The Underprepared Student, Scientific Literacy and Piaget Reflections on the Role of Measurement in Scientific Discussion Daniel J. Kurland Sophie Davis School of Biomedical Education, The City College, CUNY. New York. NY 10031 In the vears followine the Report of the ACS Chemical
ducati ion Division ~ubcommittkeon Underprepared Stu-
dents ( I ) , THIS JOURNAL has provided a forum on the needs of the underprepared, underachieving, or poor-risk student. Overall, recent articles have reflected two approaches: (1) administrative responses, whether in terms of pre- or introductory courses, (2W, or remedial courses (7-9); (2) Piagetian analyses of the underlying problems, either with an eye toward assessing student abilities for placement purposes (I(tll) or suggestions on curriculum reform at the college (12-14) or secondary school level (15).
In the remarks that follow, I would like to suggest an alternative "optic" for viewing the needs of remedial students, based on the role of measurement as the "lana guage" of science.' The analysis that follows was sparked by four incidents involving students in the Bridge to Medicine Program, a program for high school seniors anticipating college-level work in the health professions. While the setting may have been unique, the incidents are, I suspect, characteristic of experiences with students in any introductory college chemistry course. Incident I: Upon reading "Power is the rate at which energy is expended," students were unable to translate the sentence into mathematical form: P = Elt. Incident 2: Students who were able to indicate that one mole of a com~oundis eauivalent to 6 X 102holecules,and
lecular weight of 164. Incident 3: Presented with a balanced chemical equation and a table of molecular weights, students who could calculate the amount of one compound necessary to react with a given amount of another employinggrams were stymied by the same problem when the initial amount was given inpounds. Incident 4: Students asked tocomment on achart displayingdata on the freezing point depression of solutions at different concentrations were unable to indicate a trend in the data, even after having just read that the depression approached an integer value times the calculated depression with decreasing concentrations. In Piaeetian terms. these incidents mieht he explained bv the assertion that thk students were at ;he concrete operational stage of cognitive development and were not yet able t o deal with abstract concepts (the formal operational level). Indeed. "non-formal" students have been estimated to comprise a; much as fifty percent of the students in freshmen chemistrv for non-science maiors (12). T h e piagetian perspective-has directed attention to the nature of student thought processes and has offered a terminology for thinking in even the most elementary science courses. Yet aspects of the Piagetian perspective are thesource of very real concern-not the least of which is the degree to I wish to thank Dr. David Sussman for his suggestions and encouragement in this endeavor.
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which such an analysis facilitates the search for pedagogic solutions. Most teachers are unprepared to shift attention from the exnlicit oresentation of subiect matter to fosterina the devrhpment oiahstract thinking pprse. They are rrl'~cr:mrto sul)stitute "surroeate" conceots (12) and to reduce sianiflcantly the traditional course content mainly because i f the manv different neo-. auasi-, and even pseudo-Piagetian programs presently available. These teachers are concernedwith findine an immediate and efficacious means of transmitting spec& technical material than they are with long-range goak of developing abstract mental processes. What, then, if anything, might the average college teacher
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A potential answer, I suggest, lies in the recognition of the primacy of the system of measurement in scientific discussion. For aninitial sense of what I mean, let me return to the earlier incidents:
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(1) ~,With the definition of Dower. the statement was oerceived as an .+rsertionof fact, rather than as a definirim staring a mnthrmiltirill relati~,nahip.'The notwn of rare did nut rrigyrr on awnrenrss o i s srandord format aithin thr system of p h y k d drw11)twn:r m = ~
~~~~
xltime. (2) The definition of the mole was accepted in much the same terms as the notion of power. The mole was viewed as a label for an immutable number of molecules, rather than as a sub-dividable counting unit subject to mathematical manipulation. (Here the common analogy with a dozen eggs is only of limited suggestive value. One hardly refers ta 1/10 dozen.) (3) In the problem involving the chemical reaction, the students relied on a rote problem-solving approach rather than a strategy hased on an understanding of molecular weights as mass ratios (asopposed to metric ualues) that could be related to weight ratios. The appearance of oounds. rather than " erams. oresented a seeminnlv "unnram. mat~cal"qwntion. Oncr agaln, u n m eemplovrdw ~ t h i n specific problem-solving formats. (4) Finally, with the freezing-point depression data, the experimental values were perceived as isolated facts, rather than as a series of measurements subject to interpretation. The law was passively accepted as an authoritative assertion rather than as an expression of the mathematical relationship of experimental measurements. All four incidents exhibit a literal-mindedness vis-a-vis concepts of measurement, a non-reflective mode of thought in which verbal references are divorced from their underlying mathematical implications. Physical properties and units of measurement are viewed as phenomena with independent physical existence, rather than as notions within a broader svstem ~"~~ of nhvsical descriotion. Understandine basic scientific concepts, i t would seem, is not so much a matter of a generalized ability to abstract as a matter of being literate in the specific descriptive system of physical measurement. The sienificance of measurement in scientific understanding further apparent in examples of formal operational thought generally referred to in Piagetian analysis of the chemistry curriculum. Herron (10) refers to student difficulties with "any concept which involves a ratio. . . (such as) density, velocity, &eler&on, molarity, and reaction rate. . .."
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Smith (15)speaks of student problems solving mass-mass and mass-volume problems. Beistel (13) remarks on difficulties with the gas laws and the Archimedes principle. Indeed, the archetypal examples of formal thought, the notions of conservation of weight and volume, would seem to be hased on an understanding of what exactly it is one is measuring when referrinr to these ~ r o ~ e r t i e s . ~ o s t i n t r o d u c t &courses ~ do, of course, begin with a discussion of measurement, but only in terms of the "facts" of measurement (equivalences) and rote procedures for conversion. Many aspects of the traditional curriculum actually distort the role of measurement in scientific discussion while a t the same time attempting to inculcate a functional prohlem-solving understanding of scientific concepts. As noted above, students are asked to accept the independent existence of properties as natural phenomena, when the very concepts themselves are artificial constructs of the system of measurement. Physical equations are presented as statements of the relationships of properties rather than of measurements by which these properties are defined. [Force is not "equal to" mass times acceleration, whatever that might mean; force is defined in terms of measurements of these latter properties. Only within these latter terms does the notion of a direct proportionality of (the measurement of) force and (the measurement of) mass become truly accessible.] In light of the above. it is hardlvsurorisine that students learn to recoenize . . a derived unit as one contaking more than one fundamental unit without fully appreciating the implications of the mathematical relationships involved-implications apparent onlv when the Datterns underlving . the develo~mentof the system are made explicit. In the above context, Herron's observation that "Chemistry, and most of science, is formal by its very nature," (12) might he rephrased: Chemistry, along with the other physical sciences, is based on a particular language of discussion and explanation: physical measurement. We cannot then expect studvnts t~l,;~r~iculatr an understanding ofscirntific w n c & ~ t s uniil rvc ilisurt. uurselver. t hat they are iunc ii~mallvilr~icdate in this language. .\nd just 21sthere can he no rriticnl rrading withuut an assunlptlm of the inherent sul~iecti\,ityofa iext, so no real appreciation of the system of meisuremmt is possible without an awareness of the inherent artibrary nature of the fundamental units and definitions of derived properties. The preceding suggests the need for an explicit instructional component that might stress the following elements:
and explanatiom IG) The role of measurements as experimental data and as predictions in the testing of a hypothesis. (HIThe role of measurement in problem solving: (1) that academic problem solving invariably takes the form "Given these measurements, find another measurement that goes with themm-a format in which a solution is oossihle onlv when the orooerties heine measured have
anced chemical equations-that problem solving involves the assertion of the known relationship of relevant factors and the solving for unknown measurements," and thus (2) that problems can often be approached in terms of "what can be measured" and "what do we know about the relaphenomenon. (I) The interrelationship of verbal definitions, mathematical operations, and visual models and diagrams. Such a curriculum emphasized the need to increase the students' ability to employ mathematical operations as a means of physical description, to assure a true literacv in the language of~mathematicaldescription. Rather thanaimply indicating that velocity is defined as distance over time, and some time later that power is equal to energy divided by time, we might begin with a review of fractions, progressing to examples of fractions as a means of displaying measurements (e.g., 6 milesW sec) and the implications of reducing such a fraction to a unit denominator ( 2 miles11 sec). therehv establishing not only the notion of a derived unit (milesper [one) hour) but also proportionality of such measurements as fractional expressions with the same value (6/3,2/1, etc.). Only then should we recognize that measurements of time alone provide little information about an event and introduce the sagacity of measuring rate. This generalized notion can then heapplied within varTous contexts, assigning the appropriate "property" labels (velocitv, power, etc.). A t all stages in the i n s & u h m a l process, efforts must be made to assess the students' ability to apply their understanding in prohlem-solving contexts. We must explicitly check their grasp of terminology and notation, of basic geometry and algebraic manipulations, as well as the abilitito translate verhal statements into mathematical form and vice-versa. We must offer drills in the otherwise obvious or ~~~~~simplistic aspects to assure a sound base for further discussion. (Might the problems with incident 2 he traced to afacility with exponential notation, or the application of this notation in counting objects? Might incident 4 reflect lack of familiarity with the term "integer" or the notion of a value approaching a certain point? Do all students reallv know the difference between 9cm2, (9 and a 9-cm &are?) Rather than emphasizing standard prohlem-solving formats and problem types, we should challenge the students with novel problems that test their understanding-such as asking for the smallest possible fraction of a mole, or why the gas laws require the use of Kelvin degrees. Such questions can often serve to bring out points ah& the underlying nature of the system of description that would he otherwise lost in the general discussion. T h e above concerns might be brought to hear in various contexts: ~~~~
(A) The nation of measurement as a means of physical descrip-
tion. IB) The notion that physical properties and their units of measurement are based on a limited number of fundamental concepts, and the arbitrary yet orderly way in which new properties and units are derived: (1)so much of X for each unit of Y: XN 12) so much of X and Y: XY (3) recurrent formats such as (a) rate: Xltime (b) concentration: a special case of X N (c) percentage: amount of portionlamount of whole x 100. (4) additional nations such as la) coefficients representing values that vary from one substance to another (b) constants required by systems of measurement Ic) trigonometric coefficients (d) vectors as measurements rxpressln,: rC1 ' l ' h ~n o t m t h u l phv-ical ecloar~c,n~-\r.hctl~er rqui\:llcnrrc I I In. = ? 5.1cm.. I l ~ e l l c l l n t r l ~ , n s o l ' ~pr.,prrtirs ~eu !I = d 1 ,.wraprr~mrnrnlthrurvrird l;aui tP1'3 hi-areall atatemmta of the relationships of measurements. (D) The distinction between measuring absolute values and changes in value (A). (El The notion of scientific measurement as a unifying element of the physical land biological) sciences.
(1) as a self-containedpre-course incorporating material from one
or more scientific disciplines-a general science course for science majors; (2) as an introductory segment in a single course; (3) as a set of recurrent themes to be emphasized at all relevant ooints within the traditional course strwtt~re: ~~~~~~~~~~, (4) as a course in applied mathematics; 15) as a component in a scientific problem-solving course, ~
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Number 7 July 1982
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Whether there is still a developmental threshold before which these "meta-scientific" concepts can be comprehended, before which the language of scientific discuss~oncan be mastered, will, I suspect, remain a nagging concern for many Piagetian leanings. If nothing else, the analysis above suggests a way of proceeding with the job to be done, a further step in the recognition of the underlying nature of what it is that we expect students to understand-and hence another step toward a more aware approach to the presentation of material and the diagnosis of student difficulties (16). Literature Cited 111 Kotnik, L.J.,J.CHEM.EDU~., 51,165 (19741.
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Journal of Chemical Education
(2) (31 14) 151 (61 171
N i s h i b a y a s h i , S . , d . C ~ ~EDUC.. ~. 51,560 (19741. Hunter, N. W., J.CHEM. E ~ u ~ . , 5 3 , a O (1976). l 8ottineer.D. L a n d Haight, H. L., J.CHEM. EDVC..54,729 11977). Krmnich, L. K., Patrick, O.,and Pavear, J., J.CHEM.Eouc.,s4,730 (19771. Bell. R. C., Mae, 0,A., snd Neidig. H. A,, .J, CHEM EDVC..57.22 119801. Pickerine. M.. J.CHRM. E o ~ c . . S 2 . 5 1 2(19751 snd 54.438 119771.
