Inducing Formal Thought in Introductory Chemistry Students Robert D. Kavanaugh Department of Psychology William R. Moomaw Department of Chemistry, Williams College, Williamstown, MA 01267 Chemistry instructors are well-acquainted with the continuing debate over the proper approach to teaching their introductory courses. Should one use a predominantly theoretical approach and immediately introduce students to abstract concepts such as orbitals, thermodynamic variables, and equations of state and ask them to predict the properties of chemical systems; or should one develop a more descriptive approach in which students are encouraged to ohserve the properties of chemical systems and try to deduce more general principles from their ohservations? These two approaches to chemistry instruction are related directly to Piaget's theory of intellectual development, and this close correspondence is perhaps the major reason for what, a t first glance, appears rather puzzling-the repeated references in chemistry journals to the work of a man who has made a major contribution to developmental psychology. However, the enigma is resolved quickly once we recognize that Piaget is not, as he is labeled too frequently, a child psychologist. On the contrary, he is one of the few developmental theorists to take as his task a description of life-long intellectual growth. Furthermore, Piaget's description of the final stages of thought are based largely on prohlems involving physical and chemical concepts. Thus, it would appear that methods of instruction in beginning chemistry represent an obvious place for the application of Piaget's theory. Readers of this journal are by now quite familiar with the four stages of Piaget's theory of intellectual development (1,2,3), and we will not review them here. Rather, it is our purpose to comment on two basic questions arising from previous work: (a) should chemistry instruction begin a t the concrete level as the advocates of the descriptive approach have suggested, and (b) what procedures can he used to induce ahstract or formal thinking among those students who have not progressed beyond the concrete level? Chemistry Instruction There is little question that chemistry involves aspects of what Piaget calls formal operational thought. Students must deal with stoichiometry and gas law problems involving proportions, variables, and mass conservation; with abstract concepts such as chemical bonds and molecular orbitals; with intensive properties such as concentration, density, and pressure; as well as a whole host of generalized variables, including reaction rates, force, energy, and entropy. Furthermore, students are asked to understand and explain all ohservations of the macroscopic, observable world in terms of the properties of microscopic, unseen atoms and molecules. As reasonable as this may seem to the instructor, it may represent an overwhelming exercise in formal reasoning for some students. By the time most students enter college, they are well past the age (roughly 10-12) a t which Piaget believes formal concepts first emerge. I t is now clear, however, that Piaget's original speculations require some revision. The results from a number of follow-up studies show that not all subjects achieve formal thought (4). For example, when tested during the college years or even later, as few as 50 percent of the subjects in some samples demonstrated formal operations ( 5 , 6 ) .Furthermore, although the data are much less conclusive, there is reason to believe that a sizeable percentage of the
population shows formal thinking in some situations hut not others (6.7). Therefore. it is quite possible fur 18 or 19 vear olds to begin chemistry instkuctioi without the benefit of formal reasoning. Recent surveys of freshman chemistry courses ( 3 )reveal that many students do in fact enter college without formal operational skills, a t least as they are applied to the nhvsical sciences. The variability in the reasoning skills of entering freshmen oresents the instructor with a difficult choice. Should chem-
..
i i too difficult for some students,or should it begin a t the concrete level (i.e., use a descriptive approach) with the possible risk of diluting the material and thereby discouraging the formal operational students. Piagetian theory, as well as subsequent research inspired by thk theory, can he quite helpful on this point. Both sources suggest that problems involving formal reasoning are grasped&re easily when they are initially presented a t a concrete level, and that this finding holds true even for students who are already functioning a t the level of formal thought (3). For example, recasting a stoichiometric oroblem in concrete terms. oerhaos bv havine students actuaily build complex molecu1es;is an kxeriise t h 2 should profit virtually all members of the class. Inducing Formal Thought-Basic Issues Students who function comfortably a t the level of formal thought may find it helpful to have the instructor initially demonstrate a difficult problem in concrete terms, hut they are also capahle of making the transition to abstract thought when it is required. However, the student who reasons exclusivelv in concrete terms is not c a ~ a h l eof makine such a transitibn and can he expected to encounter problems in a physical science course. What should he done for this student? The instructor appears to have two options: either limit the chemistry taught to concrete operations and concepts, or employ pedagogical techniques that will induce formal thinking. While concrete aspects of chemistry are important, it is clear that one cannot develop much of an understanding of or anoreciation for the discioline without utilizine formal .. thought prucessei as well. l'r;~rtically,hou,ever, the prd,lcm uf indurinr t h n a l rhourrht in a runcrete thinker is substantial and amounts to nothing less than a restructuring of the student's cognitive style. The remainder of this paper addresses the question of whether it is possible to induce formal thought, and a t what cost to the instructor and the student. Although attempts to induce formal thought are relatively rare, several investigators have developed programs designed to achieve this goal in the physical sciences (8-10). More common are attempts cited in the psychological literature to induce the transition to one or more asoects of concrete thinking, the stage that immediately precedes formal thought (11).The exoerimental a t t e m ~ t to s eenerate both tvoes of thinking appear to have met k i t h some success. hemo ore extensive concrete operational studies have, however, raised important questions about inducing the transition to a more t most apadvanced cognlrlre stage. Two quesrims t l ~ seem plicahle tothe indurrion of lormal r h o ~ ~ gare h t (3)the possiit,. learns bility thnt thc studrnt nrquirrs n 'p;eud(,t:~~ncel~t." Volume 58
Number 3 March 1981
263
to demonstrate formal thinking on only one type of problem, nrewmnhlv nroblem used in the trainine session, and (b) r.........- ~.~ ,t,he .~~~ the pusiildity that the, student temporarily acquires a more hn,adlv" hased level (,f formal thnueht. but then auirklv reverts in the these to concrete thinking. We will ret& conclusion of this paper.
.~
~~~~~
~
~
~
lnduclng Formal Thought-Procedures There are essentially two approaches used in attempts to advance an individual's thinking. One is behaviorally oriented and owes much to the considerable influence of B. F. Skinner. The essence of this approach is to provide a problem set for the learner .-~. -..- counled with immediate reinforcement for correct or incorrect responses. The teaching machine is a familiar illustration of this aooroach. Problems are usually presented .. in structured fnihim beginning with the easiest exemplar for a eiven set and nmtinuinr- u n t i l the mure d~fficultrxrmplars " are mastered. While the behavioral approach has considerable merit, particularly in i t s adaptati(;n-for sperialiaed populations such as rvtardi.d or autistir rhildrrn. ur in t h acquisition ~ of fartual information in normal populations, we can question its utility in inducing formal thought. As Piaget has noted, formal thinking is not characterized by a particular body of knowledge, but rather by aprocess of problem solving. That is, the approach used in solving a problem is itself the indicator of formal thinking. Generally speaking, those who can adopt a systematic method of holding variables constant, manipulating one factor at a time, and establishing hypotheses about possible outcomes are engaged in formal thought. These . . pr8,resst.s arc. nnt easily shaped using traditional t~ehavioral techniques because ubtaining the sulution to a problem is nut in and of itself a guarantee that the student has mastered the underlying concepts or procedures. What can be done to alter the student's basic approach to problem solving? We believe that several teaching techniques closely tied to Piagetian theory may be effective. First, we extrapolate from Piaget's stage theory and suggest that a difficult problem should be recast in concrete terms. Thus the introduction of most concepts in freshman chemistry should begin with an overt demonstration. Moreover, as Piaget would stress, the student should actually encounter a "hands on" experience. For example, in teaching elementary stoichiometry, it may be useful to tell a student that a certain chemical reaction is observed to take place, and then allow him or her to construct reactant molerules, disassemble them, and reconstruct the atoms into prnducti. Different students will carrv out a different seauence of "reaction steos." but all shoild end up with the same products. Some of the mystery and aura (not to mention fear) of the phvsical sciences should disappear when students experience the discipline at this concrete (perhaps we might even say "sensorimotor") level. Should we expect that recasting a problem in concrete terms and even encouraging the student to experience the problems a t this level will itself promote the transition to formal thought? Theoretically and empirically, the answer is no. Goodstein and Howe (3) have pointed out already that the simple experience of working with concrete models did not cause concrete thinkers to shift to formal thought when they were presented with new stoichiometric problems. These results should not surorise us. however. oarticularlv if our orientation is Piagetian. Recycling to an earlier stage is a first step in inducing higher levels of thought, hut it is by no means a necessary and sufficient condition. To induce a transition to the next level of thought, we would advocate that the instructor create a situation in which the student discovers difficulties associated with his or her current approach to a problem. That is, the instructor begins with the student's concrete model of a problem and then asks a series of questions designed to show that certain givens, preferably physical outcomes, cannot occur with this model. ~~~~
~
~
~
~
~
264
~
Journal of Chemical Education
~
Shortly, we will illustrate the procedure in detail, but first let us outline its relationship to Piagetian theory. By creating doubts ah;)ut the student's &rent method of problem soking, the instructor has creawd a situation that Piagetiam referto as cognitive conflict. Conflict occurs when an individual has some knowledge about the solution to a oroblem and then discovers that his or her aonroach is leadine toward a contradictory or ineffective answe;. piaget believes that conflict is intellectually motivating; it demands resolution. Thus, when the student is placed in conflict about models that he or she has created, the instructor can begin to ask questions that are closely tied to the student's level. This method of question-asking also has a strong basis in Piagetian theory. Piaget believes that knowledge is acquired sequentially and that when new information is presented, maximal learning occurs only if the presentation is matched to the individual's existing level of thought. An Example Sunoose .. one is usine the valence shell electron nair renulsion pr~ncipleas a hnsis for reaching students to predict moIecular eeumetrles. Manv students are ranable of handline this prd>lemeither "in their head." ur m pnprr, hut a concrete o~eratimalthinker is likclv to exoerience difficults. We wnuld r&ommend that such a Student manipulate actual objects (molecular models) so that he or she is workina a t his or her cognitive level. In carrying out the process deccrihed t d u w it is important t n distinguish hetween the goal of teaching students the svientitir fact ufmethane'~tetrahedral structure nnri the gual uf induring the transition from cmcrete operational reasoninr u ) li~rmalthoueht 112,.Only. hv. eifectinr such a transit~onin the reasoning process can a student master an abstract ronrept and avrds .. . it tgr a new situation (9). . e.r. in this case to correctly predict steric hindrance in more complex organic molecules. T o successfully predict the geometry of the methane molecule, a student must find an arrangement that maximizes the distance between the four carbon-hydrogen bonds (and hence the hydrogen atoms) for a given carbon-hydrogen bond length. Many students, whether using models or not, quickly hit upon a planar structure with the carbon atoms at the center and the four hydrogen atoms at the corners of a square. Such a structure is not unreasonable since the 90' HCH angles do maximize the distance between hvdroeen atoms in a twodimensional molecule, hut it is of course incorrect. To realize that these bond angles can he increased to log0 in a threedimensimnl tetrahedral structure requires th(tughr proresses that are formal rather than just cunrrece. What thc instructor must do a t this point is to place the student in conflict. After praising the student for coming up with a plausible structure, the instructor might then ask if there is any way in which the HCH angles can be increased. The student can readily show with the model that any increase in one angle leads to a decrease in another. The instructor might then ask whether there is any other structure for which the bond angles remain 90'. While it is best if the student discovers that one hydrogen atom may be removed from his planar model and placed directly above the carbon atom on a line perpendicular to the plane, the instructor may have to carry out this operation. In either case the student's belief that his model is the only one that can work now conflicts with the reality of a new physical model. Even if he or she argues (correctly) that the new model does not separate all the hydrogen atoms as much as his or her old one did, they will have made the important formal leap of thinking in three dimensions instead of two. An examination of the new three-dimensional right angle model should reveal to the student possibilities for increasing the bond angles until he or she discovers the optimal tetrahedral solution (13). One could think of other approaches to get the student to correctly build a tetrahedral methane molecule. For example, one could point out that spectroscopy reveals that methane
.~ ~.~~
-
-
rotates as a spherical top (three moments of inertia are equal) rather than as a symmetric top (two moments equal one different) predicted by the planar model. One could cite crystallographic data which are inconsistent with square planar molecules, or the equality of the three polarizahility tensor components. More commonly one points out that the molecule CH2C12would he expected to exist as two isomers in the planar model of methane whereas only one is observed. All of these approaches attempt to induce cognitive conflict, hut all are poorly matched to the individual's cognitive level. Each example presents a verbal assurance or a highly formalized concept to the student who is still operating at a concrete level. Induction of formal thinking using these examples is not likely to be as effective as the approach we have suggested. Ohviously, our recommended technique is not totally concrete because the instructor must question the student about concepts such as electron repulsion. Chemistry, however, is not a totally concrete discipline. By following our approach the student is actively involved in the construction of molecules with the instructor creatine for the resolution ..oo~ortunities .. of conflicting information that is closely matched lo the student's cognitive level. ~
~
-
Conclusion We end with a note of caution. One route toward the development of formal thought is outlined here, but it is obvious that other avenues are possible. Clearly, some students reach formal thinkine on their own without anv tvDe of intervention. Although we $0 not know precisely what occurs in this naturalistic form of development, it is quite probable that the self-discovery and resolution of cognitive conflicts is only one of several orocesses involved. More to the point, there are undoubtediy additionul intenwtion techniques which aid the transirion to formal thought. Perhaps the best known of these is the Science ~ u r r i c u l u &~ m ~ r o v e m eStudy nt (SCIS). This program, developed by Karplus and others (8,9,14),outlines procedures for teaching scientific concepts a t the high school and college levels. Like our proposal, SCIS stresses the importance of an initial, concrete ("hands on") experience which the authors feel will eventually cause the student to confront issues that cannot he resolved at his or her current level of reasoning. In contrast to our proposal, the student is less directed toward attaining a specific concept. Furthermore, there is no direct involvement of the instructor in creating cognitive conflict which is supposed to occur naturally during the exploration phase in Karplus' scheme. While many students undouhtedly discover cognitive conflict on their own. rnanv do not. the transition ~ ~ ~ and hence ~ ~ ~ to formal thinking remains beyond them. Our proposal is directed a t these students. Once they are identified, the instructor can focus on their problems using the techniques described in this o. a.~ ein r a manaeeable wav. Most of the interaction with students can occur during lat~oratorysessions, and it is quite posaihle to train graduate or even undergraduate assistants in these techniques. Close supervision from the instrucmr would he required to ensure that the essentials ~
~
of the procedure were maintained, hut a division of labor is certainly possible. An additional and important advantage of our more explicit procedures is that they afford a greater opportunity to induce a stable level of formal thinking. Piaget has noted that training procedures can result in "pseudoconcepts" if they do not incorporate elements of cognitive conflict or if the learner is not ready for the training (15).The results of studies designed to promote an earlier cognitive achievement, the movement from preoperational to concrete operational thinking, reveal that this cognition is both acquired and maintained when conflict resolution is part of the training (16). Although for the moment it remains as speculation, we would hypothesize a similar level of stability with the procedures we have outlined for the transition to formal thought in chemistry students. Finally, we recognize that some instructors may have used techniques akin to the cognitive conflict model as part of their pedagogy, even though they were unfamiliar with Piaget. This use should not he surprising because the conflict model is really an extrapolation of the descriptive approach to chemistry insrruction. Teachers who are inrlined to use this method might a,ell di>coverrhe additional adrantnges that result from having students question the validity of their own efforts to solve a problem. I t is important to recognize, however, that in addition to its intuitive appeal, the conflict model has a firm basis in a powerful theory of human cognition. Piaget has suggested that the discovery and resolution of cognitive conflicts a t an appropriate developmental level is the principal means by which intellectual advancement occurs. Thus, we would argue that the conflict model deserves consideration when instructors are faced with the difficult problem of inducing.. a hieher .. level of reasonine in their ouoils. Literature Cited
99. (11) Kuhn,D..Dov.Pwch., 10,pp.S90-600(19741. (121 Kuhn, D.. Horvord Edue. Roo.. 49,pp. 3M-360 (1919).
~
(16)
1968. smeddund. J., scandin.~imJ
psych..2, pp. 156.160
(1961).
-
The authors wish to thank Williams Colleee for initiatine this rollaboration by holding a Conference on Teaching in h v e m h e r 1978. WRM wishes to thank the Camille & Henry 1)reyfus Foundation for supporting this research through the awarding of n Dreyfun 'I'eacher-Scholarship.
Volume 58 Number 3 March 1981
265
