Madeline P. Goodstein Central Connecticut State College New Britain. 06050 Ann C. Howe Department of Science Teaching Syracuse University Syracuse. New York 13210
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Application of Piagetian Theory to Introductory Chemistry Instruction
In every chemistry teacher's mind there is a complex structure of the discipline with hypotheses, theories, and philosophies interlocking to produce a supporting framework for facts. When introducing the discipline to neophytes, the teacher must make some fundamental decisions as to how to start amstructing the framework. Shall i t be a thin erecturset skrlvtnnof theentire structure with all detailsomitted? Shall it be some one small portion of the structure intimately detailed which acts as the representative of the remainder? Perhaps the entire ground floor of the structure should be described with as much detail as the allotted time permits. In the past these alternatives have been debatedand decisions have been made largely on philosophical grounds. While learning theory has contributed our ideas of how knowledge might best he imparted and absorbed, little which has been dt~k!lopedin the area of ed~lcationalpsycholcgy has been of specific significance to the tewhiny of the sciences. Recently, however. the work of Jean Piaeet has excited much interest amung chemistry teachers, who M i w e i~ may hold prumise of giving a basis tor making ~nstructionaldecisions. Piaget's Theory The work of Piaget as it relates to the discipline of chemistry has been descrihed previously in this Journal in some detail (1-3). Briefly, Piaget proposes that there are successive stages in cognitive understanding as an individual grows to maturity. Those who are studying chemistry are most likely to be a t one of two levels in this hierarchv. At the lower of the two levels. the student is ahle to c a r r i o u t certain mental operations based on observations and collected data; these operations include classification, conservation of mass and other properties, arranging data in serial ordrr, nnd t:swhliihmrnt of one-to-on(.rd:itionships hetwren sets of d a t a Thli cugn~tive level is called concrete operational thinking. At the higher cognitive level, called formal operational rhinking, the student can go I ~ e w n dd~serwhlt.dataand familiar objects and applv I hr mentill operations ro concepts, abstractions, and theories. He or she is no longer limited to personal experience or particular cases hut can extrapolate, hypothesize, and generalize. At the formal level the law of conservation of energy can he applied, relationships can be interpreted mathematically, and students can do proportional thinking. T h e formal operational thinker can understand functional relationships between relationships and thus can erect mental structures of interlocking ideas and combinations. Several investigators have examined the basic concepts taught in typical introductory secondary and college chemistry i funcnursrs and hare cuncluded [hat comprehensiun i ~the (Inmental ideas taught requires iurmal thinking i-1-61. If it is indeed true that understanding such concepts demands thinking a t the formal level, then the curriculum which explores intensively one or several basic topics must be taught only to formal thinkers. Moreover, we must consider whether a mathematical approach is effective in teaching concrete operational learners and, in fact, whether any quantitative approach can be used with students who are a t the concrete operational level. Cognitive Levels and Sclence Achievement. What proportion of first-year chemistry students are a t the formal operational level and what proportion are pre-formal?
Chiappetta (7) reviewed a number of studies and concluded that most adolescents and young adults have not attained the formal operational stage of cognitive development. McKinnon and Renner ( 8 )found that 50%of the college freshmen in their sample were concrete operational. 25% were in transition to tormal thinking, and m l y 25". cnuld IIP d ~ s s i f i r di i i formill operatiunal. Lnwsnn ( 9 ) fcund that 2200 of chemistry studenrs a t Oklahoma high school were concrete thinkers while 78% were a t the formal level. Sayre and Ball (10)investigated the relationship between cognitive development and achievement in science in grades 7-12 and found significant correlation. However, many formal operational students earned less than a grade of "B". Sayre and Ball ascribed this to failure to function consistently at the higher cognitive level. In a studv in which the ~articiwantswere fifteen elementarv school tealhers attending a ~ ' a t i o n a Science l ~oundation Summer Institute, Chiappetta ( 1 1 ) found that most of the formal operational thinkers did not achieve full understanding of a laboratory unit on chemical solubility which dealt with ratios and proportions. He reported that approximately 43% of the "formal operational suhiects were not ahle to give simple examples of the problems that they correctly soGed on the paper and pencil exam" in physical science. Together with other studies. this led the ir&estieator to conclude that the majority of those studying introhctory sciences taught a t hoth the secondarv and colleee levels tend to function a t the concrete operat i h a l level in understandin,: the iul~jectmatter even thoueh they are cauable oi furma1 thinkinr I 71. It seemsVclearihat mok subject matter taught& chemistry courses is developed on an abstract. conceptual level. but nlally students reason a ~ , , ~ . ( . ~ ' ~ ,level. ) ~ ~ i ~ i ~ Moreover. thuse callable of formal thmkinr often function I ~ I a p r e - f o r ~ alevel l dhen confronted with science concepts and problems. Does this mean that concrete operational thinkers may be taught only thosr rc,pici which om he understood at the concrete level ur is rhrre somr WHY tc, teach so that they will gain understanding of conceptual topics on a formal level? Herron ( I ) has suggested that conceptual chemistry can he expressed in terms of concrete exemplars which model the abstract concept. By expressing the concept on a concrete level, he argues, concrete thinkers will acquire a surrogate concept which can later develop into the real concept. Several investigators have reported positive results when concrete methods of instruction have been used. Sheehan (12)taught three formal Piaget tasks to 13 year-olds by hoth concrete and formal methods of instruction. He found that concrete inm,,re efiectlvr with both cnncrete and iurmal struction in he re. learners. ~ ~I I J, l l a n experiment ~ ~ of st"dents in an-introductory chemistry quired one course to construct molecular models of each substance being studied and compared the achievement of this group with that of a control group. He found that the control group achieved slightly better scores on test questions that required only recall of information hut the experimental group achieved better scores on questions posed a t higher cognitive levels. Application ol Theory: Procedure and Results. We have conducted a preliminary study in an effort to learn whether instruction based on the use of concrete models and Volume 55, Number 3, March 1978 / 171
exemplars would lead concrete operational students to achieve a qualitative understanding of a quantitative relationship. The students who participated in the study were enrolled in the introductory chemistry course in a high school in Milford, Connecticut. Students in the honors section were not included. Before beginning instruction we determined the students' levels of cognitive development by administering a battery of written tests composed of items drawn from Gray ( 1 4 ) and Wollman and Karplus (15). We found the distribution of students among Piaget levels to he as follows: Upper Formal, 40%; Lower Formal, 35%; Upper Concrete, 21%, Lower Concrete, 4%. This is a higher proportion of formal operational thinkers than McKinnon and Renner (8) found in their sample of college freshmen and is approximately the same proportion as that found by Lawson (9)in his sample of secondary chemistry students. For the tonic to he taueht we selected stoichiometw because it is one of t i e earliest foimal operational concepts to he presented in the usual introductory course. (Density may be presented earlier but is often taught in such a way that it can he learned by rote.) The experimental instructional strategy adopted involved the use of molecular models constructed by students wherever these could be introduced. For example, students initially made models of one hydrogen molecule and one oxygen molecule and were asked to use them up to make water molecules. The students only gradually came to realize that another hydrogen molecule was needed to use up the oxveen. *.therehv,nroducine another water molecule. From this simple exercise came an improved understanding of the halancine of a chemical eauation. Other molecules and eauations were modeled as discissed. Later, before an experiment on determination of oercentaee of water in a hvdrate was carried out, the students'first ~ o ~ s t r u c t ethe d hydrate model using weighted particles (approximate), weighed the model, removed the water of hydration from the model, and then reweighed the model. Whereas the control group did the mo~omolecularlayer experiment to determhe ~vogadro's number, a substitute experiment was used for the experimental group in the belief that formal thinking is required to understand the Avogadro's number experiment. In the suhstitute experiment, students worked with models to determine that ten atoms each of two different elements have the same mass ratio as one atom each of the two elements. A similar process was used for some simple molecules. Finally, each student weiehed out 0.1 mole of a eiven element and of a aiven compound; the weighed samples were lined up in order of mass in a display a t the front of the laboratory and were used in written questions to develop the concept that all the samples had the same numher of particles even though - the masses and volumes differed. For reasons of economy, we used candies initially as atom models with toothpicks as bonds. Miniature marshmallows served well for hydrogen atoms while jujubes in various sizes . . were SPIP( ted LO match the relative masirs of rariouc elemenrs. Liltw, when ihe novelty wore off. wmv students preferred to work with the less stickv nolvstvrene . snheres. We took care to point out that no food brought in& the laboratory was consumable because of oossihle dangerous contamination. We also took the opportunky to discussthe nature of models and talked a t some leneth about their im~erfectious. The instructor; also constructed models of particles wherever they could be used in lectures. Equations were given a permanent format by mounting polystyrene halved spheres in different colors onto cardboard with pins or rubber cement. Instead of using coefficients to show the numbers of particles, all of the required particles were shown. These constructions were passed around the room and later displayed on the wall. This instructional method was used with two sections of students; two other sections were taught by methods which did not use concrete exemplars and models. At the end of the instructional period, two questions were embedded in the
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172 1 Journal of Chemical Education
usual unit test to assess qualitative understanding of stoichiometrv. These auestions, which had not been previously discussed either inclass or i'n the text, were 1) Which, if either, has mare atoms, 30 gof oxygenor 30 gof chlo-
rine? (Explain your answer.) 2) 35 g of chlorine are reacted with 35 g of sodium to form NaCI. Is there exactly enough of each or willsodium be left aver or will
chlorine be left over? (Explain your answer)
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These auestions were designed to discriminate between understanding in contrast to mechanical manipulation of numerical data: answers to these auestions were used as the indicator of un'derstanding of sto~chiometrya t a basic level. Results and Discussion When the attainment of the students in the experimental sections was compared, by means of the chi square statistic, with the attainment of students in the control sections. we found that only the students a t the upper formal operational level benefitted from the use of the instructional procedures descrihed above. The performances of experimental and control students were a ~ ~ r o x i m a t ethe l v same for those a t the conrrete levd, were nc,;;igniticantl\.dit~rrent fnr thweat the ronrrete l~:vd,were nut sircnitirantls il~iferentfor those at the lower formal level, but w&e significantly different ( p
