DOCUMENT RESUME

ED 237 325 SE 043 409

AUTHOR Champagne, Audrey B.; And. OthersTITLE Cognitive Research and the Design of Science

Instruction.INSTITUTION Pittsburgh Univ., Pa. Learning Research and

Development Center.SPONS AGENCY National Inst. of Education (ED), Washington, DC.PUB DATE 83NOTE 33p.; Document is of marginal legibility.PUB TYPE Reports - Research/Technical .(143) -- Journal,

Articles (080)JOURNAL CIT Educational Psychologist; v17 nl p31-53 1982

EDRS PRICE MF01/PCO2 Plus Postage.DESCRIPTORS Cognitive Processes; *College Science; Higher

Education; *Instructional Design; *Mechanics(Physics); -OhysicS; *Problem Solving; *Schemata(Cognition); Science Education; *ScienceInstruction

IDENTIFIERS *Science Education Research

ABSTRACTPhysics learning studies demonstrate that students'

.Rre-inStructional world. knowledge is often logically antagonistic tothe principles of Newtonian mechanics taught in introductory physicsCourses. Under these conditions psychological theory predicts thatlearning will be inhibited, a prediction consistent with both theexperiences of physics teachers and the results of empiricalinvestigation. Informed by cognitive research on problem solving,'semantic memory,.and knowledge dcquisitibn, instruction has beendesigned to encourage thd reconciliation of world knowledge and=physics content among beginning physics students.- These'instructional_objectives and strategies for-mechanics instruction-are-dgr fromthe analysis of the cognitive states of uninstructed students, .

novices, and experts, groups. who with respect to .(1). thequantity and-extent.of formal mechanics instruction; (2) experiencesin.solving mechanics problems; and (3) the extent-of their verbaljeteraations about mechanics. IllUstrative prodedures which employthe Strategies (also useful for other subject-matter domains) areincluded. (Author/JN)

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COGNITIVE RESEARCH AND THE DESIGN OF SCIENCE INSTRUCTION

Audrey B. Champagne and Leopold E. K..iopfer

University of Pittsburgh

Richard F. Gunstone

Monash UniversityMelbourne, Australia

Learning Research and _-velopment Center

University of "Pittsburgh

-1983

Reprinted by permission frod -Educational Psychologist 1982, Vol. 17,

No. 1, 31-53. Copyright 1982 by division 15 of the AmericanPsychological Association, Inc.

The research reported herein was supported bythe Learning Research and

Development Center,- supported in part -as-a research and-deVelopmentcenter by funds from the National Institute 'of Education (NIE),.

Department of Education.. The= opinions expressed do not necessarilyreflect. the position or policy of NIE and noofficial endorsement shouldbe inferred..

Educational Psychs/Ingot1982. Vol. 17. No. 1.31

Cognitive Research and the Designof Science. Instruction

Audrey B. Champagne and Leopold E. KlopferLearning Research and Development Center

University of Pittsburgh

Richard F. Gun oneMonash University

Melbourne. Australia

The utilization of co' gninve psychological theory and findings fromresearch to inform the design of instruction is illustrated in this paper.

s learning studies demonstrate that students' pre-instructional worldledge is often logically antagonistic to the principles of Newtonian

taught in introductory physic'. Under these conditionslogical theory predicts that learning will be inhibited, a predicuco

tent with both the experiences of physics =rhea and the results ofempirical investigation_ Informed by cognitive research on problem solv-ing, semantic memory. and knowledge acquisition, instruction has beendesigned to encourage the reconciliation of world knowledge and physicscontent among beginning physics students.

Mon science ceramics an be criticized by drawingmention to the fact. . . -that time boob arechiefly concerned with the stueinents of resoles.Usually the most general results see put them thebeginning of the restbook. A textbook in physicsEosins by telling about molecules amid the constitu-tioo of matter or by ering some of the most WM.reedy formulated Rau-menu about the principlesof =chink; . . . The degree of enthtuasen ofthe ordinary student for these thooduaions whichhe gem in the textbooks Oval slight theleed .The student. confronted by these verbal additionsto his event-rice. gets into the habit of thinking ofscience as verbal additions to mpenence. and heEsizaully learns the words and keeps than in storewino the time when the teacher' demands rhcm(Judd. 1915. pp. 334.336)

Introduction

One recent trend in cog_nitive psychologyhas increasingly focused the attention ofresearchers on learning tasks representative ofthose which students encounter in school in-struction (Green°. 1950). Developments suchas this hold the promise of an improved.

". theoretical basis for instruction. A theoreticallyorganized and systeniatically verifiedpsychological foundation is an essential

The addnats of Audrey B. Champagne is 1..mmingResearch and Development Cent= Univenity of Fitt;-burgh: 3939 O'Hara Sum: Pittsburgh. PA 15260.

Copyright 1982 k.'y Division 15 of the Ar

requisite for effecting substantial im-provement; in instruction. However, the et-istence of such theory offers no guarantee thatinstruction systematically and veridically incor-porating principles derived from the theorywill be deiiined. A necessary condition for thesysrensatic application of theory to instruc-tional practice is a science of design as

. . .1 body of intellectually tough. analytic.partly formalizablt . partly empirical. technicaldoctrine about the deign process (Simon.1981. p. 132). Only when a science of in-structional design exists will the design processMSC to hide behind the doalt of "judgment

.enCe..'This article is.. motivated by the need to

make explicit the design process as it applies tothe design of instruction, explicit descriptionof the process being a necessar=y first step in thedevelopment of a science of instructionaldesign. We describe how we have applied thetheory and empirical findings of cognitivepsychology to dense a comae of action aimedat changing an existing situation into a desiredone (Simon. 1981, p. 129). Specifically. the--course of action h the instruction the existingsituation is the cognitive state of theuninstructed student, and the desired situa-tion is a student' a cognitive state that approx-

. inures speed. feitura characteristic of thecogve state of arrest in the field (the

le

a. loc.

32 f AUDREY B. CHAMPAGNE. LEOPOLD E. KL.OFFER AND RICHARD F. GUN ONE

The design process to-be explicated in thisarticle represents an alternative approach to. the design of instruction. Central to tith pro-eels is the analysis of customary instructionaltasks for the purpose of specifying the underly-ing cognitive processes and structures that arenecessary Cot: the successful completion of thetalk. The specification of these processes andstructures for a variety of school subject- matterdomains represents an important pan of therecent empirical findings of cognitive scienceresearch. Thug- if detailed process and strut-tore clesenruons appear to be helpful indesigning instruction in physics (as we intendm demonstrate), they should also be helpful indesigninginsnuetion in other domaiAss:-

We begin by describing the practicalrelevance of the instructional problem that in- ,

tereats us, namely, student difficulties in thelearning of classical Newtonian mechanics.

The Instructional Problem

There is a general agreement among physicsinstructors -and students that mechanics is dif-ficult to teach and .to learn (Kolody. 1977).Students 'have difficulty comprehendingclassical mechanics. and physics irsstructotsoften express disappointment with the out-come of their efforts to instruct students inclassical mechanics. This instructional problemhis been discussed at length in the literature ofphysics education where various underlyingcausal factors contributing to the problem havebeen suggested (Gerson & Primrose, 1977;Halley & Eaton. 1974; Hudson as McIntire.1977). Two distinct perspectives on this learn-ing problem are identifiable.

One perspective assumes that lemming dif-ficulties occur when the learner' is deficient inskills which are assumed to be prerequisite tothe study of physics (e.g.. Axons. 1976;Renner. Grant. & Sutherland. 1978). Theother perspective links the observed learningdifficulties with the fact that students comingco intsoduitory physics courses have firmlyembedded -conceptualizations of how and whyobjects move. and that .these concepnsaliza-dons are in clear conflict with the canonicalview of that subject-matter domain which thestudent will be required to learn. One line, ofscience education resesAkt and psychoiogicalresearch on semantic memory is particularlyrelevant to the second perspective.

escarch Background

trionzil ge and Students'

The research we examine furnishes a contextfor describing the existing- situation. theuninstructed student's cognitive hate, anddistinguishing it from the desired situation.Various empirical studies conducted by scienceeducators (including Bn.unby, in press; Driver.1973; Driver & Easley., 1978; Fleskiner, 1963;Gunstone & White. 1981; Leboutct aarrell,1976; Rowell & Davron. 1977; Singer &Benassi, 1981; Viennot, 1979) andpsychologists (including Clement. 1979;Green. McCloskey & Caramatzs. :980;Selman. Jaquette, K.supa. & Stone, in press)demonstrate that. for several science contentareas:

1. Students have descriptive and ex-planatory systems for'scientific phenomenathat develop Wore they experience formalstudy of the subject.

2: These descriptive and explanatorysystems differ in significant ways from thosethe students arc expected to learn as theresult of formal study.

3. These alternative conceptu. al systemsshow remarkable consistent' across diversepopulations.

4: These alternative conceptual systems areremarkably resistant to change by exposureto traditional instructional methods.

5_ These alternative conceptual systems arenot facilitative to the learning process.Students inte:pret instructional events (forexample. experiments and expository text)in the context of the conceptual schemethey currently hold. not the one that cue ex-periments or the tear are designed toconvey.

These effects are particularly strikini in thecornett of mechanics where prior to formalinstruction young people and adults hive aconception of motion that is more

0t let- Ithan Newtonian (Champagne.

pfcr ,olomon. & Ca Ain, 1980: -Clement.11,,,ver, 1973; Driver & Easley. 1978;

Lebrpute - Barrel]. 1976; Singer Eic Bcnassi,i9P_ 1, "-ientant. 1980). Other research findings

; remnants of the Aristotelian concep--persist with many -successful" physics

that is, with students receiving high*----ades in introductory physia courses (Cham-ragne. 'Chapter & Anderson, 1980; Gunstone& White, 1981). This research provides em-pirical support for what physics teachers havelong observed. namely. that traditional in-struction does not facilitate an appropriatereconciliation of preinstructional knowledgewith the content of instruction. (Ausubel,Novak, & Hanesian. 1978).

A study by Lehoutet-Barrell (1976) indicatesthat high school and college students havemisconceptions about &we and motion whichpersist despite instruction. The misconceptionsare described as pre-Galilean. In a study byCole and Raven (1969) with 12 to 1, year-olds.it was necessary to give the students "oppor-tunnies to reject irrelevant factors inunderstanding. the principle of flotation."Rowell and Davison (1977) also explicitly van-sidered common misconceptions when design-ing instruction on the law of floating_ Despiteefforts to refute misconceptions in instruction,some misconceptions persisted. Instructionalwork-by Fleshner (1963) in the Soviet Union

'indicates that students' intuitive ideas may co-exist with ideas derived from in.-auction. In astudy by Driver (1973). 11 and 12 year-oldstudents were interviewed prior to, during.and after instruction on several -topics of aphysical science course. Although alternativetheoretical frameworks to explain observationswere introduced to the students and used dur-ing the instruction. Driver reports thatcounter-examples and conflicting evidence didnot produce changes in students' thinking.

Our own work (Champagne. Klopfer. &Anderson. 1980; Champagne. Klopfer.Solomon. & Cahn. 1980) has demonstratedthat prior knowledge affects students' com-prehension of science instniaion. We havebeen particularly inter seed in the difficultythat beginning physics students have in learn=ing classical mechanics- Our research-:- hasdemonstrated that it is not the students' lackof prior knowledge- which makes the learningof this topic so difficult. rather their con-flicting knowledge. They come to instructionwith well-formed notions about the motion of

STRUCIIONAL DE51GN 33

objects notions that have been reinforced bytheir experiences: However, their notions maystand in contradiction to the tenets of classicalphysics, and these notions tend to thterferewith or inhibit the learning of mechanics. Thisresearch demonstrates specific ways in whichstudents' conceptions influence (a) theirunderstanding of science texts and I:xmies. (b)their observations, and (c) their interpretationsof their observations. Often the influence ofthe studen0' conceptions is to inhibit theirunderstanding or distort their observations andinterpretations of experiments.

Other research (Champagne. Klopfer, &Anderson. 1980) demonstrates that the beliefin the proposidm heavier objects fall -fasterthan lighter objects. is not readily changed byinstruction, thus demonstrating the strong in-fluence that prior knowledge has on the effec-tiveness of action 4 in this case the priorknowledge having an inhibiting effect on lear-ning. In a study of beginning college- physicsstudents. about four students in five believedthat, all other things being equal. heavier ob-jects fall faster than lighter ones. These resultswere particularly surprising since about 70% ofthe students in the sample -had studied highschool physics. some for two years. A chi-square test showed that students in the samplewho had studied high school physics did notscore significantly better than those who hadnot. This finding has been replicated infollow-up studies. -

In a report of a similar study of theknowledge of gravity possessed by beginningfirst-year-physics students at Monash Universi-ty. all of whom hadsuccessfully completed Ivoyears- of high school physics. Gunstnne &White (1981) conclude: (a) . studentsknow a let of physics but do not relate it to theeveryday world:- and (b) "In many instancesthe students used mathematical equations to

'Aristotle considered rest to or the natural state of ola.jeers. Its the absence of any cause, an object does not move:cnnversely. when an object is moving; it must have beencaused. unially by a force. Aristotle' &JO argued that the;Feld of in object is dOectly proportional to the forte ac-ting on it and inversely proportional to the resistance ofthe medium through which the object is moving in theNewtonian physics-of today. it d stated that an object willcontinue in raining state (either ai test or moving withconstant speed in a set ht line) i;tilcss it is acted on by aort forte. The wee/gram* of the object is directly propor-nonal to this net force and inversely proportional to theems of the object.

6

AUDAZY B. CHAMPAGNE. OPOLD E. KLO

=plain predictions. though often inap-propriately. which indicates that they had lotsof physic knowledge to hand [rig) but wereTmgfraled in seeing which bit applied to thegiven situation (p. 299). "' In chek conclusions. _Gunstone and White note that . . muchmore attention may have to be given to in-tegrating the knowledge acquired in school togeneral knowledge (p. 298)."

The eUffieulry is compounded by the factthat many of the terms used in classical

are also used in everyday lifeterns such as acceleration, momentum.and force. The meanings of these terms as usedby physicists are quite different from the wayin which. they are used in everyday life. Thus.we observe that students misinterpretmechanics intrrucdon because they interpretphysics lectures and textbooks in the cantina oftheir everyday understanding of the termsrather that in the way in which the teacher ortext is using the tams.

Theoretical aaalynr. These descriptions ofthe interactive effects of knowledge onunderstanding are consistent with findingsemerging from cognitive psychology thatdemonstrates the impact of existing knowledgein memory on the comprehension of text(Anderson. Reynolds. &hint= at Goetz.1977: Brantford & McCureil. 1974: Lindsay &Norman. 1972). Thii research demonstratesthat all incoming stimuli which areremembered are subject to reorganization bythe learner. The incoming stimuli are prima/.ily restructured by the learner in terms of thelearner's own past crperienco, and only secon-

rily in terms of the organizing principles ofthe material itself. In instructional situationsgenerally, students engage in active. mean-ingful structuring of test they read and lecturesthey hear in order to remember and under-stand incoming information.

Cognitive psychologists have studied ways inwhich prior semantic knowledge influencescomprehension of verbal materials. The earlystudies in the area of reading comprehensionaimed at demonstrating that snmething otherthan the linguistic suucture.pf a sentence is re-quired to =plain a person's comprehension ofthat sentence. The "something other- is

described as the person's world knowledge andis often-charaaerizecl as a="schema." .plam-or "saint." Brantford and McCazrell (1974)review studies which indicate that the processof understanding text involves creation of

ONE

' "semantic descriptions- that use both thereader's world knowledge and the sentence in-put..In this research, the contests for inter-pretation of text cither were common worldknowledge or were induced by the experi-menter. Anderson en al. (1977)-indicate-thatan individuxl`s "private" representation ofthe world can affect text comprehention. Ingeneral, studies of text comprehensionindicate the facilitative effect of schemata orworld knowledge. However. studies of physicslearning indicate that world knowledge islogicaAy anragonistic to the content to belearned and often = persists after physicsinstruction.

Cognitive Content: of Uninstrxrcsnrea'Physic: Students' Cognitive State.

From our analysis of empirical studies in-rt ring students' preinstructional concep-dons of the motion of oojects. we concludethat the following are characteristic of the con-tents of the cognitive stare of uninstructedphysics students:

1.. Concepts are poorly differentiated. Forexample, students use the terms speed,velocity, and acceleration interchangeably:thus,, the typical student does not perceiveany difference between two propositionssuch as these. (a) the speed of an object isproportional to the (net] force on the ob-ject; (b) The acceleration of an object is pro -portional to the (nett force on the object.2. Meanings physicists attribute to termsare. different from the everyday meaningsattributed to the terms.3. Propositions are imprecise and the im-precision derives from several differentsources.

_ (a) Some of the imprecision of proposi-tiorn is aiiribistable to the meaningsstudents have for technical conceptswhich are different from the canonicalmeaning. Example: More force meansmore speed.(b) Other imprecision can be interpretedas errors of scale (Gunstone & White.1981'). Example- Gravity pulls harder onobjects that are closer to the earth. (Theis

. proposition. in the &scum of an object .. falling a distance of three meters. is Cor-rect only-in-theory-because the differencein the force of gravity (approxmitily-1 parr in 10-0) is too small to measure.

7

=u rrrrrro AZ4tILKUI ANIV MS-AUCTION/a DESIGN

hf. however. the difference in distancefrom the earth were large (several bun-

kilometers), the difference in theof gravity is significant.)

er4sropositionsarejust_wmagandmay arise because of students' attempts

inappropriately formulate generalrules of motion from their erperiencm inthe real world. Example: Heavy objectsfin faster than lighter objects.

Implicatsons for instruction. Researchreviewed in section demonstrates' that thecognitive contents of the uninsuucted studentdiffers from the desired state with respect topropositions and the meaning of concepts.uninsuucted srudensi apply propositions thatlink force with motion. whereas Newtonianmechanics finks force with change in motion.Moreover, the meaning uninstructed studentsattribute to technical terminology is differentfrom the technic d meaning. For example, thetechnical meaning of acceleration is a changein the magnitude of velocity or direction ofvelocity of an object. while the meaninguninstructed students attribute to accelerationis speeding up.

Application of the Simon paradigm to thedesign process requires' detailed specificationof the -meaning concepts have for theuninstructed person and the principles thatoninsuncted persons apply in the analysis oftriotion. Such specifications are prerequisite tothe process of specifying the goals of instrue-don, and they allow for 04 the generation ofhypotheses about why certain instructionalpractices are not successful. and (b) the con-*ruction of possible mechanisms that will

in the desired changes in the learners'cognitive nate.

Differences- _like those described above bet-ween the uninstructed learners' cognitive stareand the desired cognitive state provide clearspecifications of changes . instruction shouldproduce. The instructional goal. then, is tobring about the specified changes in theloners' cognitive state. We hypothesize thatthe observed differences between theuninstructed and desired cognive states resultin certain of the ,difficulties that students ex-perience in learning mechanics, an interpreta-tion that is consistent with cognitive theory.We further hypothesize that the observed M-teractiyeeffects of prior knowledge and in-.asuman may be more eiretnounced formechanics than for other subjects.

35

The development of practical principles ofmotion is necessary for coping.with the movingobjects that are encountered M daily life.Thal, all students begin the formal study ofmediatiiesith an eat_erientially verified set ofprinciples that allow them to predict the mo-tion of objects under the conditions prevalent

in the real world. In addition, the same wordsthat are used to describe and explain motion ineveryday language also are used by physicists.

contrast this situation with thermodynamicsor chemistry where the words used fortechnical concepts are not a part of everydaylanguage (mole, enthalpy. entropy) and whereprinciples need not be developed to cope withfrequently encountered situations. In theseand sirnikr subject areas, traditional expositoryinstruction is More successful. However. inmechanics. instructional strategies need to beapplied that can make students aware of dif-ferences bedveen their everyday meanings ofwords and principles of motion and those ofthe insucrion.

Before presenting detailed hypothesesrelated to strategies which will produce thedesired changes in the cognitive contents ofuninstructed students. other relevantcharacteristics of the learners'-cognitive statewill be described.

Structural and Representational Featuresof Physic: Knowledge and AbyssesProblem Solving Strategies

The preceding analysis focused on the con-tents of memory propositions and meaningof concepts and hypothesized how studentsinterpretation of instruction understandingof lectures, text and experimenti is in=fluenced by significant differences- between thesubject matter to be learned and the students'cognitive contents. This-section focuses on theorganization of the contents of memory: itsstructural features and modes of represents.tion: the, differences between the structuralorganization and representations of expertphysicists, novices and uninstructed physicsstudents: and the implications of these dif-ferences for physics instruction.

Descriptions of the structural features andrepresentations of physics knowledge deriveprincipally from research on physics problemsolving. Rescsrthets in the domain of problem

--solvMgare_concerned with both the strategiesand structures that prObleni 5-elven

8

AUDILEy B. FAG, LEOFOLD

observed to apply in the successful solution ofproblems (e.g.. (reen°. 1978; Newell &Simon. 1972). We shall review, in turn. thepertinent research findings on structuralorganization and problem solving strategies.

Sirstaiivol orgamaarson-and representation.Research on physics problem solving providesdescriptions of the structural organizations and

esentations characteristic of expert andnovice problem solvers. The solution of physicsproblems requires both the availability of pro-blem solving strategies and the understandingof physical situations which are observeddirectly or described in the text of the pro-blem. Current theories of semantic memoryand natural language understanding (Ander-son. 1976; Anderson et al., 1977; Bransford &McCarrell. 1975; Kirioch. 1974; Lindsay &Norman, 1972; Norman & Rumelhart. 1975:

illian, 1968; Schank, 1972; Winograd.1972) tie the existence of relevant schemata tothe -process of making inferences and comingto understand a situation.

In the context of physics, understanding im-plies (a) the construction of mental reprmenta-dortspf physical situatidas that include the ob-jects that are a part of the physical situation.(b) the concepts and scientific principles thatare relevant to the situation, and (c) the rela-tionships that exist between objects. conceptsand principles (Winograd. 1972). Essential tothe construction of a mental representation isthe process of inference. Making validferencm is dependent on schemata that arcrelevant, correct and complete. Thus,understanding physical situations as physicistsunderstand them requires both that the rele-vant schema is present and that the features ofthe physical situation evoke the schema.

Recent work by Chi. Feltovich. and Glaser(1981) describes the folloWing explicit diferences in schemata of experts and novices: (a)The schemata of experts are based on physicalprinciples (for (=ample. energy conservationand Newton's Second Law),' but the schemataof novices are based on physical objects (for ex-ample. springs and inclined planes) and men-tal constructs (for example, friction and gravi-ty). (b) The contents of the schemata of expertsand novices do not differ significantly in IMO:-illation- content: however, the novices' stoic-mres lack important relations, specifically rela-tions between. the surface features of the pro-blem and the scientific principles which are thebasis for . solutions. (c) F tperts translate

OFFER AND C F. GUNSTON

surface features of the problems into canonicalobjects, State and constructs, while thenovices represent the problem in terms of theliteral objects and constructs described in thereset of the problem. (d) Links exist in the et-pens' representations of knowledge structuresbetween the abstract representation of featuresof the problems and the physical principleswhich are the basis for the solution of the pro-blem. (c) Experts' schema are organizedhierarchically along the dimension of abstract-ness; in contrm the different levels of,thenovices' knowledge are not well integrated,thus preventing easy access from one level ofabstracion to another.

Research conducted by science educators pro-vides descriptions of the organization and rep-rex-mations of mechanics knowledge (motion-of- objets schemata) in unimtructed students.Motion:of-objects schemata of unitarmaedstudents are situation-specific, thus suggestingthat no naive abstract =presentation is extant inthe schemata to make them appear to be ap-plicable to a large number of physical situations(Gunstone. 1980).

This lair, characteristic was exemplified inour work with middle-school students (Cham-pagne. Klopfer. Soloman. & Cahn. 1980). Wehave observed that, given four physical situa-tions, all of which could be explained by usingNewton's Second Law (F= ma), students nevergive any indication that they perceive that a.common explanatory system might be appliedto all four of the situations_ In fact. they nevernotice that a proposition they have used to ex--plain the motion in one of the situations isdirectly contradicted by a proposition they useto explain the motion in another 'situation.This failure co set the contradiction suggeststhat they are unaware of any need for con-sistency across situations. For example.students do not recognize that the samephysical laws apply to objects in free fall and toobjects sliding down an inclined plane. At onepoint during a class discussidn. for example.students agreed that two carts of unequalmass, but equal volume, would strike theground at approximately the same time whendropped from the same height. When theywere asked to compare the times for the cartsto slide down an incline. however. only one ofthem argued that the times would be aboutthe same.

Problem solving straregiis of experts andnovices. Cognitive research on problem solV-ing has generated ;detailed specifications of

CQGNI

problem solving strategies for many cathodes ofproblems (Greene, 1978; Nkwell ac Simon.1972; Larkin. Note 1). One finding from thisresearch that 6 particularly pertinent to the in-suuction we pmpcise is reported by Laskin. Hersays= of thinking- aloud prookols indicate thatexpert physicists ,perform a preliminary

calve analysis before proposing equationsfor the quantitative solution of the problem. Incontrast. novices immediately begin the searchfor an equation and proceed to match theinfonnation presented in the problem with ternsin the-equaricti.-

Given that the beginning nucleon' et-planatory scheinata are so situation-sp=19c. n ishardly surprising =that inch problem solvingstrategy is similarly bound to the perceived situa-lions. The students' main suategy,,for solvingmotion -of- object problems is to cry CO' recall 1rule or relationship whith they believe to be ap-pliiable to the specific simarion at hand-if ever. is there any evidence that the beginningstudents are aware of general problem solvingstrategies. related to general physical principles orlaws. which are applicable across many situawns.

es in Struetuve acrd thrartructio

Empirically- derived descriptions of thecharacteristics of the schemata of uninstructedstudents. novices, and experts are summarized inTable 1. This swims- aril:makes evident the con-trasts and similarities in the characteristics of thethree gaups' schemata with respect to principles.sari" e features. and second-order features. eachof which is briefly explained in the first column.Also summarized in Table 1 are destaiprions ofthe problem solving strategies fox etch group.

Precise descriptions of the delircrviees in then and representation of the physics

knowledge ©f individuals at differ= levelsof competence provide a further basis for the

o- of the goal and objectives for begin-ning .medics instruction and allow us togenerate hypotheses about (a) how current in-structional practice may impede the attainment

=of the goal and (b) alternative instructionalmechanisms that will facilitate the attainment ofthe objectives

Contrasting the problem solving strategies andorganition of the mechanics knowledge of ex-

res. novices and uninstructed students.Ids the following goal for beginning

ANN ZONAL DESIGN 37

ies instruction: Development ofa well in-motion-of-objects schema that is

gazited in a way that produces (a) the solutionof mechanics problems via the method ofqualitative analysis and (b) the analysis of the

-motion of objects in the real world using thetenets of Newtonian mechanic." The detailedspecilications of the mechanic knowledge

jkaticn to be accomplished as the result ofinstruction corral= the instructional objectivessubrumed under the: goai.

Empirical evidenct densonstiatm tbat currentinstructional practice does not facilitate theininment of identified goal. Students generallydo nor learn to relate theh mechanics knowledgeto real iimationsras the result of either 'highschool or beginning college physics instruction.Eased on, rcutsory Analysis. of physics tens andour knowledge of physits inset Lion. we con-clude that preliminary qualitative analysis ophysics problems is seldom if ever caught st.plicitly. In fact. problem .solving instruction inphysics textbooks makM. no attempt to -link thephysical feature of the real -world situationsdescribed in physics to the abstract concepts andprinciples of the Newtonian forneivork.

Physics texas teach .the, problem solutiiht-strategy that novices typically, use-. The last stepin sample solutions is the presentation' of theequation that will yielelaquantitative solution tothe problem. Thew 6 no attempt to insoll.a ticstudent in the =pen physicists' analytic pro-=dunes which result in 'abstract representations ofphysical situations in terms of abstract concepo.These concepts-are vital bemuse they in turn canbe linked to principles or laws of ;mechanics andformal expressions of the principle or law (for-mass) which can then be applied to reach aquantitative solution of the problem.

The traditional practice is counterproductivein two respects: (a)lt teaches a problem solutionstrategy that does not approximate the-strztexemplified by the ideal state. and (b) It does notencourage the develoPment of links in cognitivestructure between real -world situations and theabstract representations of physical situations thatcharacterize the to.be-aparoximated schernita.

-Experurrsces contributing to the expen'scognitive nate. An interesting theoretical ques-tion. with implications for both practice andtheory' should now be posed: In the-absence ofdirect instruction. how do experts come todevelop the qualitative analysis strategy and theconceptual -1)6,beriveen physical situations andthe appropriate abstract representations?

Table

Wen Solving Skokie' and Sthioa of thiottnicied Side* Novices, Ord kern

PROBLEM SOLVING STRATEGIES

oTEamil

UNINSTRUCTED

STUDENTS

Tho typical procedure for solving problems Is to find e general rule which appears to COW the physical libation de,

scribers in the problem, and then to use the relationship described in the identified rule deductively to derive an answer

to the problem,,Rules to be employed in this process may be welled from experiences with slily physical situation;,

or they may be remllections of authoritative statements from books or people,

NOVICESThe principal procedure for salving problems is to instantiate: variables In equation'. This procedure may be Chained

through a series of equitioni, Abstracted solution methods are lacking.

4PERTS

Associated with the organizing schema are its specific conditions of applicability end the necessary problem solution

methods, Experts abstract a basic solution strategy from the surf Ica features of the problem and engage in qualitative

analysis of the problem prior to determining a quantitative solution,

'FEATURES OF

SCHEMATA

SCHEMATA

wew=mast

CHARACTERISTICS OF

UNINSTRUCTED STUDENTS' CHARACTERISTICS OP

SCHEMATA NOVICES' SCHEMATA

CHARACTERISTICS OF

EXPERTS' SCHEMATA

PRINCIPLES

Ideas of some degree of general,

ity that express' relationship's;

principle: are tippled to solving

problems; can serve to organize

schemata,

Principle; are generalised rules

derived from everyday piper=

lances (world knowledge). They

are imprecise propositions, The

imprecision Is due to wont

about the meaning of concepts,

errors of scale, end inappropriate

formulations of general rules,

The principles (rules) haw

limited wail and tend to be

iiltuotionpecific, The notion

that an abstract principle can

apply to a range of different

physical, situations Is lacking or

poorly developed, There appeal

to be no awareness of the nerd

for consistency along the rules

that cover different physical :

situations,

Principles are seletionships

between physical variables ex.

pressed as equations or rules,

Some 'of the principles' are the

major physical legs expelled in

equation form, but there is no

evidence that they serve as

organizers of schemata,

principles are major phyficil

laws, which are highly abstract

end open relationships of

greet polity. Included witheach principle are the condition

under which the principle tip-

plies, Eech principle has en

associated scheme, , which Is

oriented by the content and ip.

plicebbity conditions of the

principle, The applicability cos

ditions smelly are expressed In

terms of secon4order futures,i

Is

OBJECTS AND PHYSICAL

CONDITIONS (SURFACE

FEATURES)

Physical object; and czoditions

described or presented In a pro-

blem situation; physical features

of objects and their Imes. of

motion or position that are

directly pcfoliviyi from verbal

descriptIon; diagrams or direct

observation of the physical

tituetIon.

MIIIIImeemeems

Concrete objects and the direct-

ly observable properties of oh.

facts are present. A reasonable

Inferenci it that the °bleat and

properties define the specific

physical situation which, in turn,

direct; the search in memory for

a primal tutu that coven it,

Physical objects arid their tor.

lace features are the buis for

categorizing problems. It it Inter-

red that an object or a config .

oration of objects functions as

the organizing etemvnt Modal in

its scheme for the problem. The

content of the representations

may be concrete objects or ab-

unctions it the level of

diagrams.

Concrete objects, their physical

configurations, and diagrams of

object; ere present in the

schemata, but none of these it

prominent. If I; interred that

object: serve primarily uvehicles for identifying second.

order future', and that tome.

times they trigger the ectivetlori

of a particular principlebued

schema.

PHYSICS CONCEPTS AND

SYMBOLS (SECOND-ORDER

FEATURES)

Ideelitatiom of physical objects

fag,, in elephant it represented

as a point mau ). and constructs

or entities (e.g., energy,, force);

conventional :representations of

physical entitiet vector

component!):

There It no 'Meru thattecondader teetotal ire repre .

tented in thew whemete. Coo-

ceptt and term; are present, but

many are poorly differentieted.

The meanings of the terms ere

their real-world meaningt,rerher

r i their technical meanings

In phytics.

Some conventional taproom-

liont. of physical entitle' are

present, end 144z/dons of

physical objects may be used In

problem repretentetiont. Con-

cepts and terms related to the

object; which dominate the pro-

blemolution schema ere

prelim!. Novice sport taking

fermi directly. from the problem

statement to identify equation;

that could be approximately em.

played in solving the problem.

Representations of physical

objects in their Idealised form

are prominent, with the content

of the representation; deter-

mined by the organizing schema.

Physical entitle, are represented

according to the conventions of

the field. Features abstracted

from the problem statement are

OM present, Some experts

repot that these feature; help to

select the basic approach to pro,

blern tolutiont, thus indicating

direct link; between these

second order futures and print

ciples. Concept relevant to the

organizing tcherne are preterit.

Associated with each concept

ere its interconnection; of

relations with other concepts

and with the schema"; major

physical low.

14

2

2

Oz

40 AUDREY S. GI NE. LEO W h. &Luiork_K ._ &ILI-LAW F. LILMIONh

For the purpose of our dUcussion, we con-dder three factors that differentiate the ex-periences of =pens from the experienem ofnovices; these are: (a) additional formal in-strucuon. (b) more extensive practice in solv-ing problems, and (c) more extensive verbal in-t:ractions about physics. The Chi et al. (1981)study suggests that -the contents of novices'data structures for particular types of physicsproblems are similar to those of experts withrespect to objects. concepts, and terms:however. experts' data structures contain manymore linksg= The more extensive data base.which =peas acquire as a result of theirgreater exposure -to formal instruction, is notnecessary for the successful solution of prob.blerns of the type on which the analysis ofexpert- novice differences is based. However.the additional links M experts' knowledgestructures are necessary for the successful andefficient solution of mechanics problems.

We hypothesize that these links develop as aresult of extensive practice in problem solvingand that their development is facilitated byverbal interactions. The professional activitiesof physics =pens require either verbal interac-dorm with others or the organization of physicsinformation for the purpose of communicatingit to others. We hypothesize that this type ofexperience is 'important to schema changebecause the-individual must Make explicit themeaning attributed to technical terminologyand the rules for applications of propositionand principles.

This analysis leads us to hypothesize thatproviding. beginning students with oppor-tunities to engage in the quantitative analysisof physics problems will facilitate the develop-sent of physics knowledge organized in waysthat approximate that of the organization of aphysics expert. Our selection of this instruc-tional strategy to attain this goal is based onthe recognition that: (a) The cognitive objec-tives of beginning - mechanics instructionshould approximate the skills and knowledgeapplied by experts in the solution of mechanicsproblems; (b) Explicit instruction in theknowledge and skills required for successfulnovice performance is not now a part of physicsinstruction: and (c) Part of such instructionmust focus on producing a schema change instudents which results in the incorporation andintegration of mechanics principles and inter-pretations of real-world phenomena.

We hypothesize that providing learners withopportunities for verbal interactions will

facilitate the development of correct usage oftechnical vocabulary and help skudents becomeaware of the principles they apply in theanalysis of physical situadoes and how theirprinciples are different from those beingtaught. This hypothesis is consistent withcognitive theory of schema change.

Schema change theory. The processes bywhich existing schemata are modified are justbeginning --to- be understood (Greenci,--1980). =Infurmation processing models of schemadevelopment generally have not gone beyondthe level of describing stages. Nonetheless.several valuable ideas concerning the develop-ment of schemata and suggestions for=modify-Mg schemata have been offered.

Two principal mechanisms for schemamodification have been discussed byRurnelhart and Ortony (1977). Eachmechanism is. in a sense. the antithesis of theother. Specialization occurs in a schema whenone or more of its var iables are fixed to form aless abstract schema. Conversely. generaliza-tion occurs a schema when some fixed por-tion is replaced by a viable to form a moreabstract schema. The . generalizationmechanism can be applied in a motion-of-objects schema.

The typical uninstructed student has themotion schema: A push produces motion. As aresult of appropriate instructional experiences.the student's motion schema could become: Aforce produces acceleration. The fixed portion,push. in the initial schema has been replacedby a more general variable. force, which canrake on several values in addition to push.Similarly, the general variable, acceleration.which can have different values. has replacedthe initial schema's fixed portion. motion. Thernoddied schema is considerably more abstractand, hence. should have a much broader rangeof applicability.

The hypothesized generalization mecha-nism only describes the changes and is. in, fact:not a mechanism for producing them. If. asRurnelhn and Ortony (1977) imply.-the gen-eralization mechanism is a mechanism for pro-ducing change. a reasonable implication is thatthe modification of the motion-of-objectsschema might be accomplished quite simplyby describing to students the needed moclifica-dons in definitions of terms-and restating

propositions. Empirical evidence onmechanics learning demonstrates chat this in-structional strategy is not generally effective

COON CH

and suggests that. while the gradual rmodifica-non of sr.herr.ata doubtlessly involves general-ization and specialization, in highly integrat-dgCbcrnara More &arreariC change. amountingejscorjally to a shift to a new paradigm (inKahn's [1962] sense). must also take place.

To bring about schema Change on mch alarge scale. a (Ealectiml proems appears to benecessary. Riegel (1973) poi= out that thethinking of both adults and children iis dialec-tical. and he proposes that dialectics is "thecraisformational key" in eogru,-; develop-ment. Anderson (1977) suggests that .

the likelihood of schema change is rna_ximizedwhen a person recognize; a (ficulty iniiscurrent position and comes to see that the dif-ficulty can be handled within a differentschema (p. 427).

As the mechanists for promoting dialecticsin the classroom, Anderson advocates the useof a Socratic teaching method. By participatingin the dialogues which occur in Socraticteaching. the student is forced to de-al withcounterexamples to proposals and to face con-tradictions in his or her ideas. To overcome theattacks of adversaries in the dialogues, the stu-dent must construct a new framework of ideasthat will stand up to criticism. The newly con-stnxted framework is, of course, a newschema. so it may be said that schema changehas occurred as a result of the student's par-ticipation in the di logues.

-Instructional Issues

Spec: ration oflnstrscctionalObjectives and Strategies on sheBasis of Cognitive Analysis

Table 2 summarizes instructional objectivesand strategies for mechanics instruction deriv-ed from the analysis of the cognitive states ofuninstructed students. novices. and experts.groups who differ with respect to (a) the quan-tity and extent of formal mechanics instruc-tion. (b) elperk-rice in solving mechanics pro-blems. and (c) the extent of their verbal in-teractions about mechanics.

Objectives. The objectives presented inTable 2 are based on the analysis of contrastingcognitive states and rep_resent the first in aseries of steps in the detailed specificationof instructional objectives. These objectivesspecify features of the ideal state which the

FrrtUC710NAL 1 DESIGN 41

Cr will approximate but do not detail howe learner will move along the continuumbeginning student to expert as the result

of a particular course or sequence of instnic-don Further refinement of the objectives for acertain instructional sequence must take intoaccount many other factors. including the con-tent the instruction will cover, the time avail-able for instruction. and the age and academicaptitude of the students for whom the instruc-tion is intended. However. the analysis here il-lusrxacm one important principle employed inthe cognitive approach to design. That princi-ple is the comparison of the cognitive states ofindividuals at different levels of competence(Gretna: 1976). Furthermore, the design re-quires that the initial specification of objec-tives be based on the cognitive features thatdistinguish the learner for whom' the instruc-tion is designed from individuals competent inthe field.

An observation worthy of comment is thedifference between these objectives based oncognitive analysis and objectives that derivefrom the logical analysis of the subject matteror from the identification of to-he-learnedbehaviors. Objectives derived from these twoprocesies are deficient in at least two respects.First. cognitive analysis identifies significantobjectives not identified by either analysis ofbehaviors or logical analysis. Second. logicalanalysis does nor identify the structuralorganization of knowledge which the instruc-tion should produce. For example, logialanalysis would not identify qualitative analysisof physic' problems as an objective of instruc-tion. nor would it produce information aboutthe optimal structural organization ofmechanics knowledge for competent problemsolving.

Instructional strategies. The first approxima-tion of instructional objectives derivm from thecomparison of the cognitive states of unin-structed students and experts. Possible instruc-tional strategies for the attainment of theobjectives derive from comparisons of the cogni-tive =tot of uninstructed students. novices.and experts, and from examinations of themechanic- relevant experiences of novices andexperts. Having specified the differences incoy-drive states and relevant experiences we cangenerate hypotheses for explaining the observeddifferences M cognitive states on the basis of dif-ferences in experiences. These hyPotheses, inturn suggest possible instructional strategies.

Table 1

Contrasting km in Copulae State] and Their Related long:ion' Objectivn and Siralegiel

Contrasting Features in Cognitive

States of Uninstructed Students

Novices (Ni, and boots (El

Instructional Objectives

Derived from the Contrasts

Instructional Strategies

to haste Attainment of

Instructionel Objectives

CONCEPT MEANING

Meanings attributed to technical terms by

U differ in significant ways from the

meanings of f and N.

Example: U acceleration means speeding

up; E and N acceleration means a change

in the magnitude or direction of velocity.

CONCEPT DIFFERENTIATION

U do not differentiate mechanics comp's.

Example: U wait and mag are the

same thingfl end E mass end weight are

perfectly correlated but distinct.

;7.

Students know both the everyday meaning

and the canonical definition of mechanics

and can gaily differences between the

everyday and canonical meanings

Internal dialogue: Provides students with

opportunities to become mere of the

meanings they attribute to phyticil CM,

Cepit, how thesaimeanings differ from con

text to context

Examples; (I) doing physics problems or

describing a Orin' event to a Mend,

or (7) doing mechanics problems In which

there Is no motion.

Dialogue provide; students with opportun

lilts to wrest their meanings of concepts

with those of the physicists.

In sniping a given physical situttion,

students can explain which of two poorly

differentiated concepts is the, relevant

concept to epply,

Intetvid Moir Provides students with

opportunities to verbalise their inalysls of

physiiii situations in a way that simply sub.

diluting 9 g foil mass (ml or 45 dynes for

weight (F) In an equation does not We

hypothesise that the varbelliallon will help:

Newlin) weight (a force) expressed in

dynes from miss expressed In gam. 'Alto

tee strata on Structural Futures row

below)

I--PROPOSITIONS IN SCHEMATA

U presence in schima of incorrect

position

Eample: oo1 irnplie formN presence in schema of conflicting pro.

positions. which are applied in different5:tuitions,

Example: Motion implies force pro:

position applied in the analysis of reol.

world iiivationa. Change in motion

implies; force proposition applied in the

quentitative solution of physics problems.

E propositions prevent in schema are in

tonally consistent and widely applicable,'

Example: Change of motion implies force

proposition, is applied in analyzing all

pertinent pttblems.

Students apply chin In motion implies

force position in real-world situations.

Students contrast Implications of the dif-

ference in the two reimionships between

force and motion expressed by the proposi.

lioni II) Motion implies force, and 12)

Change in motion implies force,

Instructional dialogue to change contents

at mechanic; Khans: Provides opportunity

lormodents to 11) he explicit about the pro-

positions they assume in invoking the pre-

sence of farces in physical situation (For

example, generally Invokes forces only in

situations where there ti motion.) and (2)

make explicit the relationship between

motion and fog in the propositions they

use.

STRUCTURAL FEATURES

Concept integration of U and N it sparse,

with fewer links among concepts than for E,

Exemple: N experientially derived

schema is not into,

grated, or reconciled with Newtonian

mechenici scheme.

Integrat:an of representations in U and N is

poor, o'hile they are wellintegrated in E,

Exampie: N representations of wake

features of physical situations are poorly

integrated with abstract representations

of physical situations; these, in turn, are

poorly integrated with: propositions

which link canonical objects and physlest

constructs used in abstract represent'',

lions; E representations of surface

features of physical situations are into,

grated both with abstract representations

of physical Situations and with propos',

fiord linking the canonical able; and

constructs of abstract representations.

Students qualitatively analyze mechanics

problems:

Produce in abstract representation of e

physical situation.

12) Recognize that situations with very dif-

leant surface flames can have the semi

abstract representation, (For an Beim*,

see Appendix A where the situations of

Problems have the same abstract zepre.

senation.)

(1) Recognize that the problems can be

salved by the application of the same

mithenics principle,

Qualitative Analysis of problems to dim

structural feature; of machanla schema!

Forges links between the physical situetion,

its abstract representation using canonical

objects and mechanics constructs, and the

pnclptes (Newton's second law, F a ma)

which link properties of the canonical ,

objects and constructs, Also forget links

between concepts fag., between mu and

weichtl to integrate them better, thereby

contributing to concept differentiation,

Table 2 (continued on next pop)

PROBLEM SOLVIION STRATEGY

U solution stratv: search for a rule ihe

3Pp lieS to the Oven

Example: Problem of coMparing speeds

of two tailing diem mks the rule

Heavy obitos fall faster than lighter

objects;

N solution strategy; search for an equation

E solution strategy: qualitative pelysis

Table 2 icontinued)

Student; tog* In qualitiative enalysis

of physics problems before attempting

quantitative solutions.

Mteractivt dielogue: Noinowes that the

eame ibitfiel representations and diagrems

derive from problems with different suffice

leatura Also demonstretes the usefulness

of I morel principle for solving loge

number of problems with different surface

features.

Qualitative analysis of mechanics problems:

Provides practice in using the desired

strategy.

2122

0

COGNITIVE R.E5 EARCI4

The potential for effectiven s of alternativeinstructionel strategies is then evaluated interms of relevant psychological theory.

The availebility of empirical descriptions ofdifferences berween unirsstructed srudents andraovices is panicolsrly important to the processof selecting instmctionai strategim informationabout these differences leads to the identifica-tion of instructions.' strategies which are effec-tive and those which are not effective orcounterproductive. The observation thatnovices' cognitive coot_ ents resemble those of es-perti IS an ind.iatiskin that die didactic methoddf instruction is effeoive for imparting discretebits of information.. However. the detailedanalysis of problem-solving behaviors of novicesBugg =s that their scruentral organization of in-formation resulting from exposure- to didacticinstruction is less than satisfactory.

In the case of mechanics. this analysis alsoreveals that the problern-solving strategy taughtin physics tectbooli3 is indeed demonstrated bynovices, but. as we discussed earlier. phisstrategy does not produce certain desired linksin cognitive structure. specifically those betweenphysical situations and mechanics concepts.This lack of strumiral integration soevidenced by the fact that many novices con-rite to apply non-Ntoniari principles whenasked to analyze real- world situations.

The analysis of novice-expert differences is atrul source of possible alternative instruc-tional strategies. For example. the proposed M-fluence of problem-solving and verbal interac-don in the development of correct and well-integrated cognitive structures are derivedelL-ectly from cognitive difference analysis. Thisinterpretation of the differences is consistentwith cognitive theory and with educationalpractice and philosophy. The cognitive analysisprovides an ceplicit causal Lilt fees thestrategy and the outcomes. thus making possi-ble More convincing empirical tests of the effec-dveness of the strategy. Our assertion thatengaging in qualitative analysis of mechanicsproblems will develop a bier integration ofreal-world situations and their abstract represen-tation utilising the concepts and symbols of

ewtonian physics = 6-empirically testable.

PrOcectural Description of MeProposed Ms:ructionise

Although the strategy of using dialogues ininstruction has been specified in relation to the

UCTIONAL DESIGN 45

attainment of instructional objectives (Table2). we have not yet described how this strategyis implemented. Illustrative procedures whichemploy the strategy are outlined in this sec-tion. In one mode of the dialogues stsategy.students engage in interactive dialogues witheach other.

First the =dents are presented with a set ofmechanics problems which require qualitativeanswers. A typical set of sit such problems isshown at the right side of Appendix A. Theeproblems are qualitative restatements of sorts-blems from five different physics textbooks.The physical situations or =race features ofthese problems (in both the qualitative andquantitative versions) are-very dEferent, but allproblems can Fe represented in the sameabstract form (diagram or verbal descriptionusing mechanics concepts) and can- be solvedusing the same mechanics principle. F.ach stu-dent produces a solution to each of iscie pro-blems and then shares with the elms the pro-blem anslysis, the solution of the problem.and definitions of technical terms used in tiesolution or the analysis. This procedure forcesstudents to be explicit about the idiosyncraticmeanings attributed to technical terms and theprinciples and propositions that they apply inthe analysis of the problem. Each student cancontra t his or her 'solution strategy for a pro- ,blem with the strategies presented by otherstudents.

When all of the problems in the set havebeen considered by the class. the teacher willpre Sent the physicists' analysis of the problemby mean of diagrams and verbal explanationsusing the technical vocabulary of mechanics.The expert analysis is based on the commondeep structure of the six problems. as shown inAppendix A. The teacher will demonstratethat the abstract representation is the same foreach of the problems and that the same princi-ple will-produce a solution to all the problemsin the set. Then_ students will analyze theirsolutions to the problems in light of thephysicists' solution and will speedy how theirinterpretations differ from that of thephysicists.

The teacher's presentation of the physicists'analysis and solution of qualitative problems isin the mode of an instructional dialogue. Inorder to explain and illustrate this mode of thedialogues Strategy. we have analyzed physicsproblems from introductory texts in the man.ner shown in Appendix B. The general wise-cure of the analysis is simple. Initially the

46 ALM_

textbook problem was rewritten as atative problem and subsidiary qui:mons

were added asking about the assumptions andphysics principles used in obtaining the answerto the problem. Then a realist=ic minimumnate in twins of relevant prior knowledge andexperience was selected. and a strategy forworking from that state to a successful solutionwas waked out. At this stage. when we do not1:6--e the insights to be derived from data, it is-assumed that other. more developed responseson be accommodated by beginning at a laterpoint in this sample strategy.

The strategy has been outlined only. It in-float= a series of logical steps. Within eachstep. the essential concepts) to be develop_edand the purpose of the step in teams of theproblem solution are indicated. In some casesa particular in.strucriona methodology to be

Of a step is shown, while in the remain-ing cases only instructional dialogue is an-ticipated. For each the rationale for the pro-cedure is described. referring to the techniquesidentified by Collins (1977) and Collins andStevens (1981) when appropriate. A strategy#for handling a correct sumer to the questionsmined so as 'to develop a solution strategy forthe problem is also given.

Concluding Remarks

In diis article we have recounted how our in-ns:tat in a particular instructional problem inintroductory physics. nucleon' difficulty inlearning mechanic. provided the occasion forutilizing Simon's characterization of a scienceof design as a guide in proceeding to design aninstructional strategy that can be used to helpstudents leers mechanics effectively. We haveshown how the theory and empirical _findingsof cognitive science and the cognitive psycho!.ogist's analytical tools and procedures werebrought to bear on every stage of the designprocess. We have sought to make explicit theparticular principles of instructional designwhich both evolved and were applied in thecourse of the inquiry. We suspect that these in-structional design principles may be applied invarious school subject-nutter domains, thoughonly their application in physics was illustratedhere.

t. r. 1.-/NC

The instructional strategy for guidinguninstructed physics students in their learngof N'ewieniza meithartic is now available. butour inquiry is not at an end. We are nowpreparing to investig-aze empLri...ally severalrues which were rased dining the proc=s ofdesigning the instructional strategy. The majorh esis to be tested in our pronice-arch is that engaging uninsuuctecl physicstudents in instructional dialogues focused onehe qualitative analysis of mechanic - problemswill produce in_the shuients- motion-of-objeas schrtnata A further hypothesis isthat, after completion of the specified imsr_ruc-hon. the students' cognitive state will approk-inmate significant features which arecharacteristic of the cognitive stare of a physics=pen.

We can admire the great psychologUu ofearlier days. such 25 Charles H. Judd. whomwe quoted at the start of the paper. for theirkeen perspective o students' learning ofabstruse school subjects like physics. Judd's in-sight (or perhaps. intuition) seems so right andtrue that we cannot help being amazed. Alsoamazing is the realization that the situationwhich Judd described seven decades ago stillrings true for physics textbooks and physiclearning today. Hardly anything seems to havechanged. in the interim. Why is this so?

The main reason. we believe, is that,although Judd recognized, e problem, hecould not .prescribes solution.Because he was unable to describe the problemprecisely. Judd had no basis on which toevaluate the probability of the effectiveness ofpossible instructional strategies. Today, thestatus is dffetent. Empirical and theoreticalresearch in cognitive psychology make possiblethe construction of theorer.L.al models. onwhich predictions can be based. The applica-tion of a model of understanding of physicalphenomena leads to detailed specification of astrategy for beginning physics instructionwhich can be expected to produce desiredchanges in students.- The difference betweenour present possibilities and those of Judd'sday is demonstrated in this article.-

Rafe_ _ce Notes

Larkin. J. H. S44( u/sumo* fir Wong ploy.ticsPaper .pr tinted at the meeting of the

Prychobomie Society. Phoen. November 1979.

24

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26

Appendix A

Six Physics Problems with Different Surface Features and the Same Deep Structure

QUANTITATIVE VERSION

1. Boy and Wagon Problem

--A b.6.9-f i 20iTIdinj1n 1Wigois of mass 10kg The

boy lumps off to the right with a speed of 2o misc. What happens

to the wagon? (Ignore friction.)

(Hulsirer & Lazarus, 1972, p. 187)

2. Boy and Raft Problem

A 50 kilogram boy Is standing 0:4500kilogram raft floating on

a lake. The raft is at rest. It can move on the surface of the lake

with negligible friction. Starting from rest, the boy begins to walk

with constant speed 1 meter/sec (relative to ground) and con.

tinues to walk for 20 seconds. How far does the raft move in

this time?

(Smith & Cooper, 1979,p. 152)

3. Rifle and Bullet Problem

'A 31 bullet is fired from a 2.4-kg rifle with a velocitydr

north. Find the momentum of the bullet and the recoil vt, of the rifle, assuming that no other bodies are involved.

(Smith 8i Cooper, 1979, 0,13).

Is.

4. Skaters Problem

Two skaters are stationary in the center of a circular rink. They

then push on ,one another so that they fly apart. One of the

skaters has a mass of 90 kg and acquires in initial velocity of 0.8

m. sec. If the other skater has a mass of 75 kg, what is his initial

velocity?

(Atkins. 1965. p. 119)

27

QUALITATIVE VERSION

A boy Is standing in a wagon. The boy jumps off one nd 9f the

wagon. Ignoring friction, describe the motion of the wagon.

How does the velocity of the wagon compare with the velocity

of the boy?

A boy is standing on a floating raft on a lake. The raft Is at rest. It E

can move on the surface of the lake with negligible frictijon.

Standing from rest, the boy begins to walk with constant speed

towards the shore. Describe the motion of the raft. How does the aspeed and direction of motion of the rat compare with the speed

and direction of the boy? I.90z

A bullet. is fired from a rifle. Describe the motion of thfillitHow does the velocity of the rifle compare with the velocity of V

the bullet?

Two *kers are stationary in the center of a circular rink. The

skaters push on each olher. Descry the motion of each Outer.

How do their velocities compare?

0z

0

%13

Appendix A (continued)

6. CÜIi Id Spring Problem

Two heavy frictionless carts are at rot, They are held together by

a loop of string. A light spring compressed between them (see

drawing), When the suing is burned, the spring expands from 2.0

cm to 3,0 cm, and the carts move sort, Both hit the bumpers

heed to the table at the same Instant,

but cart A moved O45 meter while

Cart It moved 0,81,meter. What Is the

ratio of

(1).. The- toted of A to that of

after the Interaction?

lb) !heir masses?

Two heavy frictionless carts are it rut. They ire held together by

e loop of string, A light spring is compressed between them. The

string is burned and the spring expands. Describe the motion of

the carts, How does the velocity of art A compere with the

velocity of cart B?

(Habertchalm it al., 1976, p, 321)

6. Compressed Spring Problem

Two objects of mass mA end ma are held together by a strong

light thread, and are also acted on by a light spring that Is-cam .

pressed as shown in the figure, When the restraining thread is

broken, the two objects fly apart with

velocities -eA and + en. Use the law

of conservation of momentum to solve

For the ratio of the velocities, vAIv9.

Two °Weis of mess mA and ma are held together by a strong

light !hind, and are also acted on bye light spring that Is corn!

,-presikt When the restral&ng thread Is borken, the two objects

fly apart with velocities vA and

v Use the law of conservation of+

momentum to solve for the ratio of

the velocities, eAlva,

(Miller, Dillon, & Smith, 1974, p. 112)

PHYSICIST'S ANALYSIS

Forces of equel magnitude and opposite in direction ere

exerted on two unequal masses at -rest. How do the vibe.

dies of the Masses come? How do the displacements of

the masses compare?

rfl

COG. LICTIONA_I DESIGN

Appendix B

Example of Proposed Instructional Dialogue The Gun and Bullet Problem

original ProblemA gun has a mass of 2.00 kg. It fires a bullet of mass 0.005 kg towards the right with a speed of

5430 m/sec. How does the gun recoil? (Give its speed and direction of motion.)-(Hulsizer & Lazarus. 1972. p. 1137)

Problem Restated in Qua litative Form

When a gun is fired, the bullet leaves the gun with some weed. How does the bullet's weed at themuzzle of the gun compare with the gun's weed at that time? How does the direction of the bullet'smotion compare with the direction of the gun's motion?

Subsidiary questions (i) What assumptions did you make to arrive at your answers?(ii) What principles of physics/laws of motion did you apply k the situation

in coming to your answers?

Knowledge/skills assumed in following outlines of Instructional Dialogue strategies

1. "Physics" knowledge: it is assumed that students have completed a study of kinematics.2. General (or -world-) knowledge: Awareness of medieva' cannons, rifles, handguns (see

step Al below):

Strategy A Outline of strategy to be used for responses to the qualitative problem of the form"don't know" or "gun doesn't move."

Steps in the Strategy Purpose of Steps Commentary on Steps

Given scale drawings Alla) and (b). To establishof a small pistol, rifle, small that in the real world, mass/mortar, medieval cannon and weight of gun > mass/weightshells/bullets fired by each, of bullet or shell.student is asked to match theguns and shells/bullets.

A 1 (b). Ask student whymatchings were made.

A2. Ask the student whythe bullet/shell comes out ofthe gun when the gun is fired.

13. Show the student adrawing of a metal tube,closed at one end and with alighted fire cracker placedon it.

Asked what will happen whenthe fire cracker goes_ off.

To establish the role of ex-plosion in this phenomenon.If this notion- is present, goto 14; if not, go to A3.To establish the effect of ex-plosion on the mass in thetube, i.e., the cracker. If thisexercise does not establishthe notion, move further toconsidering a medieval can-non where the explosive andpropelled object are separate.

31

Collins (1977) has proposed aseries of production rules forthis form of instructional dia-logue. Strategy- Al (a) is anexample of Rule 1: Askabout a known case. In hissubsequent reorganization ofthese riles (Collins & Stevens.1981), this is an exampleof Case Selection Strategy 1:Pick a positive exemplar fora set of factors.

Collins (1977) Rule 2: Askfor any factors.

Collins (1977) Rule 2 (seeabove).

Collins (1977) Rule 3: Askfor inteRneelists factors. Forsome students this wilt alsobe a prompt to meal I ',le-vant previous experiivsce.relevant existing world kneow-

52 ALM B. W E. Kr_opra

Appendix B (continued)

Steps in the Strategy Purpose of Steps

A4. Using two labor-atory trolleys, one containinga spring plunger (plZSC), anda number of bricks.°

(a) hare student' exper-iment qualitatively with-theeffect of placing two cartswith loaded spring betweenand releasing the spring,with varying masses on thecarte,(b) have students exper-iment with one cart carryingvarious masses placed withloaded spring against theirhand and then released.

AS. By drawing on Al-A4, assist the student toestablish (and, if appropriate,to link to relevant existingknowledge/experience):

(i) that in the case of theexploding cart!, *he ex-pending spring exec's forceson the carts p14L. ' , eitherend of the sprrr,r2, 7i d thrtthese two forces are equal inmagnitude.(ii) that, in the case of theexploding carts, equal forcesfrom the spring acting oncarts of different mass resultin different cart velocitiesafter explosion.(iii) that, in the case of ex-ploding carts, when one carthas a mass considerably lar-ger than the other this situa-tion is in some ways anal-ogous to a- gun firing a

bullet. (Of the limitations tothe analogy, the most im-portant to be dr:orn outhere is that the relative massdifferences for gun andbullet are much greater thanfor the cam.)

A6. Return to qualitativeproblem. After successfulsolution of the prciblem as

asked, use strategy B below ifappropriate.,

To establish the separation ofall masses involved in an ex-plosion; to establish thatsmaller mass pieces movemore uickly than larger masspieces.

To establish that a mass ex-ploded away from a -'rigid"body results in a force onthat rigid body.

To establish the generaliz-ations needed in order to beable to analyze and salve theoriginal qualitative problem.

Commentary on Steps

Direct observation

Direct loservation

This step is similar to Step Al(b) (see Footnote a) in thatthe production rules to beapplied will vary from subjectto subject, depending both oneach individual's existingknowledge and beliefs, and

_ .on each individual's interpre-tations of steps Al to Ad.

32

COGNITTIVI

Ap continued)

DESIGN

Strategy B Outline of strategy to be used for responses to the qualitative problem of the form "speedof bulletvery much greater than speed of gun and in opposite direction- (i.e., correct answer toquestions asked).

Steps in the Strategy Purpose of Steps Commentary on Steps

51 Ask student if they can To establish that the ratiobe more precise about of speeds is the inverse ratiothe relative values of the of the weights/masses in-bullet and gun speeds. volved, If this is not forth-

coming, go to strategy A.beginning at A4. If some suchstatement is produced, go to62.

62 Repeat subsidiary ques-tions (i) and (ii) from thequalitative problem.

Collins (1977) Rule 4: Askfor prior factors.

To elicit a statement of See commentary on Step A.Newton's Third Law and tohave the student authwita-tively link this law to thegun/bullet phenomenon.

b

Numbers of other rules (e4., Rules 3.11) may be applied in the exploration of individual re-sponses. For example, it may be necessary to ask -Could the cannon ball be fired from thepistol?" (Rule 6: Pick a counter example for an insufficient factor.)

Previous experience suggests that a physical mark (e.g., a chalk line) needs to be made to indicatethe position of cans before the explosion so that a reference is available for consideringpost-explosion effects.

If friction effects provide an interfering concept, further by using an air track far explosionsand then returning to trolleys.