David W. Brooks John J. Scholz and Thomas J. Tipton University of Nebraska-Lincoln Lincoln, Nebraska 68588
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Concrete illustrations of Formal Concepts
Through recent . naners . J. Dudlev Herron has focused chemists' attention upon Piagetian notions of intellectual develonment (1.2).Short of radicalizina the curriculum, are Piagetian oriented strategies availahle to teachers? We searched our course for traditional content areas which many students perceived as difficult, which involved a formal concept readily described using formal means, and which might reipond well to a unifying concrete illustration. In the first lectures of the general chemistry course, we introduce word definitions of intensive and extensive properties to deal with conceptual problems related to heatltemperature and massldensity (3).These benefit some students. After several years, we began to introduce the following formalism Extensive Property = R = Zbi Intensive Property = R = b, These powerful abstractions helped those students who were already successful in dealing with the word definitions. Unfortunkely, the difficultiesof unsuccessful students were increased by these equations. A trivial lecture demonstration illustrating the two equations has been developed. Four beakers, two about 1-1in volume and two only half as large are employed. One large heaker is filled with a colored liquid. With the assistance of a volunteer student, the liquid is distributed equally between the two large beakers. Once this is accomplished, the lecturer (in a cavalier manner) transfers the contents of one large heaker unequally into the two smaller beakers. Students are then asked to name nronerties. As these Dronerties are called out. . . . . thc lecturer indicates that: "the ternpernturr ofthe liquid in each uf the small hrakrrs i.; tbt, sanw i ~tlvat i in the lnree - heaker, and this is characteristic of an intensive property;" "the volume in this heaker plus the volume in this beaker equals the volume in this (large) heaker, and this is characteristic of an extensive property;" and so forth. After several properties are thus classified, the lecturer then introduces the equations and relates each specific example to one of the two equations. Using this strategy, "concrete" students quickly achieve almost 10096 success in classifying properties familiar to them (volume, weight, temperature, "sweetness") as being intensive
or extensive. They more easily learn to deal with properties initially less familiar to them (concentration, vapor pressure, heat. densitv). The demonstration has potential pitfalls. For example, you should decide in advance how to deal with suggested properties of color and color intensity. There is one advantage of using aqueous scotch as the liquid; if a student asks you to classify the property of surface area, you can drink the demonstration, thereby simultaneously destroying the "evidence" and helping you forget this entire exercise. The strategy we describe does lead to student success with respect to performance in one ohjective among hundreds in a traditional curriculum. Whether the result of the development of intellect or. more likelv. the memorization of a couCrete prohlem-solving algorithm based upon the illustration, students successfullv learn using this strategy. The important are th& we valuethe content ohjective discussed; a strategy which improves performance relative to this ohjective has been developed; the improved strategy . . came from a conscious consideration of Piagetian epistemology. Herron's recent comments distinguishing teacher's use of illustrations from their use of analogies seem to us to he valid ones (4). This example is one of an illustration. Though Herron provides us with a ". . . . Plan for Inaction," his writings actually give us reason to he encouraged. The task is for us to distinguish illustrations from analogies, a nontrivial task. For several years, one of us taught equation balancing by e avnroach dionhantiue eauations 15). . . Todav .we ~. e r c e i v this .. as too formal, and we opt for a more traditional "inspection" method. In the absence of evidence that a radical curriculum revision is availahle and desirable, you, too, may find objectives for which concrete illustrations are availahle. You, too, may decide that some of your favorite strategies are too formal. Literature Ciled (1) Herron.J. D.. J.CHEM. EDUC..S2, 146 1197hl. (2) Herran, J. D., "More Piseef for Chemise: The Things I Wish I Had Told You: paper prssentad at2YC1 Conference in Kansas City. MO. October 29. 1976. (3) Brown,T. L.. and i.eMay, H. E., dr., "Chemistry: The Central Science: Printice-Hall, In?. F.nslerod- ClilR. N.I. 1971. 0. 11. (4) Herr0n.J. ~ . ; " ~ i a g e t ~ p b i i Suggeslions ed: for inaction," paper presentad at 173rdACS National Meeting. New Orleans. LA. April 23. 1977. ( 5 ) CraLer,R..J.CHF.M. EDUC.45.731 (1966). ~
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Volume 55. Number 3, March 1978 I 173
