What can Science Educators Teach Chemists about Teaching Chemistry? A symposium
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How Can Chemists Teach Problem Solving? Suggestions Derived from Studies of Cognitive Processes F. Reif Physics Department and Group in Science and Mathematics Education, University of California, Berkeley, CA 94720 Scientists do not hehave scientifically in all domains. Thus, we pursue our own discipline (e.g., chemistry) analytically and systematically, seek to develop a theoretical understanding of underlying processes, and try to achieve practical gods (e.g., chemical svnthesesi on the basis of our theoretical insights. On the other hand, we commonly approach tasks outside our own discinline (even chemicallv related tasks such as gardening or nutrition) hy the seati of our pants, content toiely on rules of thumb and on common-sense notions of questionable validity. Usually we tend to be equally unscientific in our teaching. A serious interest in teaching scientific prohlem solving warrants, however, a more systematic approach. Not only is prohlem solving of crucial importance in any science if students are to achieve the ability to deal flexibly with diverse and novel situations, hut problem solving, particularly in well-develo~edscientific disciplines, is also a highly complex approaches the teaching enterprise from a systematic and scientific point of view. Such a scientific approach is not only required to achieve practical teaching effectiveness, hut also has intrinsic intellectual interest as a field of study in its own right. Indeed. recent vears have seen substantial progress in . . our understanding of complex intellectual processes, as these have been studied in exciting new fields such as information-processing psychology or artificial intelligence (1-3). My aim in this paper is to point out some central ideas emerging from a systematic approach to teaching scientific orohlem-solving skills. My comments will he generally ap&cable to probiem solving in quantitative scikces, such as physics, chemistry, or engineering. (I myself have done most of my own work in the context of physics.) Within the limited space available to me, I shall focus my attention selectively on some major points and shall deliberately slight many important details. Rudiments of a Systematic Approach Teaching or learning can he viewed as a transformation process analogous to a chemical reaction of the form S,
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Teaching versus Performance I t is clear that one must first have a good understanding of performance, both in the initial and final states, before one can svstematicallv address tasks of learning or teaching. In
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how students, after instruction, are expected to perform in order to achieve effective problem solving, e.g., what thought processes they are expected to use, how they are expected to organize their information, etc. (Indeed, it is a research challenge to understand theoretically such underlying cognitive processes leading to good human problem-solving performance.). Onlv nood understanding- of " after one has achieved a initial performance, and of the desired final performance, can one hone to teach students how to become effective problem solvers. Naturalistic versus Effective Functioning Useful information about learning or teaching obviously can he obtained by observing and studying the performance of actual novice students and of actual experts. However, such naturalistic or "descriptive" studies have only limited interest. By contrast, a more general question, transcending a mere concern with naturalistic functioning, asks how effective functioning comes about. For instance, purely naturalistic studies of flying, by observing birds and insects, may lead to an understanding of how flying is achieved by flapping wings. However, asking the more general question about effectiue flying may lead to the realization that flying can he achieved even hetter with fixed wines. as modern airnlanes do.
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i r e underlying thought processes leading to good human oerformance (such as Droblem solving) - without necessarily simulating what actual experts do?" This more "orescrintive" auestion is both scientificallv interesting and htlghly germane t o practical instruction (4). 1n particular, this question does not make the unwarranted assumption that actual experts always perform optimally. Furthermore, since it does not restrict inquiry to naturally occurring modes of
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In this process a student Si,in an initial state where he or she cannot do certain things (such as prohlem solving) is supposed to he transformed into a student SFin a final state where he or she can do these thines effectivelv
suggested by observing the behavior ofactual experts, they may also he suggested by purely theoretical analyses. The more general prescriptive question about good performance is also centrally important for teaching tasks or any
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students as a result of instruction, can merely mimic what experts actually do. Indeed, students often must he taught explicit processes to achieve performance which actual experts can do almost automatically hecause they immediately recognize situations familiar to them as a result of years of experience.
Th s art cle s uasea on an nv led paper oresenlea a1 the meerlng of the Amerran Cnem ca Soc!ety. -as Vegas. March 1982 Some of dSED 79-20592 fne 4nocr v nq work *as partnal v supported ov. qranl . from the ~ationalscience ~oundatiin.
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Journal of Chemical Education
Detailed Observations versus Gross Statistical Data To understand the underlvine thought leadine - nrocesses . to good problem-solving perf&&ce, it is essential to ohserve in detail the thought processes of indiuidual persons. By contrast, statistical data derived from test scores on many persons are of much less utility because they urovide onlv . verv" gross information. These comments are not intended to denigrate the utility of statistical data. But, as someone once said: "Statistics are like a bikini bathing suit. What they reveal is suggestive, hut what they conceal is vital." There is a great deal of wisdom in this quotation. Insights Derived from Naturalistic Studies Before discussing in greater detail some of the thought wrocesses needed for effective scientific nrohlem solvine. -~ it, is worth mentioning some insights derived from detailed observations of the naturallv occurrine nroblem-solvine" behavior ~~of novice students and experts. Detailed data of this kind can he ohtained bv askine individual persons to talk out loud about their thought while they are solving problems. The transcript of a person's tape-recorded verbal statements, together with the person's written work, constitutes then a "protocol" which provides a rich source of data about the person's thought processes. Needless to say, even such a detailed protocol reveals only a small part of a person's thoughts since many of these are not overtly verbalized. Nevertheless, such protocols provide data much more useful and detailed than would be obtained by test results, questionnaires, or other similar gross measures.
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experts (5-12) and point out some of their implications. Preexisting Knowledge of Students The observations indicate that novice students possess complex conceptual structures derived from prior experience and from informal cultural transmission. These conceutnnl structures are useful to explain and predict many of the phenomena encountered in dadv life. However. unlike scientific conceptual structures, they are often ambiguous, vague, inconsistent, and not accurately predictive. One implication of these observations is that the learning of a science involves much more than the acquisition of new knowledge hy a blank mind. Instead, it involves a substantial restructuring of me-existina knowledee. a restructurine in surprising that adequate restructuring can be a difficult and time-consuming process prone to many errors and confusions. Another implication of these observations is that the modes of learning required in science (modes which require unambiguity, precision, and great care that all language is clearly related to observations) are quite unlike modes of learning familiar from daily life. Such new modes of learning are, therefore, quite difficult to acquire without carefully designed instruction. Tacit Knowledge of Experts Detailed observations indicate that experts possess knowledge which is remarkably large and well-organized. Much of this knowledee is "tacit." i.e.. used automaticallv without any conscious awareness. k e t this tacit knowledge $ essential to good uerformance and sometimes auite subtle. which can reveal much about the nature of expertise. ' Another implication is that science teaching is often of not evenapparent to the teachers themselves.
Significant Differences between Experts and Novices Observations reveal that significant differences do indeed exist between the problem-solving behavior of novice studena and of experts. For example, novice students usually try to assemble problem solutions by proceeding, in linear sequential fashion, to piece together various mathematical formulas. By contrast, experts often approach problems by using qualitative arguments and seemingly vague language, thus formulating plans which only later get refined into more mathematical language. These observations show that experts' superior performance is not merely due to their large store of accumulated knowledge, but also to problem-solving strategies more effective than those used by students. As we shall see, such expert strategies are also theoretically expected to he more powerful and some of them should be teachable to students. General Analysis of Effective Problem Solving After these comments about information derived from naturalistic observations, let me turn to a more general analysis of the kinds of procedures and knowledge essential for good human problem-solving performance (13, 14). I shall begin by pointing out some general issues which must be addressed by any theoret,ical model of good prohlem solving. Then I shall examine some of these topics in slightly greater detail. According to an analysis developed by myself and some coworkers, problem solving involves some general problemsolving procedures used in conjunction with a knowledge base containing particular knowledge about a specific domain (such as mechanics, or thermodynamics, or electric circuits, etc.). The eeneral nrohlem-solvine urocedures break the uroblemsolving process into several successive stages which address the following suhprohlems: (a) How can one initially describe and analyze a prohlem so as to facilitate the subsequent search for its solution? (b) How can one synthesize a solution of the problem, using appropriate planning and subsequent implementation, bv making iudiciouslv the mauv decisions needed to find a path to the s&ion? ( c j ~ o w can bne finally test the resulting solution to ascertain whether it is correct and reasonably optimal, so that suitahle improvements can be made? The nrecedine ~roceduresare to he used in coniunction with a knowledge bask containing specific knowledge about the particular domain of interest. Any such knowledge base must have general characteristics which facilitate the implementation of the preceding procedures, characteristics which must also be specified by a model of good performance. For example, what types of knowledge should he included in such a knowledee base? What kinds of ancillarv knowledee must u accompany any concept or principle so that it becomes usable and can thus serve as a conceutual buildine block? Finallv. how must the entire knowledgebase be organyzed so that l a r k amounts of information can he easily remembered and appropriately retrieved in complex problem-solving contexts? An understandine" of how -eood human uroblem-solvinnperformance can be achieved requires answers to all the preceding questions. In the following paragraphs I shall merely outline some of the major ideas which have emerged in our work addressing these questions. ~~
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Problem-Solving Procedures Initial Problem Description The manner in which a problem is initially described is crucially important since it can determine whether the subsequent solution of the problem is easy or difficult-or even impossible. The crucial role of the initial description of a problem is, however, easily overlooked because it is a preVolume 60 Number 11 November 1983
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ORIGINAL PROBLEM STATEMENT
MOTION
INTERACTION
t i m e I.. A MAN SITS AT THE 10P OF A SEIODTH HEMISPHERICAL OWE. OF PdDIUS R. COVERING A FACTORY O N HORIZONTAL GROUND.
IF THE MN STARTS SLIDING,
AT WHAT MIGGHT ABOVE THE GROUND DOES HE SLIDE OFF THE WMt?
BASIC DESCRIPTION
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Figure 1. Original statement and basic description at a mechanics problem.
liminary step which experts usually do rapidly and automatically without much conscious awareness. A model of effective problem solving must thus, in particular, specify explicitly procedures for generating a useful initial description of any problem. The first stage of such a description procedure aims to generate a "basic description" of a problem. This is achieved by using general domain-independent knowledge to put the problem into a form where it is readily understandable to the problem solver. Thus, the basic description summarizes the information specified and t o he found. introduces useful svmbols. and exuresses available information in various useful symbolic forms (e.g., in verbal statements as well as in diagrams). Fieure I illustrates an example. The next stage of the descriution urocedure is more complex. I t aims togenerate a "theoretical description" of the problem, i.e., a description which deliberately aims to redescribe the problem in terms of the special concepts provided by the knowledge base for the relevant knowledge domain. The resulting problem description greatly facilitates the subsequent search for a problem solution since all urineiples in the knowledge base are expressed in terms of these special concepts and thus become readily accessible.
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should s p e k y how to identify, in any problem situation, those entities of prime interest in this domain, what special concepts should be used to describe these entities, what properties of these special concepts can he exploited, and how to check that the resulting description is consistent with known principles (15). For example, the knowledge base for the science of classical mechanics can usefully be accompanied by explicit rules specifying explicitly how to describe any prohlem in mechanics. These rules suecifv that the entities of interest are particles (or systems co&t& of several such particles). They specify that the motion of any such particle should be described by special concepts such as "position," "velocity," and "acceleration." They also specify that the interaction between such particles should be specified by special concepts such as "forces" or "potential energies." The description rules also ~ p r ~ how t y 1;) rxploit tht, properties ,,I' lhe.+~. m7:wepts. l'cor in;tsncv, they spcciiy that iont..;r;tn he s?~tematiu,~lly enumerated bv first considerine. . lone-ranee .. .. forces (such as erav~ I \ I;ml thrn ~ d w t i t : ~ ~t n l ~y e ~ h o r t m iwcesm n~c ally partitlt. C d ) i ~ r t which s tolt[h t m
