J. Dudley Herron Purdue University West Lafayette. Indiana 47907
Piaget in the Classroom Guidelines for applications
"Piaget for Chemists" ( I ) offered an explanation for the fact that many students do not do well in chemistry. It stimulated numerous requests for information on applying Piaget's theory in the classroom. This paper includes responses to some of these requests. ~
~
ldentificationof Students
Several people have asked how they can identify students who are operating a t the concrete operational or formal operational level. Is there a test that can he administered to students for this nurnose? Many people h'ave'worked hard to develop a short answer test which can be administered to large groups of students (2-12). There have been some partial successes. The test developed in France by Longeot (I0,l l ) and translated and used in this country by Sheehan (7) has heen used by several people and is undoubtedly of some value but it has limitations. The problem is that when you are trying to classify students as concrete operational or formal operational, you are interested in the reasoning that the student uses. Whereas individual interviews such as those used by Piaget and Inhelder in their work do provide some opportunity to see how the student is thinking, quick scoring, paper-and-pencil tests provide little opportunity to do this. Here is an illustration: The Island Puzzle was described by Karplns several years ago and the following adaptation was used by Tom Sills in a preliminary version of the test he developed a t Purdue.'
short-answer questions designed to measure hypotheticodeductive logic, one of the characteristic of formal thoueht. In addition to the problem of formal students giving what are considered to he concrete answers, concrete operational students may give answers that appear to be characteristic of formal thought. For example, the following question appears to involve proportional reasoning, a characteristic of formal thought. If 2 apples cost ZOcents, the largest number of apples I can buy with 50centsis:a)l h ) 2 e ) 3 d ) 4 e ) 5 When this item was given to a group of students, many of whom operated a t the concrete level, 88% gave the correct answer of 5. Are they using the proportional reasoning characteristic of formal thought? No, they are not. When yon interview the students to see how they answered the question, you find that most of them cannot tell you. They are usually unaware of the reasoning employed. If a student does explain his answer, it often goes something like this: "Well, 2 apples cost (correspond to) 206, then 1apple costs (corresponds to) 106, and 5 apples cost ( c o r r e ~ ~ o n d ~506." to) The reasoning involves seriation and correspondence, the logic of concrete operational thought. If the prohlem is changed to read, "If 2 apples cost 230, how many apples can be bought for 57$?," most concrete operational students are unable to solve the problem because the seriation and corresoondence is less obvious. An excention would be found in cases where the concrete operational student recalls an algorithm for oroblems of this kind and a . ~.o l i e sit without reasoning of any kind. Is Identification Necessary?
Islands A, B, C, and D are four islands in the ocean. People have been traveling among these islands by boat for many years but recently an airline started in business. Carefully read the following s1nlrrnrnl.i almut the lmis1lh plnnc trip* at p r r w ~ l 'I'lw trips 1,ctwpen &nds tnny Ih- d~rrcror intl~destops nnd plnnr channwun nn islnnd \Vhm n trip is posqihlt, it ran Ire madr ineither direction between the islands. ~ e & ecan go by plane between islands C and D. People cannot go by plane between islands A and B. People can go by plane between islands B and D. Can people go by plane between islands A and C? A) No, because no statement was made ahout a dam connection to island A. B) No, because if you could fly between islands A and C, then you could fly between islands A and B which is not possible. C) No, because since you can fly between islands C and B, you could fly between islands A and B which is not possible. D) Not enough information is given to know.
It can he argued that the logic characteristic of concrete operational thought would lead to choices A and D whereas logic characteristic of formal operational thought would lead to choices B and C. Still, many formal operational thinkers arrive a t choice A or D. Subtle interpretations given to the word "between" can lead to various interpretations of the problem. Similar difficulties have been encountered with most
Why would chemistry teachers want to identify concrete students a t the beginning of the term? If the purpose is nlacement of students in "slow" or "fast" classes. one should consider factors such as reading ability, existing knowledge of chemical facts, and knowledge of mathematics skills in addition to intellectual development. Measures such as SAT and the Toledo Chemistrv Exam mav be iust as useful for screening purposes as a teBt of intellectual h e v e ~ o ~ m e n t . Perhaps people want to identify students a t the concrete operational level so that they can help them. Fine, hut a formal test may not be the most efficient way to do this. An alternative is to make no attempt to classify students as concrete or formal hut to try to identify instances of concrete operational thought through informal discussion. Students having difficulty with problems involving proportional reasoning can he contacted during lab or some other convenient time and asked to explain orally how they go about solving a problem. Knowing the characteristic reasoning required here, a teacher soon gets a fairly good reading of the student's ability to use proportional reasoning or to employ other aspects of formal reasoning. This paper is a condensation of "MorePiaget for Chemists: Things That I Wish I had Told You" presented at the YCBConference in Kansas City on October 29, 1976 and "Piaget Applied: Inaction>2presented at the ACS convention in N~~ orleans,
~~~~h23, ,977. For further discussion of the island D U Z Z ~and its value in measuring formal thought, see Blake, et al. i13).
Volume 55. Number 3. March 1978 / 165
From the noint of view of the classroom teacher, perhaps it is less important to classify students as formal or concrete and more important to know: (a) if they are comfortable with hypothetico:dednctive reasoning (what we normally call "scientific reasoning"), (h) if they habitually think in terms of all possibilities, (c) if they systematically examine all ~ossihilities.(d) if they see the logical necessity of "all other things being equal," (e) if they use proportional reasoning, and so forth. Informal contact in the laboratory, laboratory reports, responses to essay questions, homework problems, and informal class discussions provide ample opportunity to gain clues concerning the student's reasoning abilities. T o know these things, the teacher probably needs to be familiar with the characteristics of formal and concrete operational thought and must give some attention to the reasoning students seem to be using in arriving a t their responses. Concrete Operational Thought Many chemists who have developed a recent interest in Pineet " mav have incorrect or incomnlete notions about what is meant by concrete operational thought. For example, one chemist seemed to equate concrete operational thought with those who do things well with their hands but not with their heads. This renresents a cross misunderstanding of the idea. Piaget is talk& about intellectual developme&, not psychomotor development. A concrete operational student may or may not be good with his hands. The distinction is in the reasoning that the student uses and his or her ability to go beyond actual experience to reason in terms of what has not been experienced. This I;utrr point was illustra~erlrather nicely hy a cummrnt made hv Jane Copes in desrrihiny questims that she uses t u see how students-are thinking (14). One question involves a turtle that can fly a certain distance in one time and a rabbit that can flv a different distance in another time: students being asked to tell which flies faster or, if they cannot solve the problem, to explain why. Some students respond that the problem cannot be solved because turtles and rabbits cannot fly. Such a response represents a rather profound inability to divorce oneself from experience and operate in the realm of nossibilitv. Most college students are beyond this point but it does iliustrate the ~ h b l e m . In discussing an experiment in which students add zinc to a fixed amount of hydrochloric acid and collect the zinc chloride produced, concrete operational students may have difficulty in seeing what would happen if they had added more zinc to the fixed amount of HC1 or added more and more HCI to a fixed amount of zinc. They need to see it happen-or a t least see the results obtained when other students in the class do the exneriment under these hvoothesized conditions. .. Formal crperationnl .itudcnts more e m l y divorce themselves fnnn the world of "what 1 actuall\.saw hap~en"andolwatc in the world of "if I did this, what kffect would it have on what I saw happen." As indicated earlier, the logic commonly used by concrete operational students is one of seriation and correspondence. This reasoning is il!ustrated by an approach used by students in an experiment on linear expansion as a function of temperature. The apparatus had a rod laying on a needle with a cardboard disk attached. As the rod expanded, it rolled the needle and caused the cardboard disk to rotate. A rotation of 360 degrees would correspond to a linear expansion of the rod eouivnlent to twice the circumference of the needle. In the experiment, typical expansion caused a rotation of 5 degrees and the nroblem was to find the change in leneth of the rod. Many &dents proceeded as follows ~~~~~~
.
7
~~~
-
360' 180" 2
~
-
-
~
~
-
-
~
~~
~
~
~
~
corresponds to 0.20 em (twicethe circumference of the needle) corresponds to 0.10 cm
For further discussion of this point see Piaget (15).
166 / Journal of Chemical Education
90'
corresponds to 0.05 em
5.1j25~ corresponds to 0.003125 em so the rod expanded alittle less than 0.003125 em. I wouldsay about
0.003. Here the student obtained a series of corresponding values by successive division by 2 and arrived at an answer that was nerfectlv satisfactory to them. The answer that they got was close enough. Indeed, l expect that in virtually any e\,eryday application of propwtionnl reasoning, this procedure e o u l d prwide an answcr that is close enough. However, the ilrateg'y is certainly not 3s universally applicable as the proportionnl one that we would use to arrive 111 the answer of 2.d X 10-:' cm. A formal onerational student might solve this problem in exactly thesame way, partirdarly if theexperience isentirely new u, the sntdmt.'There are tmo reasons fur this; one i> that we tend to use reasoning that we have used successfully in the nast and the other is that we alwaw need to describe and order kxperience (concrete reasoning) before we explain experience (formal reasoning). To illustrate, consider the basketball player who has just learned to shoot left-handed crip shots. In the beginning it is awkward and uncomfortable. He can do it but it is easier to shoot right-handed. He will often revert to shooting righthanded crip shots when a left-handed shot is more appropriate. In a similar fashion, when a student begins to use formal reasoning, it is awkward. Under stress, the student is likely to revert to concrete reasoning which the student has practiced repeatedly, even in cases where formal reasoning is more appropriate. When the student is plowing unfamiliar mound, as students were in the linear expansion experiment, it% always necessary to describe and order experience before explaining it or manipulating the information obtained from that experience in a formal wav. The seriation and correspondence strategy may be used b i a student to get a clear idea of how the exnansion of the rod is related to the rotation of the cardboard disk. It may e\.en be a nwessary step l~eforethe student can use tho proportional reasoning that we would use to solve tnt! The difference, then, between the formal student and the concrete student is that after describing and ordering the experience using concrete operational thought, the formal student will be able to understand the strategy for solving the problem which employs proportional reasoning when it is pointed out. He will probably adopt this formal strategy for solving similar problems hecause of its obvious advantages. The concrete o
