Application of Advances in Learning Theory and Philosophy of Science to the Improvement of Chemistry Teaching Joseph D. Novak Cornell University, ithaca. NY 14853
A Philosophical Foundation for Learning
For more than 300 years, the dominant philosophical position regarding the nature of science was that established by Francis Bacon in his "Nouum Organum." Bacon took a proper stand against the then prevalent "natural philosophy" that stressed study of Greek and Roman writers and logical argument, favoring instead the necessity of careful obseruation. Bacon held that our understanding of the universe would be best advanced if we observed events or objects in the world while scrupulously avoiding constraining preconceived notions or ~hilosophicalviews. Gradually Bacon's views became dominant in science and these views were reinforced in the writings of Karl Pearson as we entered the twentieth century. With the growth of science teaching in secondary schools and universities in the late 1800's, science textbwks stressed that science is based on unbiased observation and that science research in time leads to truth about nature. This mythical view of science remains dominant todav in manv textbooks and in the general population contributing in part to the Dublie misunderstandine of science. By 1947, however, distinguished scientists such as James Conant were presenting views that departed significantlyfrom those of Bacon, Pearson, or the Logical Positivists of the early Twentieth Century. In his "On Understanding Science," Conant, who made his reputation as a research chemist, was arauina that scientists invent and use "conceptual schemes" and that these conceptual schemes are modified over time and occasionally discarded ( I ) . Conant's prot(rg6, Thomas Kuhn, further expanded this idea in his 1962 book, "The Structure of Scientific Revolutions" ( 2 ) , and Stephen Toulmin (3) elaborated the evolutionary nature of concepts and the role that concepts play in human understanding. This has led to almost a new orthodoxy, where science is seen as the constant modification and refinement of conceptual models and associated research methodologies ( 4 , 5 ) . More recently, my colleague D. B. Gowin has developed a heuristic device. which we have found to be es~eciallv " helnful . with professors and students, for representing the interplay of conce~ts.nrinci~les.and theories with obse~ationof events or ohjec'ts i d prbcedural aspects of record making, record transformation. and construction of knowledae and value r shows e the general form o f ~ o w i n ' sVee claims (6). ~ i ~ " 1 heuristic device as it has evolved in our work. Gowin's Vee scheme is consistent with Baconian and Pearsonian stress on observation, for a t the point of the Vee he has placed those things scientists observe. However, the Vee also lays stress on the role of concepts1 since our concepts not only help us to ~~
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Most concepts acquire meaning through propositions, which are two or more concepts linked together, such as gram is a unit of mass. Concepts grow in meaning as an individual learns more new propositions in which a given concept is embedded.
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GOWIN'S EPISTEMOLOGICAL V METHOL
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Events Objects Figure 1. Gawin's Vee heuristic to show key elemems in the structure of knowledge and knowledge production (epistemology).Elements on the "ien" actively interplay with elements on the "right" in production or interpretation of knowledge about events or objects. select ohjectx or rvrnts for obsrrvation hut aisu guide the kind of recurds and record transformations wr make. I'rinciplri and theories represent relationships between concepts which have their origins at least in part in the regularities observed in objects andlor events. Thus Gowin's Vee also incorporates key ideas from modern philosophical views of science that stress the active interplay between what we observe or do in science and the evolving concepts, principles, and theories that guide scientific inouirv. . , If we instruct sludrnts or teachers in the nmnenclature of Gowin's Vee. we have found the Vrr to br a nnwerful heuristic device for coh~eptualiein~ laboratory work. w e have used this heuristic device successfully with students in secondary schools and universities and will discuss this work further in a later section of this paper. Concept Learning a s the Focal Element In Learning. Given a developing philosophical view that placed concepts a t the source of human understandinp, it was natural that we should seek a learning theory that centered on the nature of concepts and concept learning in school settings. No such theory existed before 1963, so we used Weiner's "cybernetic" model in our early research until we became familiar with Ausubel's "Psychology of Meaningful Verhal Learning" (7) and later, his "Educational Psychology: A Cognitive View" (8).Behavioral nsvcholow had so dominated universities (and journal editoriai board g a s ) in the 1950's and 1960's in ~ o r t h America that few American educators have been trained in a learning psychology that stresses the role that concepts play in acquisition, retention, and application of knowledge in classroom settings. Although Piagetian developmental psyVolume 61
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chulogy became popular in education circles in the USA after 19fi0, his theory of cognitive development has only limited relevance to learning in school settings (9). Over the past decade and a half. we have found Ausuhel's coenitive learnine" " theory to he the most useful in guiding the learning euents we have constructed either for research nurnoses . . or in our efforts to improve science instruction. His work also provided the nsvcholoeical foundation concents for a first effort to construct a &eory of education ( I O ~ . Ausuhel's assimilation theory of learning has appealed to us for hoth its simplicity in the kind and numher of key concepts and its comprehensiveness in terms of the school learning events to which it is relevant. With respect to knowledge acquisition, the theory meets the criterion of parsimony; it also has significant implications for skill or motor learning and the acquisition of positive feelings or "affect." Seven key concepts in Ausuhel's theory function to guide research and teaching. Each of these will be discussed as they apply to instruction in chemistry. 1) Meaningful Learning. The central idea in Ausuhel's theorv is that of meaninpful learnine. -. which he defines as "nonarhitrary, substantive, nonverhatim incorporation of new knowledge into cognitive structure." Cognitive structure is the framework of knowledge stored in our minds that grows and develops from childhood to senescence. By nonarhitrary incorporation of knowledge, Ausuhel means that the learner must make a conscious effort to relate new knowledge to knowledge he or she already has. For example, a student learning new information on reactions of sodium with nonmetals would consciously relate this knowledge to what he or she already knows about chemical reactions in general and, more specifically, reactions of metals and nonmetals. Substantive learning occurs when the learner makes a conscious effort to identify the key concepts in new knowledge and to relate these concepts to other concepts. For example, one recognizes sodium as an active metal and recognizes chlorine as a unit which reacts with an active metal. Nonarhitrary and suhstantive learnine eo hand in hand: both reouire a deliberate effort on the &it of the learner. ~ o n v e r h a t i mlearning is simolv the nroduct of nonarhitrarv. .. suhstantive learnine.". since the latter active learning processes necessarily alter the meaning of the new knowledge learned. If a student simply memorizes verhatim that "an acid plus a base forms a salt" without consciouslv thinking about "what is an acid?" or "what is a base?", then verbatim, arbitrary and non-snhstantive learning has occurred. I t can lead to success on exams that require verhatim recall of definitions, hut such learning has little practical value and may interfere with later learning. 2) Rote Learning. This is a t the opposite pole from meaningful learning and results when &dents incorporate new information into cognitive structure in an arbitrary, verbatim, nonsubstantive-way. In practice, it is improbable that any student learns any chemistry in a completely rote manner, and hence Ausuhel stresses that the rote/meaningful distinction is not a dichotomy but a continuum. Unfortunately, most students in secondary schools (and in university introductory courses) learn most of their chemistry in a nearly rote manner. 3) Subsumption. This is the concept lahel Ansuhel uses to represent the idiosyncratic nature of meaningful learning and the fact that new knowledge is usually incorporated (subsumed) into more general concepts.2 Each person's cognitive structure is unique, and hence subsumption of new knowledge produces a cognitive interaction product that is dependent both on what concepts or misc&ceptions the ~
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Subsumption is somewhat related to Piaget's concepts of assim ilation and accmnm?ation, except that Ausubel's subsumption relates to smcific conceots in coanitive structure and alwavs involves both some new information bekg incorporated (assimilated) and some change in the existing concept(s)(accommodations).
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Journal of Chemical Education
learner already has and the material presented. Essay exam questions, when they require more than verbatim recall of information, often show the idiosyncratic nature of subsumptive learning. For example, students often confuse concepts of weight and density and hence will claim that a small quantity of a dense substance will weigh more than a proportionately larger quantity of a less-dense substance; or they may claim that a small quantity of hot water has more heat energy than a much larger quantity of cool water. In both cases, pre-existing "common sense" concepts are subsuming (and distorting) new knowledge acquired regarding density andlor heat energy. 4) Progressive Differentiation. From early childhood onward, concepts one holds are being constantly modified, elaborated, made more precise and hoth more exclusive and more inclusive; this is what Ausubel means by progressive differentiation of concepts. For example, to a young child, eating gives you energy, but so does sleeping. Later, children come to recognize that although one may feel more energetic in the morning, only oxidizable foods provide energy. Progressive differentiation of concepts is never complete, for even scientists working a t a research frontier are still differentiating their concepts. At this point, our psychology of learning merges with an epistemology that holds that concepts in a discipline are, to a t least some degree, constantly evolving. 5) Superordinate Learning. Most meaningful learning involves suhsumption, hut occasionally new, more general concepts are learned that also provide meaningful relationships between two or more existing concepts. For example, when students acquire the concept of a mole, they relate atomic-molecular properties of matter to volume, weight, mass, and density concepts of substances and to Avogadro's numher. If they are successful in this superordinate learning (that is, they do more than memorize verhatim the definition of a mole), suhsumed concepts take on new meaning and new relationships to one another. Since we usually sequence subject matter to present more general concepts first, suhsumptive learning more commonly occurs. Furthermore, one could argue that even concepts such as mole are suhsumed under relevant, prior, more general concepts such as "suhstance" or "matter." 6) Integrative Reconcilation. When two or more concepts are seen to relate to each other in a new way, perhaps to describe a new perceived regularity, integrative reconcilation of concepts has occurred. Weight, mass, volume, density, and gravity are some of the concepts whose meanings may seem to he a t first unrelated or contradictory, hut which are later integratively reconciled into a more powerful cognitive framework. Superordinate learning always results in some new integrative reconcilation, and both this and subsumption result in additional progressive differentiation of concepts. 7) Advance Organizer. In order to facilitate incorporation of new knowledge into cognitive structure in a substantive, nonarbitrary manner, Ausubel has proposed a pedagogical strategy of using advance organizers. An advance organizer is a small learning episode that is more general and more inclusive than the learning material that follows and that is perceived by the learner to serve as a cognitive bridge between what he or she already knows and what is to be learned. For example, one of my colleagues uses an analogy with twoholed doughnuts to illustrate the concept of mole as a quantity of material. Students are used to thinking of doughnuts by the dozen or the gross, so they can readily see that a dozen twoholed doughnuts would have twenty-four holes and a gross of doughnuts would have 288 holes. The concept of molar equivalents can thus he linked to students' existing concepts with such an analogy, albeit, many students still have difficulties with numbers expressed as exponents as in the case of Avogadro's number. There is more to Ausubel's theory than I have presented here; these seven concepts, however, are the key ideas that can be applied to the design of instruction and research in edu-
cation in chemistry. I t is also important to distinguish between learning approach and instructional approach. This is another area in which Ausuhel has made an important contribution. Figure 2 shows that learning can vary from essentially rote to highly meaningful independently of the kind of instructional strategy employed. One of the mistakes made during the "curriculum reform movement" in the USA in the 1950's and 1960's was a failure to distinguish between teaching approach and learning approach (11). If there is a new series of science curriculum improvement efforts, we trust that these will profit from new insights into human learning. Concept Mapplng
In our research based on Ausuhel's learning theory, we have struggled with the problem of assessing changes in cognitive structure as the result of meaningful learning. Referring to Gowin's Vee (Fig. l), our problem has been to devise new record-making procedures and record-transforming procedures that could he used to make valid claims regarding
MEANINGFUL LEARNING
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meaningful learning events designed especially to encourage concept learning and integration of concepts into hierarchically organized segments of cognitive structure. Modified Piagetian clinical interviews (see Pines, (12)) were useful, hut individual interviews with students were time-consuming and the tape-recorded records were also time-consuming to analyze. A decade of testing alternative evaluation strategies led to a technique we call concept mapping. Figure 3 shows an example of a concept map constructed to represent the key concepts and propositions discussed in this paper. Figure 4 shows a more recent map constructed by a professor a t the University of North Carolina in planning revised lectures. In our early maps, we assumed that the linkages between concepts were more or less self-evident and we did not lahel the lines. This was still a useful procedure when we were trying to illustrate what we believed were the concept relationships in a segment of subject matter, or to represent the concept framework as we interpreted it from the analysis of a clinical interview. However, when we began to instruct students in concept mapping, we found it crucially important to emphasize a hierarchical structure and careful labeling of the lines if the maps were to augment student learning. Concept mapping serves several useful purposes in encouraging meaningful learning. Concept mapping requires that students explicitly identify key concepts in a segment of learning material. This always leads to recognition that a few key concepts are already somewhat familiar to them. However, when students begin to construct a map and to identify relationships between concepts as they seek to lahel the lines, they soon recognize that their understanding of even "familiar" concepts is inadequate, i.e., not sufficiently differentiated. The result is that they have difficulty forming linkages between concepts. A good hierarchical organization of concepts for a given topic of study might be structured in avariety of ways, hut all of these organizations should reflect that more specificconcept meanings can be subsumed under more inclusive concepts. T o organize a concept map hierarchically, a student must make a conscious effort to ascertain, what the most inclusive concept for the topic is. This effort requires an active process on the part of the learner to reassess what he or she knows that
Figure 3.A wncept map representing Uw key concepts (in ovals) and principles presented in this paper. Ausubel. Twlmin, and Gowin's Vee are specific cases of theories.
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NaCl
% Naf(aq)+C1-(aq)
H20 % Ht(aq)+OH-(aq)
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Figure 4. A concept map for solutions constructed from the lecture f w a chemistry course. Specific examples are not concepts, althoughthey have the regularities of the conce~tsthat subsume them. Examples are not enclosed (Afler J. Wiiley).There is some disagreement among chemists as to the description of some concepts shown (see Herron. 18)
Level One of hierarchy
Level Two of hierarchy
Level Three of hierarchy
L e v e l Four of hierarchy
Cross
inks (if
valid 1 0 x 3 = 3 0 significant) 64 points totol
1) Propositions. Is the meaning relationship between two concepts indicated by the connecting line and linking ward@)?Is the relationshipvalid. For each meaninaful. valid Draoosition shown. scare one ooint. . . 21 Hierarchy Does the map show h erarcny? Is each sbbadmmte concept more specifc, man me concept drawn aoove n (in the -!en of me m a t ~ l abe l ng milppea19 Score fwr points for each vallo levelof tne hierarchy (see scoring model).
3) Cross links. Does the map show meaningful Conhections between one segment of the concept hierarchy and another segment? Is me relationship shown significant and valid? Smreten points far eachcross link that is both validand significant and two points for each crdss link that isvalid but does not iilushale a synthesis between sets of related concepts or propositions. Cross links can be an indicator of creative abiiityand hence special care should be Sffwded to identifying and rewardinglhis expression. Sometimes surplisingly unique and creative cross links may be drawn and these might receive special recognition.
Figure 5. Scoring key far concept maps. Based on Ausubel's cognitive learning theory, a varlety of similar scoring keys can be devised For example, the instnrctor cen construct his or her own criterionmncept map for a ten ar amer study materialand score student maps ai (Student score)/(Criterion m e ) X 100. Some students will get aver 100% on this basis, which cwld have positive affective cansequences H shwld be rememberedW t mis s w i n g is samewhat arbitrary and can be modified to apply to each teacher's scaring criteria.
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Journal of Chemical
ducati ion
is relevant and what he or she is unclear about for each of the key concepts. As we move from topic to took, some of the same concepts will reappear on concept map; hut, perhaps, in substanti&y different locations on the map hierarchies. This reflects, in part, that as we consider different events or ohjects in our studies, alternative conceptual hierarchies may confer greater explanatory power. viewed from the perspe&.ive of dowin's Vee, new events or objects can have different conceptual frameworks laid upon them, and thus we can enrich and expand the claims that validly follow. The remarkable property of human cognitive structure is that it is somewhat like a crystal and the image (map) we see depends upon the orientation from which the crvstal is viewed. Pribram (13) and t,thers havesuggrsrrd that hurnansn,n>truct imagrst~fthi.ir knuwlrdri! "h~rlorr~ohicallv." While the ~tt~urihiolow remulns .. . obscure, concept maps appear to have psychological validity as well as oedaaoaical value. We have desjsed a variety of scoring keys for concept maps; a more recent key isshown in Figure 5. We also h a w found it useful to provide students withcopies of the key to help explain to them how they should proceed to construct better (more meaningful) concept maps. The scoring key was designed to incoroorate Ausuhel's learnine orincinles. Relat~onshipsbetween concepts are propositions and these reflect the deeree of differentiation of the comoonent conceots. For example, Figure 4 illustrates a discrimination between solute and solvent molecules. linking these c o n c e ~ t with s other relevant concepts in chemistr;of solutions. The number of hierarchies identified also signals the extent of differentiation of component concepts in that subtle relationships between concepts are indicated by hierarchy, denoting in part fine discriminations between the extent of inclusiveness and exclusiveness of concept meanings. Cross links, when they show significant relationships between concepts in different segments of the hierarchy, can be good indicators of intearative . reconcilation of meanings, and in some cases some very creative interrelationships may be suggested. There remains much research to be done with students to evaluate and refine further the strategy of concept mapping as a tool for helping students learn and as a method for record-making and record-transformation in cognitive learning studies. At this ooint. I can onlv .reoort . that our enthusiasm for concept mapping has been increasing with each year of new exoeriences and research. Mav I suezest that vou trv to annlv .. . thk strategy with your studknts and/or inupreparation of teaching materials.
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Gowin's Vee Applied to Laboratory Teaching.. As noted earlier, Gowin's Vee (Fig. 1) derived from our efforts to improve science lahoratorv instruction. Workina primarily with university science courses, we found that students were preoccupied with making observations, records of observations, and, especially in physics, transforming their records. Seldom did they glve careful and explicit attention to the events or objects they were observing or to the regularities they were seeking to observe. Conststent with the latter problem, students rarely asked what concepts, principles, or theories were guiding their observations. One consequence of the lack of concern for a conceotual-theoretical orientation to their work was that students saw little relationship between lahoratorv work and lectures or textbook readings. I n short. they were preoccupied with the doing, right-hand side of Gowin's Vee and were inattentive to or unaware of the important guiding function that the thinkwag, or left-hand side, of the Vee could have orovided. The conseauence is that lahoratory work seldomhas meaning for the-students and hence does not contrihute significantly to their conceptual understanding. Of course, laboratory work should also contribute to skills and techniques of lahoratorv manipulations, hut clear understanding ofrelevant concepts and principles will also contrihute to these goals.
Our experience has been that most students will not conscientiously consider the role of concepts and theories in selecting events or ohjects for ohservation and constructing records or transformations even though they are admonished that this is very important. Partly for this reason, the research evidence indicates that little or no improvement in understanding science results from lahoratory work as compared with lecture or lecture-demonstration instruction alone. Scientists are generally agreed that lahoratory work is important for understanding, based on their own experiences, so the contrasting student attitude and lack of achievement has been an enigma. What we are finding in our work is that scientists more or less unconsciouslv imuort conceotual-theoretical ideas into their ivoik; students d d n o t , and often cannot, do this. This holds true even in chemistrv lectures: Leo West and Jan 1.4ktr;ilia)an. now finding that Gerard ar Monvsh I.'n~vr.rs~tv what is uritren on the hlackhimrd or rmr)hnsizrd in the lecture are primarily those things that would be on the right side of Gowin's Vee. To a surprising degree, they are finding that they must import concepts and principles from their knowledge of chemistry to understand material presented in the lecture, even though the lecturer was selected for his superior teaching record. To alleviate the prohlem descrihed in the last paragraph, we have found it useful to instruct students in the nomenclature of Gowin's Vee and the use of this heuristic device for interpreting laboratory work. Most of the research we have comuleted is a t the secondarv school level (aees 12-16 vears).., but bur work began with and is continuing with college students, including chemistry students (see Cullen, (14)). Figure 6 shows a sample of Vee maps constructed by eighth-grade (13-16-year-olds) students in a research project recently completed (15). A similar experiment with college students mieht use three or four solutions (with ionizing and non-ionking solutes) and more solute concentration ievels, hut the kind of reasonine that would he rewired is the same. Naturally, we would expect college students to apply a larger framework of concepts and principles to their interpretations. In the United States and manv other countries, there is a growing concern regarding the lack of public understanding of science. which results in a aeneral public aoathv toward science and science education and alsotoward the support of scientific research. The effects of this apathy have had dire consequences as reported recently in a National Science Fcmndation report to the President (16). Some of this apathy may have derived from disillusionment resulting from the V~etnamWar, Watergate, the Iranian hostages crisis, and
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Figure 6. Experiment an saluiion chemistry done wRh eighth grade students with results reporled on Mwin's Vee map.
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economic decline, hut part of the apathy might also he attrihuted to inappropriate or inadequate science education. The introductory chapters of most secondary school science texthooks (and colleae texts) oresent an obsolete Baconian or Pearsonian modelof science and fail completely to show the interdependence between science and technolow. Gowin's Vee can b e a useful heuristic twl, for we can illustr& how the conceptual-theory-based need to create new events or new ways to record observations in the pursuit of scientific inquiries has led t o new chemistry, new fabrics, transistors, oscilloscopes, television, and election microscopes. All of modem technology can he shown to be derived from the conceptualtheoretical press for better observation of new evehts or objects and new record-making or record-transforming devices. Research is also needed for product development and this too can henefit from analysis with the Gowin Vee. We have shown (15. 17) that voune students can successfullv understand and apply the c e e hkwistic method, and in time we expect to show that this understandine can sienificantlv enhance public understanding of science and empathetic suooort . . for science. When wnwpt mapping is intn~ducedto students prior to Goain's Vee. "comoosite maos" mav he constructed that show both the hierarchical c ~ n c ~ ~ tframework ual the student is applying in an inquiry and the records, transformations, and claims that derived from the inquiry. Vee maps with concept maps are an alternative form of laboratow report that can he much more revealing of students' thinking and easier to evaluate than written, conventional lahoratorv reports. Of course, research journals are not prepared t ~ - ~ u b l i Vee sh maps, so it is necessary to have students prepare some expository reports as well. Another use of Gowin's Vee has been to apply it in the analvsis of ouhlished research reports. The Vee heuristic device derived in part from five que'stions Gowin constructed to help students analyze scholarly d ~ u m e n t sand , ~ we find that it is a useful shorthand for reporting a published work to a journal club or research group. Once the members of the group hecome familiar with the Vee, a single page with schematic reoresentation of elements of Gowin's Vee as thev " amear .. in the report can summarize the paper. Some reports may require two or more Vees. as when exoeriments are reoeated $;it11 some changed events or rcconli; hrrt. the Vre h r h t i r d r v i ~ vcan hrlne into sharp focus the key differences in the experiments or inquiries. The language of the Vee can facilitate discussions in such groups . . since we can ask simple . ques. lions s w h as "Do the rrmrds represent salient dimensions of the event9 (or ohiects) ohwrv~d?"or "Arr the rcrurd transI'ormations the best ones that could have been used to generate the knowledge claims?" and so on. Combined with explicit discussion of relevant concepts and principles, such questions Gowin's five questions developed to analyze the structure of knowledge in scholarly materials were (1) What are the "telling questions" (major questions)?(2)What are the key concepts used? (3)What methods of inquiry (procedural commitments)are used? (4)What are the major knowledge claims? (5)What are the major value claims?
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Journal of Chemical Education
can he more illuminating than the usual discussions in journal clubs or seminar groups. We are also finding the Vee heuristic method useful to younger researchers who are trying to define a good thesis problem or to reorient their research careers toward more oroductive uuestions or methodoloeies tareeted a t kev conceptual or thkoretical problems current in th;: discipline. ~ v e n senior research scholars report that using the Vee heuristic device has given them new insights into their research. Herein lies an additional henefit in apolying concept maooina and Vee mapping to the design uf iectures or labo&oriespreparation time devoted to teaching can have significant payoff in terms of new research insights. In university settings where teaching is necessary hut research is the criterion of achievement, the latter payoff can be most welcomed. In summary, my major claims have been that recent advances in eoistemoloev ooint toward the evolvine nature of scientific concepts and the central role that concepts play in scientific inquiry. Complementary to these insights has been a growing understanding of human cognitive learning (knowledge acuuisition) that also olaces central emohasis on the key role tha't an individual's concepts (or miscon>eptions) and concept frameworks play in new learning and problem solving. Out of these theoretical advances and the associated research conducted. two oedaeoeical strateeies or forms of "instructional technolog;" h:a; been deviloped: concept mapping and Gowin's Vee mapping. We believe the limited research data available at this time indicates that wider use of these pedaaoeical strategies is warranted. We invite you to join with us a i d to share experiences in the use of these strategies. Literature Cited i l l Canant. J. H.. "On Underatanding Scienrr,"Yale University Press. New Haven, CT. ,a"" (2) Kuhn. T. S.,"The Structure of Scientific R e ~ ~ l ~ t i i iUuiiirsity i." of ChiigoPees8,
Chicwo, 1362. (31 Toulmin, S. "Human Understanding. Volume 1: TheCnllectiveUsesnd Evolution ui Concepts." Princeton Univenifv Press. Princeton, NJ. 1372. (41 Lakston, I.,"Falaificationsnd tho MeUlodolog~ofScientiflcResearehP?ogrammea." in "Criticism and theGrowth ofKnowledye," (Editors: Lakstos. I.. and Musgrave. A,), Cambridge University P ~ o s sAberdeen, . 1976. (5) Brom,H.I.,"Pe~~~tion.ThwandCommitmentTheNewPhilosophyofS~en~e." UniversifyofChirsgu Press.Chicsgo. 1973. (6) Goain, D. 8.."Educating,"Cornall University Press, Ithacs. NY. 1961. (7) Ausuhel. D. P.."The PhysioioyyofMeaningful Verbal Lesrning."Gmneand Stratton. New York. 1963. 181 Ausubel. D. P.. "Educational Psvcholaw: A Comitive View." Holt. Rinehart. and
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(9) Nouak, J. D.,Sri. Edur.,71,453 i1977);Sfud.Sci.Educ.,5.1(1978l. ( l o ) Nouak. J. D., "ATheoryof Education." Corneii University Pres8. Ithaca, NY, 1917. (11) Navsk, J. D.,Srhool Sri. Marh.,777 (May 1969). 1121 Pi".. . A. L.. Nouak. .1.0.. posner. G. J.. and VanKirk. J.. "The c1iniesi Interview: A ,--,~~~~~, Method f o r ~ r a l & t i ~ g ~ o g n i t~i & t ~ ~ & e . " ~ e s e a k h ~ e p o #6,Departmentof rt Mucation. Cornell University, 1978. in Learning." in "Promedings of the (13) Pribram. K. A,. "Neurabinlogical Limi+~tioionr AmherstSympasiumon theOptirnum Utililsti~nof Knmledge." (Edifors:Baulding. K., and Senosh, L.I. Westview Press. Boulder. CO, in press 114) Cullen, John,"Coneqlt Leamin~andProblem Sol%v,:The Useofthehtmw Concept in Cdiege Chemia&: ~ h D & ~ iCornell ~. University, 1963. (15) Novsk, J. D.."The Use ofConept Mapping and Gowin's Vee Mappinglnstrunioml Strategies in Junior High Schml Science, unpublished research report, Carneli 77"; .,*.* .i, , $16) Nal~,mrl.+#enre Prunclal~un.'Sc~mrr and Kng.nnrlq Ed~alronIar the 1980'980'and Br, ."a," l S(imcmmm, Pr,n,,ng O1licr. HirhinrIAn. n(' 1990. ,nl Y O S ~ LJ n ,her n.
