theme, however, is Kuhn's claim that the formalism must also be attached to nature "at the bottom" (1,14) by indicating, by more or less concrete gesture, the things to which the theoretical terms apply (their referents). Since the decline of the positivistic schools of philosophy of science, hope has dwindled for finding a mechanism or algorithm for attaching theoretical terms to nature (15). Kuhn suggests that, in fact, no such mechanism exists, and that the referent of a theoretical term is by no means intuitively obvious to a science novice. Rather scientists and students of science learn the meaning and application of theory by studying concrete "exemplars" provided by teachers.
Exemplars take the form of concrete sample puzzle solutions, exhibitions of the concrete circumstances in the laboratory where the theory is applied, or a concrete physical object which is displayed simultaneously with the theoretical term that refers to it. Exemplars are thus concrete examples which provide supralinguistic and supralogical ties between theory and nature, where no other ties can exist. In solving puzzles by applying the correct formalism, students exhibit tacit knowledge which cannot be formulated as an algorithm and thus cannot be taught in words. The familiar claim by a student that he understands the chapter but cannot do the problems at the end may indicate not lack of theoretical knowledge (or ability to do Piagetian formal operations) but inability to see how the theoretical terms attach to the world (16). This problem can be solved only by providing concrete exemplars. The conclusion of the modern day Piagetians (17) that it is good to present concrete examples along with our discussions of more abstract elements of chemistry is a truism if we accept Kuhn's description of science, which further suggests that communication by exemplar should not be limited to "concrete operational" students alone.
The ability that allows students to see new problems as similar to previously studied examples is thus characterized as "tacit knowledge" by Kuhn. That this essential knowledge is not, in fact, imbedded in formal generalizations or theories is demonstrated by the applications of even the simplest formal generalization: "The whole equals the sum of its parts" attaches differently to pneumatic chemistry where additivity of volumes (or better, pressures) are theoretically pertinent than it does to the preparation of aqueous alcohol solutions where volumes are not additive, pressures are relatively unimportant, and the formalism applies to the masses of the components only. Information that is auxiliary to the theory is essential to its application in each case and this information is carried by exemplars. Clearly, a presentation of chemistry as a framework of theoretical constructs alone is not just pedagogically self-defeating, but it misrepresents science. The concrete referents of symbols are inscrutable,5 and we come to know how to apply symbols, only through exemplars.
I have strongly suggested that theoretical chemistry is unintelligible without exemplars, or loosely speaking, a descriptive counterpart. But what about the proponent of descriptive chemistry who contemplates avoiding theoretical chemistry? Should we avoid thermodynamics while we discuss blast furnace reactions? Can "concrete" chemistry exist independent of theoretical chemistry, or, in the present context, can "concrete" chemistry be taught successfully without theoretical chemistry? The attempt to do so would be illadvised for at least three reasons, according to philosophers of science.
First, science as practiced develops theory and exemplar together in its disciplinary matrix, and we probably should teach science as it is practiced. Philosophers, including Kuhn, argue convincingly that measurements would be unintelligible if they were not made with some theory assumed. The received notion that a scientist gathers facts and only then proposes a theory to fit them probably reverses the process as it occurs (18). Regularities in nature, rather than being hard to find, are inescapable (19, 20), and which regularity of nature is detected or selected is predetermined by theory choice.6 We must give students a notion of why we are presenting an apparent collection of specifics by proposing unifying generalizations.
This leads to the second reason that theories must not be ignored. Any finite set of data is consistent with an infinite number of theories, some of which are mutually inconsistent (21). The facts do not "speak for themselves" to arbitrate a theory choice (22). Although philosophers have accepted as axiomatic the proposition that any set of measurements may support equally two opposing theories, many science teachers find it disturbing, and may even base their pedagogy on the denial of this proposition. It would seem that we should want to teach the theories that are currently accepted in practice, rather than avoiding theory, at the risk that a student will devise one of the currently unacceptable alternatives.
Finally, in order to supply the two essential elements of science, foresight (prediction) and understanding (theoretical explanation of why the prediction should be true) (23), a non-trivial causal argument must be supplied to explain even the most concrete fact. By non-trivial, I mean that an explanation cannot apply to a particular fact. To say that vinegar reacts with baking soda is as barren chemically as the explanation offered by Moliere's doctor, for the sleepinducing effect of opium in terms of its "dormitive principle," was barren physiologically. Theoretical frameworks supply the generalizing, organizing, and rationalizing powers that are necessary to render explanations scientific. Explanations are merely tautologous when n distinct phenomena require n explanations, and "descriptive chemistry" must avoid presenting several reactions with the assertion that "they work," without presenting some unifying principle or theory that tells why. Mere prediction does not a science make, even if it is perfect prediction. Ptolemy's universe is not a scientific one, although it makes prediction of a ship's passage possible.
1The ideas that developed into this paper were presented at the Internationai Introductory Chemistry Conference, McMaster university, June 19-23, 1978, where they prompted one conference organizer to stand on his head and sing, to the tune of Waltzing Matilda," the following lines: Waltzing exemplars/Dreadful exempkars/Who'll work on Piaget and pedagogy . . . Who'll come a hunting for theories with me. " The second verse is unprintable.
2 Jean Piaget would despair at his work being treated philosophically. In his autobiography he expresses thankfulness that his early study of mollusks saved him from seduction by the "demon of philosophy." Another irony: The use of juxtaposition in paragraph one is a concrete operation.
3 See reference (4). Whewell asserts, "In a Fact, the Ideas are applied so readily and familiarly, and incorporated with the sensations so entirety, that we do not see them, we see through them." Here Whewell uses "Idea" to imply theoretical idea. On p. 39 he suggests, "And even with regard to the simpler facts, as the motion of the stars around the pole, although this may be a Fact to one who has watched and measured the motions of the stars, one who has not done this, and who has only carelessly looked at these stars from time to time, may naturally speak of the circles which the astronomer makes them describe, as Theories." On the necessity of theories to make facts intelligible, Whewell says, in Volume 11, p. 48: "The pearls are there, but they will not hang together till some one provides the string."
4 The illusion that we know "nature" or, in particular the referent of a symbol Ike "m" comes from our repeated exposure to exemplars in textbooks. That there is a uniform nature in which a referent for the symbol "m" exists is, for Kuhn, a purely hypothetical conjecture. When scientific revolutions occur the theories and exemplars of the new science constitute an entirely new "nature" whose entities will be different from those indicated by the prerevolutionary science.
5 Willard V.O. Quine used the phrase "inscrutability of referents" to suggest that we never do have a direct link with the aspects of nature that symbols name. These aspects of nature are understood in terms of linguistic and theoretical convention, and when conventions change, so does nature.
6 The most important problem in modern philosophy of science is determining how data that are collected under the direction of a theory can be used against the theory to correct it (20). Data cannot be collected without a theory, but when they are collected with a theory in mind, they are necessarily biased.