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Cognitive research and the design of instruction

Educational Psychologist

March 1982
17(1):31-53

DOI:10.1080/00461528209529242

Authors:

Leopold E. Klopfer

University of Pittsburgh

Richard Gunstone

Monash University (Australia)

The utilization of cognitive psychological theory and findings from research to inform the design of instruction is illustrated in this paper. Physics learning studies demonstrate that students' pre‐instructional world knowledge is often logically antagonistic to the principles of Newtonian mechanics taught in introductory physics. Under these conditions psychological theory predicts that learning will be inhibited, a prediction consistent with both the experiences of physics teachers and the results of empirical investigation. Informed by cognitive research on problem solving, semantic memory, and knowledge acquisition, instruction has been designed to encourage the reconciliation of world knowledge and physics content among beginning physics students.

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Cognitive research and the design of science instruction

Audrey B. Champagne

, Leopold E. Klopfer

& Richard F. Gunstone

Learning Research and Development Center , University of Pittsburgh , 3939 O'Hara Street,

Pittsburgh, PA, 15260

Learning Research and Development Center , University of Pittsburgh ,

Monash University , Melbourne, Australia

Published online: 01 Oct 2009.

To cite this article: Audrey B. Champagne , Leopold E. Klopfer & Richard F. Gunstone (1982) Cognitive research and the design

of science instruction, Educational Psychologist, 17:1, 31-53

To link to this article: http://dx.doi.org/10.1080/00461528209529242

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Educational Psychologist

1982,

Vol. 17, No. 1, 31—53

Cognitive Research and the Design

of Science Instruction

Audrey B. Champagne and Leopold E. Klopfer

Learning Research and Development Center

University of Pittsburgh

Richard F. Gunstone

Monash University

Melbourne, Australia

The utilization of cognitive psychological theory and findings from

research to inform the design of instruction is illustrated in this paper.

Physics learning studies demonstrate that students' pre-instructional world

knowledge is often logically antagonistic to the principles of Newtonian

mechanics taught in introductory physics. Under these conditions

psychological theory predicts that learning will be inhibited, a prediction

consistent with both the experiences of physics teachers and the results of

empirical investigation. Informed by cognitive research on problem solv-

ing, semantic memory, and knowledge acquisition, instruction has been

designed to encourage the reconciliation of world knowledge and physics

content among beginning physics students.

Most science textbooks can be criticized by drawing

attention to the fact. . . .that these books are

chiefly concerned with the statements of results.

Usually the most general results are put near the

beginning of the textbook. A textbook in physics

begins by telling about molecules and the constitu-

tion of matter or by giving some of the most com-

pactly formulated statements about the principles

öf mechanics .... The degree of enthusiasm of

the ordinary student for these introductions which

he gets in the textbooks is very slight indeed ....

The student, confronted by these verbal additions

to his experience, gets into the habit of thinking of

science as verbal additions to experience, and he

faithfully learns the words and keeps them in store

against the time when the teacher demands them.

(Judd, 1915, pp. 334-336)

Introduction

One recent trend in cognitive psychology

has increasingly focused the attention of

researchers on learning tasks representative of

those which students encounter in school in-

struction (Greeno, 1980). Developments such

as this hold the promise of an improved

theoretical basis for instruction. A theoretically

organized and systematically verified

psychological foundation is an essential

The address of Audrey B. Champagne is Learning

Research and Development Center; University of Pitts-

burgh; 3939 O'Hara Street; Pittsburgh, PA 15260.

requisite for effecting substantial im-

provements in instruction. However, the ex-

istence of such theory offers no guarantee that

instruction systematically and veridically incor-

porating principles derived from the theory

will be designed. A necessary condition for the

systematic application of theory to instruc-

tional practice is a science of design as

". . .a body of intellectually tough, analytic,

partly formalizable, partly empirical, technical

doctrine about the design process (Simon,

1981,

p. 132)." Only when a science of in-

structional design exists will the design process

cease to hide behind the cloak of "judgment"

or "experience."

This article is motivated by the need to

make explicit the design process as it applies to

the design of instruction, explicit description

of the process being a necessary first step in the

development of a science of instructional

design. We describe how we have applied the

theory and empirical findings of cognitive

psychology to devise a course of action aimed

at changing an existing situation into a desired

one (Simon, 1981, p. 129). Specifically, the

course of action is the instruction, the existing

situation is the cognitive state of the

uninstructed student, and the desired situa-

tion is a student's cognitive state that approx-

imates specified features characteristic of the

cognitive state of an expert in the field (the

ideal state).

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AUDREY B. CHAMPAGNE, LEOPOLD E. KLOPFER AND RICHARD F. GUNSTONE

The design process to be explicated in this

article represents an alternative approach to

the design of instruction. Central to this pro-

cess is the analysis of customary instructional

tasks for the purpose of specifying the underly-

ing cognitive processes and structures that are

necessary for the successful completion of the

task. The specification of these processes and

structures for a variety of school subject-matter

domains represents an important part of the

recent empirical findings of cognitive science

research. Thus, if detailed process and struc-

ture descriptions appear to be helpful in

designing instruction in physics (as we intend

to demonstrate), they should also be helpful in

designing instruction in other domains.

We begin by describing the practical

relevance of the instructional problem that in-

terests us, namely, student difficulties in the

learning of classical Newtonian mechanics.

The Instructional Problem

There is a general agreement among physics

instructors and students that mechanics is dif-

ficult to teach and to learn (Kolody, 1977).

Students have difficulty comprehending

classical mechanics, and physics instructors

often express disappointment with the out-

come of their efforts to instruct students in

classical mechanics. This instructional problem

has been discussed at length in the literature of

physics education where various underlying

causal factors contributing to the problem have

been suggested (Gerson & Primrose, 1977;

Halley & Eaton, 1974; Hudson & Mclntire,

1977).

Two distinct perspectives on this learn-

ing problem are identifiable.

One perspective assumes that learning dif-

ficulties occur when the learner is deficient in

skills which are assumed to be prerequisite to

the study of physics (e.g., Arons, 1976;

Renner, Grant, & Sutherland, 1978). The

other perspective links the observed learning

difficulties with the fact that students coming

to introductory physics courses have firmly

embedded conceptualizations of how and why

objects move, and that these conceptualiza-

tions are in clear conflict with the canonical

view of that subject-matter domain which the

student will be required to learn. One line of

science education research and psychological

research on semantic memory is particularly

relevant to the second perspective.

Research Background

Pre-instructional Knowledge and Students '

Interpretation of Instruction

The research we examine furnishes a context

for describing the existing situation, the

uninstructed student's cognitive state, and

distinguishing it from the desired situation.

Various empirical studies conducted by science

educators (including Brumby, in press; Driver,

1973;

Driver & Easley, 1978; Fleshner, 1963;

Gunstone & White, 1981; Leboutet-Barrell,

1976;

Rowell & Dawson, 1977; Singer &

Benassi, 1981; Viennot, 1979) and

psychologists (including Clement, 1979;

Green, McCloskey & Caramazza, 1980;

Selman, Jaquette, Krupa, & Stone, in press)

demonstrate that, for several science content

areas:

Students have descriptive and ex-

planatory systems for scientific phenomena

that develop before they experience formal

study of the subject.

These descriptive and explanatory

systems differ in significant ways from those

the students are expected to learn as the

result of formal study.

These alternative conceptual systems

show remarkable consistency across diverse

populations.

These alternative conceptual systems are

remarkably resistant to change by exposure

to traditional instructional methods.

These alternative conceptual systems are

not facilitative to the learning process.

Students interpret instructional events (for

example, experiments and expository text)

in the context of the conceptual scheme

they currently hold, not the one that the ex-

periments or the text are designed to

convey.

These effects are particularly striking in the

context of mechanics where prior to formal

instruction young people and adults have a

conception of motion that is more

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COGNITIVE RESEARCH AND INSTRUCTIONAL DESIGN

Aristotelian' than Newtonian (Champagne,

Klopfer, Solomon, & Cahn, 1980; Clement,

1979;

Driver, 1973; Driver & Easley, 1978;

Leboutet- Barrell, 1976; Singer & Benassi,

1981;

Viennot, 1980). Other research findings

show that remnants of the Aristotelian concep-

tion persist with many "successful" physics

students, that is, with students receiving high

grades in introductory physics courses (Cham-

pagne, Klopfer & Anderson, 1980; Gunstone

& White, 1981). This research provides em-

pirical support for what physics teachers have

long observed, namely, that traditional in-

struction does not facilitate an appropriate

reconciliation of preinstructional knowledge

with the content of instruction. (Ausubel,

Novak, & Hanesian, 1978).

A study by Leboutet-Barrell (1976) indicates

that high school and college students have

misconceptions about force and motion which

persist despite instruction. The misconceptions

are described as pre-Galilean. In a study by

Cole and Raven (1969) with 12 to 15 year-olds,

it was necessary to give the students "oppor-

tunities to reject irrelevant factors in

understanding the principle of flotation."

Rowell and Dawson (1977) also explicitly con-

sidered common misconceptions when design-

ing instruction on the law of floating. Despite

efforts to refute misconceptions in instruction,

some misconceptions persisted. Instructional

work by Fleshner (1963) in the Soviet Union

indicates that students' intuitive ideas may co-

exist with ideas derived from instruction. In a

study by Driver (1973), 11 and 12 year-old

students were interviewed prior to, during,

and after instruction on several topics of a

physical science course. Although alternative

theoretical frameworks to explain observations

were introduced to the students and used dur-

ing the instruction, Driver reports that

counter-examples and conflicting evidence did

not produce changes in students' thinking.

Our own work (Champagne, Klopfer, &

Anderson, 1980; Champagne, Klopfer,

Solomon, & Cahn, 1980) has demonstrated

that prior knowledge affects students' com-

prehension of science instruction. We have

been particularly interested in the difficulty

that beginning physics students have in learn-

ing classical mechanics. Our research has

demonstrated that it is not the students' lack

of prior knowledge which makes the learning

of this topic so difficult, rather their con-

flicting knowledge. They come to instruction

with well-formed notions about the motion of

objects — notions that have been reinforced by

their experiences. However, their notions may

stand in contradiction to the tenets of classical

physics, and these notions tend to interfere

with or inhibit the learning of mechanics. This

research demonstrates specific ways in which

students' conceptions influence (a) their

understanding of science texts and lectures, (b)

their observations, and (c) their interpretations

of their observations. Often the influence of

the students' conceptions is to inhibit their

understanding or distort their observations and

interpretations of experiments.

Other research (Champagne, Klopfer, &

Anderson, 1980) demonstrates that the belief

in the proposition, heavier objects fall faster

than lighter objects, is not readily changed by

instruction, thus demonstrating the strong in-

fluence that prior knowledge has on the effec-

tiveness of instruction — in this case the prior

knowledge having an inhibiting effect on lear-

ning. In a study of beginning college physics

students, about four students in five believed

that, all other things being equal, heavier ob-

jects fall faster than lighter ones. These results

were particularly surprising since about 70% of

the students in the sample had studied high

school physics, some for two years. A chi-

square test showed that students in the sample

who had studied high school physics did not

score significantly better than those who had

not. This finding has been replicated in

follow-up studies.

In a report of a similar study of the

knowledge of gravity possessed by beginning

first-year physics students at Monash Universi-

ty, all of whom had successfully completed two

years of high school physics, Gunstone &

White (1981) conclude: (a) "... students

know a lot of physics but do not relate it to the

everyday world;" and (b) "In many instances

the students used mathematical equations to

Aristotle considered rest to be the natural state of ob-

jects.

In the absence of any cause, an object does not move;

conversely, when an object is moving, it must have been

caused, usually by a force. Aristotle also argued that the

speed of an object is directly proportional to the force ac-

ting on it, and inversely proportional to the resistance of

the medium through which the object is moving. In the

Newtonian physics of today, it is stated that an object will

continue in its existing state (cither at rest or moving with

constant speed in a straight line) unless it is acted on by a

net force. The acceleration of the object is directly propor-

tional to this net force and inversely proportional to the

mass of the object.

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34 AUDREY B. CHAMPAGNE, LEOPOLD E. KLOPFER AND RICHARD F. GUNSTONE

explain predictions, though often inap-

propriately, which indicates that they had lots

of physics knowledge to hand [sic] but were

unskilled in seeing which bit applied to the

given situation (p. 299)." In their conclusions,

Gunstone and White note that "... much

more attention may have to be given to in-

tegrating the knowledge acquired in school to

general knowledge (p. 298)."

The difficulty is compounded by the fact

that many of the terms used in classical

mechanics are also used in everyday life —

terms such as acceleration, momentum, speed,

and force. The meanings of these terms as used

by physicists are quite different from the way

in which they are used in everyday life. Thus,

we observe that students misinterpret

mechanics instruction because they interpret

physics lectures and textbooks in the context of

their everyday understanding of the terms

rather than in the way in which the teacher or

text is using the terms.

Theoretical analysis. These descriptions of

the interactive effects of knowledge on

understanding are consistent with findings

emerging from cognitive psychology that

demonstrates the impact of existing knowledge

in memory on the comprehension of text

(Anderson, Reynolds, Schauert, & Goetz,

1977;

Bransford & McCarrell, 1974; Lindsay &

Norman, 1972). This research demonstrates

that all incoming stimuli which are

remembered are subject to reorganization by

the learner. The incoming stimuli are primar-

ily restructured by the learner in terms of the

learner's own past experiences, and only secon-

darily in terms of the organizing principles of

the material

itself.

In instructional situations

generally, students engage in active, mean-

ingful'structuring of text they read and lectures

they hear in order to remember and under-

stand incoming information.

Cognitive psychologists have studied ways in

which prior semantic knowledge influences

comprehension of verbal materials. The early

studies in the area of reading comprehension

aimed at demonstrating that something other

than the linguistic structure of a sentence is re-

quired to explain a person's comprehension of

that sentence. The "something other" is

described as the person's world knowledge and

is often characterized as a "schema," "plan,"

or "script." Bransford and McCarrell (1974)

review studies which indicate that the process

of understanding text involves creation of

"semantic descriptions" that use both the

reader's world knowledge and the sentence in-

put. In this research, the contexts for inter-

pretation of text either were common world

knowledge or were induced by the experi-

menter. Anderson et al. (1977) indicate that

an individual's "private" representation of

the world can affect text comprehension. In

general, studies of text comprehension

indicate the facilitative effect of schemata or

world knowledge. However, studies of physics

learning indicate that world knowledge is

logically antagonistic to the content to be

learned and often persists after physics

instruction.

Cognitive Contents of Uninstructured

Physics Students' Cognitive State.

From our analysis of empirical studies in-

vestigating students' preinstructional concep-

tions of the motion of objects, we conclude

that the following are characteristic of the con-

tents of the cognitive state of uninstructed

physics students:

Concepts are poorly differentiated. For

example, students use the terms speed,

velocity, and acceleration interchangeably;

thus,

the typical student does not perceive

any difference between two propositions

such as these — (a) the speed of an object is

proportional to the [net] force on the ob-

ject; (b) The acceleration of an object is pro-

portional to the [net] force on the object.

Meanings physicists attribute to terms

are different from the everyday meanings

attributed to the terms.

Propositions are imprecise and the im-

precision derives from several different

sources.

(a) Some of the imprecision of proposi-

tions is attributable to the meanings

students have for technical concepts

which are different from the canonical

meaning. Example: More force means

more speed.

(b) Other imprecision can be interpreted

as errors of scale (Gunstone & White,

1981).

Example: Gravity pulls harder on

objects that are closer to the earth. (This

proposition, in the context of an object

falling a distance of three meters, is cor-

rect only in theory because the difference

in the force of gravity (approximately

1 part in lO"'-

) is too small to measure.

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COGNITIVE RESEARCH AND INSTRUCTIONAL DESIGN

If, however, the difference in distance

from the earth were large (several hun-

dred kilometers), the difference in the

force of gravity is significant.)

may arise because of students' attempts

to inappropriately formulate general

rules of motion from their experiences in

the real world. Example: Heavy objects

fall faster than lighter objects.

Implications for instruction. Research

reviewed in this section demonstrates that the

cognitive contents of the uninstructed student

differs from the desired state with respect to

propositions and the meaning of concepts.

Uninstructed students apply propositions that

link force with motion, whereas Newtonian

mechanics links force with change in motion.

Moreover, the meaning uninstructed students

attribute to technical terminology is different

from the technical meaning. For example, the

technical meaning of acceleration is a change

in the magnitude of velocity or direction of

velocity of an object, while the meaning

uninstructed students attribute to acceleration

is speeding up.

Application of the Simon paradigm to the

design process requires detailed specification

of the meaning concepts have for the

uninstructed person and the principles that

uninstructed persons apply in the analysis of

motion. Such specifications are prerequisite to

the process of specifying the goals of instruc-

tion, and they allow for (a) the generation of

hypotheses about why certain instructional

practices are not successful, and (b) the con-

struction of possible mechanisms that will

result in the desired changes in the learners'

cognitive state.

Differences like those described above bet-

ween the uninstructed learners' cognitive state

and the desired cognitive state provide dear

specifications of changes instruction should

produce. The instructional goal, then, is to

bring about the specified changes in the

learners' cognitive state. We hypothesize that

the observed differences between the

uninstructed and desired cognitive states result

in 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 in-

teractive effects of prior knowledge and in-

struction may be more pronounced for

mechanics than for other subjects.

The development of practical principles of

motion is necessary for coping with the moving

objects that are encountered in daily life.

Thus,

all students begin the formal study of

mechanics with an experientially verified set of

principles that allow them to predict the mo-

tion of objects under the conditions prevalent

in the real world. In addition, the same words

that arc used to describe and explain motion in

everyday language also are used by physicists.

Contrast this situation with thermodynamics

or chemistry where the words used for

technical concepts are not a part of everyday

language (mole, enthalpy, entropy) and where

principles need not be developed to cope with

frequently encountered situations. In these

and similar subject areas, traditional expository

instruction is more successful. However, in

mechanics, instructional strategies need to be

applied that can make students aware of dif-

ferences between their everyday meanings of

words and principles of motion and those of

the instruction.

Before presenting detailed hypotheses

related to strategies which will produce the

desired changes in the cognitive contents of

uninstructed students, other relevant

characteristics of the learners' cognitive state

will be described.

Structural and Representational Features

Physics

Knowledge and Physics

Problem Solving Strategies

The preceding analysis focused on the con-

tents of memory — propositions and meaning

of concepts — and hypothesized how students

interpretation of instruction — understanding

of lectures, text and experiments — is in-

fluenced by significant differences between the

subject matter to be learned and the students'

cognitive contents. This section focuses on the

organization of the contents of memory: its

structural features and modes of representa-

tion; the differences between the structural

organization and representations of expert

physicists, novices and uninstructed physics

students; and the implications of these dif-

ferences for physics instruction.

Descriptions of the structural features and

representations of physics knowledge derive

principally from research on physics problem

solving. Researchers in the domain of problem

solving are concerned with both the strategies

and structures that problem solvers are

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AUDREY B. CHAMPAGNE, LEOPOLD E. KLOPFER AND RICHARD F. GUNSTONE

observed to apply in the successful solution of

problems (e.g., Greeno, 1978; Newell &

Simon, 1972). We shall review, in turn, the

pertinent research findings on structural

organization and problem solving strategies.

Structural organization and representation.

Research on physics problem solving provides

descriptions of the structural organizations and

representations characteristic of expert and

novice problem solvers. The solution of physics

problems requires both the availability of pro-

blem solving strategies and the understanding

of physical situations which are observed

directly or described in the text of the pro-

blem. Current theories of semantic memory

and natural language understanding (Ander-

son, 1976; Anderson et al., 1977; Bransford &

McCàrrell, 1975; Kintsch, 1974; Lindsay &

Norman, 1972; Norman & Rumelhart, 1975;

Quillian, 1968; Schank, 1972; Winograd,

1972) tie the existence of relevant schemata to

the process of making inferences and coming

to understand a situation.

In the context of physics, understanding im-

plies (a) the construction of mental representa-

tions of physical situations that include the ob-

jects that are a part of the physical situation,

(b) the concepts and scientific principles that

are relevant to the situation, and (c) the rela-

tionships that exist between objects, concepts

and principles (Winograd, 1972). Essential to

the construction of a mental representation is

the process of inference. Making valid in-

ferences is dependent on schemata that are

relevant, correct and complete. Thus,

understanding physical situations as physicists

understand them requires both that the rele-

vant schema is present and that the features of

the physical situation evoke the schema.

Recent work by Chi, Feltovich, and Glaser

(1981) describes the following explicit dif-

ferences in schemata of experts and novices: (a)

The schemata of experts are based on physical

principles (for example, energy conservation

and Newton's Second Law), but the schemata

of 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 experts

and novices do not differ significantly in infor-

mation content; however, the novices' struc-

tures lack important relations, specifically rela-

tions between the surface features of the pro-

blem and the scientific principles which are the

basis for solutions, (c) Experts translate

surface features of the problems into canonical

objects, states, and constructs, while the

novices represent the problem in terms of the

literal objects and constructs described in the

text of the problem, (d) Links exist in the ex-

perts'

representations of knowledge structures

between the abstract representation of features

of the problems and the physical principles

which are the basis for the solution of the pro-

blem, (e) Experts' schema are organized

hierarchically along the dimension of abstract-

ness;

in contrast, the different levels of the

novices' knowledge are not well integrated,

thus preventing easy access from one level of

abstraction to another.

Research conducted by science educators pro-

vides descriptions of the organization and rep-

resentations of mechanics knowledge (motion-

of-objects schemata) in uninstructed students.

Motion-of-objects schemata of uninstructed

students are situation-specific, thus suggesting

that no naive abstract representation is extant in

die schemata to make them appear to be ap-

plicable to a large number of physical situations

(Gunstone, 1980).

This last characteristic was exemplified in

our work with middle-school students (Cham-

pagne, Klopfer, Soloman, & Cahn, 1980). We

have observed that, given four physical situa-

tions,

all of which could be explained by using

Newton's Second Law (F= ma), students never

give any indication that they perceive that a

common explanatory system might be applied

to all four of the situations. In fact, they never

notice that a proposition they have used to ex-

plain the motion in one of the situations is

directly contradicted by a proposition they use

to explain the motion in another situation.

This failure to see the contradiction suggests

that they are unaware of any need for con-

sistency across situations. For example,

students do not recognize that the same

physical laws apply to objects in free fall and to

objects sliding down an inclined plane. At one

point during a class discussion, for example,

students agreed that two carts of unequal

mass,

but equal volume, would strike the

ground at approximately the same time when

dropped from the same height. When they

were asked to compare the times for the carts

to slide down an incline, however, only one of

them argued that the times would be about

the same.

Problem solving strategies of experts and

novices. Cognitive research on problem solv-

ing has generated detailed specifications of

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COGNITIVE RESEARCH AND INSTRUCTIONAL DESIGN

problem solving strategies for many categories of

problems (Greeno, 1978; Newell & Simon,

1972;

Larkin, Note 1). One finding from this

research that is particularly pertinent to the in-

struction we propose is reported by Larkin. Her

analyses of thinking-aloud protocols indicate that

expert physicists perform a preliminary

qualitative analysis before proposing equations

for the quantitative solution of the problem. In

contrast, novices immediately begin the search

for an equation and proceed to match the

information presented in the problem with terms

in the equation.

Given that the beginning students' ex-

planatory schemata are so situation-specific, it is

hardly surprising that their problem solving

strategy is similarly bound to the perceived situa-

tions.

The students' main strategy for solving

motion-of-objects problems is to try to recall a

rule or relationship which they believe to be ap-

plicable to the specific situation at hand. Rarely,

if ever, is there any evidence that the beginning

students are aware of general problem solving

strategies, related to general physical principles or

laws,

which are applicable across many situations.

Differences in Structure and their

Instructional Implications

Empirically-derived descriptions of the

characteristics of the schemata of uninstructed

students, novices, and experts are summarized in

Table 1. This summary makes evident the con-

trasts and similarities in the characteristics of the

three groups' schemata with respect to principles,

surface features, and second-order features, each

of which is briefly explained in the first column.

Also summarized in Table 1 are descriptions of

the problem solving strategies for each group.

Precise descriptions of the differences in the

organization and representation of the physics

knowledge of individuals at different levels

of competence provide a further basis for the

specification of the goal and objectives for begin-

ning mechanics instruction and allow us to

generate hypotheses about (a) how current in-

strucrional practice may impede the attainment

of the goal and (b) alternative instructional

mechanisms that will facilitate the attainment of

the objectives.

Contrasting the problem solving strategies and

organization of the mechanics knowledge of ex-

perts,

novices and uninstructed students

yields the following goal for beginning

mechanics instruction: Development of a well in-

tegrated motion-of-objects schema that is

organized in a way that produces (a) the solution

of mechanics problems via the method of

qualitative analysis and (b) the analysis of the

motion of objects in the real world using the

tenets of Newtonian mechanics. The detailed

specifications of the mechanics knowledge

organization to be accomplished as the result of

instruction constitute the instructional objectives

subsumed under the goal.

Empirical evidence demonstrates that current

instructional practice does not facilitate the at-

tainment of identified goal. Students generally

do not learn to relate their mechanics knowledge

to real situations as the result of either high

school or beginning college physics instruction.

Based on a cursory analysis of physics texts and

our knowledge of physics instruction, we con-

clude that preliminary qualitative analysis of

physics problems is seldom if ever taught ex-

plicitly. In fact, problem solving instruction in

physics textbooks makes no attempt to link the

physical features of the real-world situations

described in physics to the abstract concepts and

principles of the Newtonian framework.

Physics texts teach the problem solution

strategy that novices typically use. The first step

in sample solutions is the presentation of the

equation that will yield a quantitative solution to

the problem. There is no attempt to instruct the

student in the expert physicists' analytic pro-

cedures which result in abstract representations of

physical situations in terms of abstract concepts.

These concepts are vital because they in turn can

be linked to principles or laws of mechanics and

formal expressions of the principle or law (for-

mulas) which can then be applied to reach a

quantitative solution of the problem.

The traditional practice is counterproductive

in two respects: (a) It teaches a problem solution

strategy that does not approximate the strategy

exemplified by the ideal state, and (b) It does not

encourage the development of links in cognitive

structure between real-world situations and the

abstract representations of physical situations that

characterize the to-be-approximated schemata.

Experiences contributing to the expert's

cognitive state. An interesting theoretical ques-

tion, with implications for both practice and

theory, should now be posed: In the absence of

direct instruction, how do experts come to

develop the qualitative analysis strategy and the

conceptual links between physical situations and

the appropriate abstract representations?

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Table 1

Problem Solving Strategies and Schemata of Uninstructed Students, Novices, and Experts

PROBLEM SOLVING STRATEGIES

UNINSTRUCTED

STUDENTS

NOVICES

EXPERTS

The typical procedure for solving problems is to find a general rule which appears to cover the physical situation de-

scribed 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 recalled from experiences with similar physical situations,

or they may be recollections of authoritative statements from books or people.

The principal procedure for solving problems is to instantiate variables in equations. This procedure may be chained

through a series of equations. Abstracted solution methods are lacking.

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

methods. Experts abstract a basic solution strategy from the surface features of the problem and engage in qualitative

analysis of the problem prior to determining a quantitative solution.

SCHEMATA

FEATURES OF

SCHEMATA

CHARACTERISTICS OF

UNINSTRUCTED STUDENTS'

SCHEMATA

CHARACTERISTICS OF

NOVICES' SCHEMATA

CHARACTERISTICS OF

EXPERTS' SCHEMATA

PRINCIPLES

Ideas of some degree of general-

ity that express relationships;

principles are applied to solving

problems; can serve to organize

schemata.

Principles are generalized rules

derived from everyday exper-

iences (world knowledge). They

are imprecise propositions. The

imprecision is due to vagueness

about the meaning of concepts,

errors of scale, and inappropriate

formulations of general rules.

The principles (rules) have

limited scope and tend to be

situation-specific. The notion

that an abstract principle can

apply to a range of different

physical situations is lacking or

poorly developed. There appears

to be no awareness of the need

for consistency along the rules

that cover different physical

situations.

Principles are relationships

between physical variables ex-

pressed as equations or rules.

Some of the principles are the

major physical laws expressed in

equation form, but there is no

evidence that they serve as

organizers of schemata.

Principles are major physical

laws,

which are highly abstract

and express relationships of

great generality. Included with

each principle are the conditions

under which the principle ap-

plies.

Each principle has an

associated schema, which is

oriented by the content and ap-

plicability conditions of the

principle. The applicability con-

ditions usually are expressed in

terms of second-order features.

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OBJECTS AND PHYSICAL

CONDITIONS (SURFACE

FEATURES)

Physical objects and conditions

described or presented in a pro-

blem situation; physical features

of objects and their states of

motion or position that are

directly perceivable from verbal

description; diagrams or direct

observation of the physical

situation.

Concrete objects and the direct-

ly observable properties of ob-

jects are present. A reasonable

inference is that the objects and

properties define the specific

physical situation which, in

turn,

directs the search in memory for

a general rule that covers it.

Physical objects and their sur-

face features are the basis for

categorizing problems. It is infer-

red that an object or a config-

uration of objects functions as

the organizing element (node) in

its schema for the problem. The

content of the representations

may be concrete objects or ab-

stractions at the level of

diagrams.

Concrete objects, their physical

configurations, and diagrams of

objects are present in the

schemata, but none of these is

prominent. It is inferred that

objects serve primarily as

vehicles for identifying second-

order features, and that some-

times they trigger the activation

of a particular principle-based

schema.

PHYSICS CONCEPTS AND

SYMBOLS (SECOND-ORDER

FEATURES)

Idealizations of physical objects

(e.g.,

an elephant is represented

as a point mass), and constructs

or entities

(e.g.,

energy, force);

conventional representations of

physical entities

(e.g.,

vector

components).

There is no evidence that

second-order features are repre-

sented in these schemata. Con-

cepts and terms are present, but

many are poorly differentiated.

The meanings of the terms are

their real-world meanings, rather

than their technical meanings

in physics.

Some conventional representa-

tions of physical entities are

present, and idealizations of

physical objects may be used in

problem representations. Con-

cepts and terms related to the

objects which dominate the pro-

blem-solution schema are

present. Novices report taking

terms directly from the problem

statement to identify equations

that could be approximately em-

ployed in solving the problem.

Representations of physical

objects in their idealized form

are prominent, with the content

of the representations deter-

mined by the organizing schema.

Physical entities are represented

according to the conventions of

the

field.

Features abstracted

from the problem statement are

also present. Some experts

report that these features help to

select the basic approach to pro-

blem solutions, thus indicating

direct links between these

second order features and

prin-

ciples. Concepts relevant to the

organizing schema are present.

Associated with each concept

are its interconnections of

relations with other concepts

and with the schema's major

physical law.

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AUDREY B. CHAMPAGNE, LEOPOLD E. KLOPFER AND RICHARD F. GUNSTONE

For the purpose of our discussion, we con-

sider three factors that differentiate the ex-

periences of experts from the experiences of

novices; these are: (a) additional formal in-

struction, (b) more extensive practice in solv-

ing problems, and (c) more extensive verbal in-

teractions about physics. The Chi et al. (1981)

study suggests that the contents of novices'

data structures for particular types of physics

problems are similar to those of experts with

respect to objects, concepts, and terms;

however, experts' data structures contain many

more linkages. The more extensive data base,

which experts acquire as a result of their

greater exposure to formal instruction, is not

necessary for the successful solution of prob-

blems of the type on which the analysis of

expert-novice differences is based. However,

the additional links in experts' knowledge

structures are necessary for the successful and

efficient solution of mechanics problems.

We hypothesize that these links develop as a

result of extensive practice in problem solving

and that their development is facilitated by

verbal interactions. The professional activities

of physics experts require either verbal interac-

tions with others or the organization of physics

information for the purpose of communicating

it to others. We hypothesize that this type of

experience is important to schema change

because the individual must make explicit the

meaning attributed to technical terminology

and the rules for applications of proposition

and principles.

This analysis leads us to hypothesize that

providing beginning students with oppor-

tunities to engage in the quantitative analysis

of physics problems will facilitate the develop-

ment of physics knowledge organized in ways

that approximate that of the organization of a

physics expert. Our selection of this instruc-

tional strategy to attain this goal is based on

the recognition that: (a) The cognitive objec-

tives of beginning mechanics instruction

should approximate the skills and knowledge

applied by experts in the solution of mechanics

problems; (b) Explicit instruction in the

knowledge and skills required for successful

novice performance is not now a part of physics

instruction; and (c) Part of such instruction

must focus on producing a schema change in

students which results in the incorporation and

integration of mechanics principles and inter-

pretations of real-world phenomena.

We hypothesize that providing learners with

opportunities for verbal interactions will

facilitate the development of correct usage of

technical vocabulary and help students become

aware of the principles they apply in the

analysis of physical situations and how their

principles are different from those being

taught. This hypothesis is consistent with

cognitive theory of schema change.

Schema change theory. The processes by

which existing schemata are modified are just

beginning to be understood (Greeno, 1980).

Information processing models of schema

development generally have not gone beyond

the level of describing stages. Nonetheless,

several valuable ideas concerning the develop-

ment of schemata and suggestions for modify-

ing schemata have been offered.

Two principal mechanisms for schema

modification have been discussed by

Rumelhart and Ortony (1977). Each

mechanism is, in a sense, the antithesis of the

other. Specialization occurs in a schema when

one or more of its variables are fixed to form a

less abstract schema. Conversely, generaliza-

tion occurs in a schema when some fixed por-

tion is replaced by a variable to form a more

abstract schema. The generalization

mechanism can be applied in a

motion-of-

objects schema.

The typical uninstructed student has the

motion schema: A push produces motion. As a

result of appropriate instructional experiences,

the student's motion schema could become: A

force produces acceleration. The fixed portion,

push,

in the initial schema has been replaced

by a more general variable, force, which can

take on several values in addition to push.

Similarly, the general variable, acceleration,

which can have different values, has replaced

the initial schema's fixed portion, motion. The

modified schema is considerably more abstract

and, hence, should have a much broader range

of applicability.

The hypothesized generalization mecha-

nism only describes the changes and is, in fact,

not a mechanism for producing them. If, as

Rumelhart and Ortony (1977) imply, the gen-

eralization mechanism is a mechanism for pro-

ducing change, a reasonable implication is that

the modification of the motion-of-objects

schema might be accomplished quite simply

by describing to students the needed modifica-

tions in definitions of terms and restating sim-

ple propositions. Empirical evidence on

• mechanics learning demonstrates that this in-

structional strategy is not generally effective

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COGNITIVE RESEARCH AND INSTRUCTIONAL DESIGN

and suggests that, while the gradual modifica-

tion of schemata doubtlessly involves general-

ization and specialization, in highly integrated

schemata more dramatic changes, amounting

essentially to a shift to a new paradigm (in

Kuhn's [1962] sense), must also take place.

To bring about schema change on such a

large scale, a dialectical process appears to be

necessary. Riegel (1973) points out that the

thinking of both adults and children is dialec-

tical, and he proposes that dialectics is "the

transformational key" in cognitive develop-

ment. Anderson (1977) suggests that "...

the likelihood of schema change is maximized

when a person recognizes a difficulty in his

current position and comes to see that the dif-

ficulty can be handled within a different

schema (p. 427)."

As the mechanism for promoting dialectics

in the classroom, Anderson advocates the use

of a Socratic teaching method. By participating

in the dialogues which occur in Socratic

teaching, the student is forced to deal with

counterexamples to proposals and to face con-

tradictions in his or her ideas. To overcome the

attacks of adversaries in the dialogues, the stu-

dent must construct a new framework of ideas

that will stand up to criticism. The newly con-

structed framework is, of course, a new

schema, so it may be said that schema change

has occurred as a result of the student's par-

ticipation in the dialogues.

Instructional Issues

Specification of Instructional

Objectives and Strategies on the

Basis of Cognitive Analysis

Table 2 summarizes instructional objectives

and strategies for mechanics instruction deriv-

ed from the analysis of the cognitive states of

uninstructed students, novices, and experts,

groups who differ with respect to (a) the quan-

tity and extent of formal mechanics instruc-

tion, (b) experience in solving mechanics pro-

blems, and (c) the extent of their verbal in-

teractions about mechanics.

Objectives. The objectives presented in

Table 2 are based on the analysis of contrasting

cognitive states and represent the first in a

series of steps in the detailed specification

of instructional objectives. These objectives

specify features of the ideal state which the

learner will approximate but do not detail how

far the learner will move along the continuum

from beginning student to expert as the result

of a particular course or sequence of instruc-

tion. Further refinement of the objectives for a

certain instructional sequence must take into

account many other factors, including the con-

tent the instruction will cover, the time avail-

able for instruction, and the age and academic

aptitude of the students for whom the instruc-

tion is intended. However, the analysis here il-

lustrates one important principle employed in

the cognitive approach to design. That princi-

ple is the comparison of the cognitive states of

individuals at different levels of competence

(Greeno, 1976). Furthermore, the design re-

quires that the initial specification of objec-

tives be based on the cognitive features that

distinguish the learner for whom the instruc-

tion is designed from individuals competent in

the field.

An observation worthy of comment is the

difference between these objectives based on

cognitive analysis and objectives that derive

from the logical analysis of the subject matter

or from the identification of to-be-learned

behaviors. Objectives derived from these two

processes are deficient in at least two respects.

First, cognitive analysis identifies significant

objectives not identified by either analysis of

behaviors or logical analysis. Second, logical

analysis does not identify the structural

organization of knowledge which the instruc-

tion should produce. For example, logical

analysis would not identify qualitative analysis

of physics problems as an objective of instruc-

tion, nor would it produce information about

the optimal structural organization of

mechanics knowledge for competent problem

solving.

Instructional

strategies.

The first approxima-

tion of instructional objectives derives from the

comparison of the cognitive states of unin-

structed students and experts. Possible instruc-

tional strategies for the attainment of the

objectives derive from comparisons of the cogni-

tive states of uninstructed students, novices,

and experts, and from examinations of the

mechanics-relevant experiences of novices and

experts. Having specified the differences in

cognitive states and relevant experiences we can

generate hypotheses for explaining the observed

differences in cognitive states on the basis of dif-

ferences in experiences. These hypotheses, in

turn suggest possible instructional strategies.

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Table 2

Contrasting Features in Cognitive States and Their Related Instructional Objectives and Strategies

Contrasting Features in Cognitive

States of Uninstructed Students (U),

Novices (N), and Experts (E)

Instructional Objectives

Derived from the Contrasts

Instructional Strategies

to Facilitate Attainment of

Instructional Objectives

CONCEPT MEANING

Meanings attributed to technical terms by

U differ in significant ways from the

meanings of E and N.

Example: U - acceleration means speeding

up;

E and N - acceleration means a change

in the magnitude or direction of velocity.

Students know both the everyday meaning

and the canonical definition of mechanics

and can specify differences between the

everyday and canonical meanings.

Interactive dialogue: Provides students with

opportunities to become aware of the

meanings they attribute to physical con-

cepts,

how these meanings differ from con-

text to context.

Examples: (1) doing physics problems or

describing a physical event to a friend,

or (2) doing mechanics problems in which

there is no motion.

Dialogue provides students with opportun-

ities to contrast their meanings of concepts

with those of the physicists.

CONCEPT DIFFERENTIATION

U do not differentiate mechanics concepts.

Example: U - weight and mass are the

same thing; N and E -

mass

and weight are

perfectly correlated but distinct.

In analyzing a given physical situation,

students can explain which of two poorly

differentiated concepts is the relevant

concept to apply.

Interactive dialogue: Provides students with

opportunities to verbalize their analysis of

physical situations in a way that simply sub-

stituting 9 g for mass (m) or 45 dynes for

weight (F) in an equation does not- We

hypothesize that the verbalization will help

differentiate weight (a force) expressed in

dynes from mass expressed in grams. [Also

see strategy on Structural Features row

below.]

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PROPOSITIONS IN SCHEMATA

U - presence in schema of incorrect pro-

positions.

Example: motion implies force.

N - presence in schema of conflicting pro-

positions which are applied in different

situations.

Example: Motion implies force pro-

position applied in the analysis of

rèal-

world situations. Change in motion

implies force proposition applied in the

quantitative solution of physics problems.

E - propositions present in schema are in-

ternally consistent and widely applicable.

Example: Change of motion implies force

proposition is applied in analyzing all

pertinent problems.

Students apply change in motion implies

force proposition in real-world situations.

Students contrast implications of the dif-

ference in the two relationships between

force and motion expressed by the proposi-

tions (1) Motion implies force, and (2)

Change in motion implies force.

Instructional dialogue to change contents

mechanics

schema:

Provides opportunity

for students to (1) be explicit about the pro-

positions they assume in invoking the pre-

sence of forces in physical situation (For

example, U generally invokes forces only in

situations where there is motion.) and (2)

make explicit the relationship between

motion and force in the propositions they

use.

!»

STRUCTURAL FEATURES

Concept integration of U and N is sparse,

with fewer links among concepts than for E.

Example: N - experientially derived

motion-of-objects schema is not inte-

grated,

or reconciled with Newtonian

mechanics schema.

Integration of representations in U and IM is

poor, while they are well-integrated in E.

Example: N • representations of surface

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 physical

constructs used in abstract representa-

tions;

E - representations of surface

features of physical situations are inte-

grated both with abstract representations

of physical situations and with proposi-

tions linking the canonical objects and

constructs of abstract representations.

Students qualitatively analyze mechanics

problems:

(1) Produce an abstract representation of a

physical situation.

(2) Recognize that situations with very dif-

ferent surface features can have the same

abstract representation. (For an example,

see Appendix A where the situations of 6

problems have the same abstract repre-

sentation.)

(3) Recognize that the problems can be

solved by the application of the same

mechanics principle.

Qualitative

,analysis

of problems to change

structural features of mechanics schema:

Forges links between the physical situation,

its abstract representation using canonical

objects and mechanics constructs, and the

principles (Newton's second law, F = ma)

which link properties of the canonical

objects and constructs. Also forges links

between concepts

(e.g.,

between mass and

weight) to integrate them better, thereby

contributing to concept differentiation.

Table 2 (continued on next page)

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Table 2 (continued)

PROBLEM SOLUTION STRATEGY

U solution strategy: search for a rule that

applies to the given situation.

Example: Problem of comparing speeds

of two falling objects evokes the rule •

Heavy objects fall faster than lighter

objects.

N solution strategy: search for an equation

E solution strategy: qualitative analysis

Students engage in qualitative analysis

of physics problems before attempting

quantitative solutions.

Interactive dialogue: Demonstrates that the

same abstract representations and diagrams

derive from problems with different surface

features. Also demonstrates the usefulness

of a general principle for solving a large

number of problems with different surface

features.

Qualitative analysis of

mechanics

problems:

Provides practice in using the desired

strategy.

5»

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COGNITIVE RESEARCH AND INSTRUCTIONAL DESIGN

The potential for effectiveness of alternative

instructional strategies is then evaluated in

terms of relevant psychological theory.

The availability of empirical descriptions of

differences between uninstructed students and

novices is particularly important to the process

of selecting instructional strategies. Information

about these differences leads to the identifica-

tion of instructional strategies which are effec-

tive and those which are not effective or

counterproductive. The observation that

novices' cognitive contents resemble those of ex-

perts is an indication that the didactic method

of instruction is effective for imparting discrete

bits of information. However, the detailed

analysis of problem-solving behaviors of novices

suggests that their structural organization of in-

formation resulting from exposure to didactic

instruction is less than satisfactory.

In the case of mechanics, this analysis also

reveals that the problem-solving strategy taught

in physics textbooks is indeed demonstrated by

novices, but, as we discussed earlier, this

strategy does not produce certain desired links

in cognitive structure, specifically those between

physical situations and mechanics concepts.

This lack of structural integration is also

evidenced by the fact that many novices con-

tinue to apply non-Newtonian principles when

asked to analyze real-world situations.

The analysis of novice-expert differences is a

useful source of possible alternative instruc-

tional strategies. For example, the proposed in-

fluence of problem-solving and verbal interac-

tion in the development of correct and well-

integrated cognitive structures are derived

directly from cognitive difference analysis. This

interpretation of the differences is consistent

with cognitive theory and with educational

practice and philosophy. The cognitive analysis

provides an explicit causal link between the

strategy and the outcomes, thus making possi-

ble more convincing empirical tests of the effec-

tiveness of the strategy. Our assertion — that

engaging in qualitative analysis of mechanics

problems will develop a better integration of

real-world situations and their abstract represen-

tation utilizing the concepts and symbols of

Newtonian physics — is empirically testable.

Procedural Description of the

Proposed Instruction

Although the strategy of using dialogues in

instruction has been specified in relation to the

attainment of instructional objectives (Table

2),

we have not yet described how this strategy

is implemented. Illustrative procedures which

employ the strategy are outlined in this sec-

tion. In one mode of the dialogues strategy,

students engage in interactive dialogues with

each other.

First the students are presented with a set of

mechanics problems which require qualitative

answers. A typical set of six such problems is

shown at the right side of Appendix A. These

problems are qualitative restatements of pro-

blems from five different physics textbooks.

The physical situations or surface features of

these problems (in both the qualitative and

quantitative versions) are very different, but all

problems can be represented in the same

abstract form (diagram or verbal description

using mechanics concepts) and can be solved

using the same mechanics principle. Each stu-

dent produces a solution to each of the pro-

blems and then shares with the class the pro-

blem analysis, the solution of the problem,

and definitions of technical terms used in the

solution or the analysis. This procedure forces

students to be explicit about the idiosyncratic

meanings attributed to technical terms and the

principles and propositions that they apply in

the analysis of the problem. Each student can

contrast his or her solution strategy for a pro-

blem with the strategies presented by other

students.

When all of the problems in the set have

been considered by the class, the teacher will

present the physicists' analysis of the problem

by means of diagrams and verbal explanations

using the technical vocabulary of mechanics.

The expert analysis is based on the common

deep structure of the six problems, as shown in

Appendix A. The teacher will demonstrate

mat the abstract representation is the same for

each of the problems and that the same princi-

ple will produce a solution to all the problems

in the set. Then students will analyze their

solutions to the problems in light of the

physicists' solution and will specify how their

interpretations differ from that of the

physicists.

The teacher's presentation of the physicists'

analysis and solution of qualitative problems is

in the mode of an instructional dialogue. In

order to explain and illustrate this mode of the

dialogues strategy, we have analyzed physics

problems from introductory texts in the man-

ner shown in Appendix B. The general struc-

ture of the analysis is simple. Initially the

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AUDREY B. CHAMPAGNE, LEOPOLD E. KLOPFER AND RICHARD F. GUNSTONE

textbook problem was rewritten as a

qualitative problem and subsidiary questions

were added asking about the assumptions and

physics principles used in obtaining the answer

to the problem. Then a realistic minimum

state in terms of relevant prior knowledge and

experience was selected, and a strategy for

working from that state to a successful solution

was worked out. At this stage, when we do not

have the insights to be derived from data, it is

assumed that other, more developed responses

can be accommodated by beginning at a later

point in this sample strategy.

The strategy has been outlined only. It in-

dicates a series of logical steps. Within each

step,

the essential concept(s) to be developed

and the purpose of the step in terms of the

problem solution are indicated. In some cases

a particular instructional methodology to be

used for 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 techniques

identified by Collins (1977) and Collins and

Stevens (1981) when appropriate. A strategy

for handling a correct answer to the questions

asked so as to develop a solution strategy for

the problem is also given.

Concluding Remarks

In this article we have recounted how our in-

terest in a particular instructional problem in

introductory physics, students' difficulty in

learning mechanics, provided the occasion for

utilizing Simon's characterization of a science

of design as a guide in proceeding to design an

instructional strategy that can be used to help

students learn mechanics effectively. We have

shown how the theory and empirical findings

of cognitive science and the cognitive psychol-

ogist's analytical tools and procedures were

brought to bear on every stage of the design

process. We have sought to make explicit the

particular principles of instructional design

which both evolved and were applied in the

course of the inquiry. We suspect that these in-

structional design principles may be applied in

various school subject-matter domains, though

only their application in physics was illustrated

here.

The instructional strategy for guiding

uninstructed physics students in their learning

of Newtonian mechanics is now available, but

our inquiry is not at an end. We are now

preparing to investigate empirically several

issues which were raised during the process of

designing the instructional strategy. The major

hypothesis to be tested in our proposed

research is that engaging uninstructed physics

students in instructional dialogues focused on

the qualitative analysis of mechanics problems

will produce changes in the students' motion-

of-objects schemata. A further hypothesis is

that, after completion of the specified instruc-

tion, the students' cognitive state will approx-

imate significant features which are

characteristic of the cognitive state of a physics

expert.

We can admire the great psychologists of

earlier days, such as Charles H. Judd, whom

we quoted at the start of the paper, for their

keen perspective on students' learning of

abstruse school subjects like physics. Judd's in-

sight (or perhaps, intuition) seems so right and

true that we cannot help being amazed. Also

amazing is the realization that the situation

which Judd described seven decades ago still

rings true for physics textbooks and physics

learning today. Hardly anything seems to have

changed in the interim. Why is this so?

The main reason, we believe, is that,

although Judd recognized the problem, he

could not prescribe an effective solution.

Because he was unable to describe the problem

precisely, Judd had no basis on which to

evaluate the probability of the effectiveness of

possible instructional strategies. Today the

status is different. Empirical and theoretical

research in cognitive psychology make possible

the construction of theoretical models, on

which predictions can be based. The applica-

tion of a model of understanding of physical

phenomena leads to detailed specification of a

strategy for beginning physics instruction

which can be expected to produce desired

changes in students. The difference between

our present possibilities and those of Judd's

day is demonstrated in this article.

Reference Notes

Larkin, J. H. Skill acquisition for solving physics pro-

blems. Paper presented at the meeting of the

Psychonomic Society, Phoenix, November 1979.

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Appendix A

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

QUANTITATIVE VERSION

QUALITATIVE VERSION

Boy and Wagon Problem

A boy of mass 20 kg is standing in a wagon of mass 10kg. The

boy jumps off to the right with a speed of 20 m/sc. What happens

to the wagon? (Ignore friction.)

(Hulsizer & Lazarus, 1972, p. 187)

Boy and Raft Problem

A 50 kilogram boy is standing on a 500 kilogram 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 3-g bullet is fired from a 2.4-kg rifle with a velocity of 360 m/s

north.

Find the momentum of the bullet and the recoil velocity

of the rifle, assuming that no other bodies are involved.

(Smith & Cooper, 1979, p. 93)

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 an 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)

A boy is standing in a wagon. The boy jumps off one end of 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

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

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

towards the shore. Describe the motion of the raft. How does the

speed and direction of motion of the raft compare with the speed

and direction of the boy?

A bullet is fired from a rifle. Describe the motion of the rifle.

How does the velocity of the rifle compare with the velocity of

the bullet?

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

skaters push on each other. Describe the motion of each skater.

How do their velocities compare?

Downloaded by [Monash University Library] at 02:15 10 February 2014

Appendix

(continued)

5. Carts

and

Spring Problem

Two heavy frictionless carts

are at

rest. They

are

held together

a loop

string.

light spring

compressed between them

(see

drawing). When

the

string

burned,

the

spring expands from

2.0

to 3.0 cm, and the

carts move apart. Both

hit the

bumpers

fixed

to the

table

at the

same instant,

but cart

moved

0.45

meter while

cart

moved

0.87

meter. What

is the

ratio

of:

(a)

The

speed

of A to

that

of B

after

the

interaction?

(b) their masses?

(Haber-Schaim

et al.,

1976,

p. 321)

6. Compressed Spring Problem

Two objects

mass

m^ and

IVQ

are

held together

by a

strong

light thread,

and are

also acted

on by a

light spring that

is com-

pressed

shown

in the

figure. When

the

restraining thread

broken,

the two

objects

fly

apart with

velocities

—

I/A

and + i/o. Use the law

of conservation

momentum

solve

for

the

ratio

of the

velocities,

V^/VQ.

(Miller, Dillon,

Smith, 1974,

p. 112)

Two heavy frictionless carts

are at

rest. They

are

held together

a loop

string.

light spring

compressed between them.

The

string

burned

and the

spring expands. Describe

the

motion

the carts.

How

does

the

velocity

cart

compare with

the

velocity

cart

Two objects

mass

m^ and

m^are held together

by a

strong

light thread,

and are

also acted

on by a

light spring that

is com-

pressed.

When

the

restraining thread

borken,

the two

objects

fly apart with velocities —

v^ and

+yg.

Use the law of

conservation

momentum

solve

for the

ratio

the velocities,

V^/VQ.

PHYSICIST'S ANALYSIS

p Forces

equal magnitude

and

opposite

direction

are

^*" exerted

on two

unequal masses

rest.

How do the

veloc-

ities

of the

masses compare?

How do the

displacements

the masses compare?

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COGNITIVE RESEARCH

AND

INSTRUCTIONAL DESIGN

Appendix B

Example of Proposed Instructional Dialogue — The Gun and Bullet Problem

Original Problem

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

500 m/sec. How does the gun recoil? (Give its speed and direction of motion.)"

(Hulsizer & Lazarus, 1972. p. 187)

Problem Restated

Qualitative Form

When

a gun is

fired,

the

bullet leaves

the gun

with some speed.

How

does

the

bullet's speed

at the

muzzte

of the gun

compare with

the

gun's speed

that time?

How

does

the

direction

of the

bullet's

motion compare with

the

direction

of the

gun's motion?

Subsidiary questions:

(i)

What assumptions

did you

make

arrive

your answers?

(ii) What principles

physics/laws

motion

did you

apply

to the

situation

in coming

your answers?

Knowledge/skills assumed

following outlines

Instructional Dialogue strategies:

"Physics" knowledge: it is assumed that students have completed a study of kinematics.

General (or "world") knowledge: Awareness of medieval cannons, rifles, handguns (see

step A1 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

AI (a). Given scale drawings

of a small pistol, rifle, small

mortar, medieval cannon and

shells/bullets fired by each,

student is asked to match the

guns and shells/bullets.

A1(b). Ask student why

matchings were made.

A2.

Ask the student why

the bullet/shell comes out of

the gun when the gun is

fired.

A3.

Show the student a

drawing of a metal tube,

closed at one end and with a

lighted fire cracker placed

on it.

A1(a) and (b). To establish

that, in the real world, mass/

weight of gun ^> mass/weight

of bullet or shell.

Asked what will happen when

the fire cracker goes off.

To establish the role of ex-

plosion in this phenomenon.

If this notion is present, go

to A4; if not, go to A3.

To establish the effect of ex-

plosion on the mass in the

tube,

i.e., the cracker. If this

exercise does not establish

the notion, move further to

considering a medieval can-

non where the explosive and

propelled object are separate.

Collins (1977) has proposed a

series of production rules for

this form of instructional dia-

logue.

Strategy A1(a) is an

example of Rule 1: . Ask

about a known case. In his

subsequent reorganization of

these rules (Collins & Stevens,

1981),

this is an example

of Case Selection Strategy 1:

Pick a positive exemplar for

a set of factors.

Collins (1977) Rule 2: Ask

for any factors.

Collins (1977) Rule 2 (see

above).

Collins (1977) Rule 3: Ask

for intermediate factors. For

some students this will also

be a prompt to recall a rele-

vant previous experience,

relevant existing world know-

ledge.

Downloaded by [Monash University Library] at 02:15 10 February 2014

AUDREY B. CHAMPAGNE, LEOPOLD E. KLOPFER AND RICHARD F. GUNSTONE

Appendix B (continued)

Steps in the Strategy

Purpose of Steps

Commentary on Steps

A4.

Using two labor-

atory trolleys, one containing

a spring plunger (PSSC), and

a number of bricks.

(a) have students exper-

iment qualitatively with the

effect of placing two carts

with loaded spring between

and releasing the spring,

with varying masses on the

carts,

(b) have students exper-

iment with one cart carrying

various masses placed with

loaded .spring against their

hand and then released.

A5.

By drawing on A1-

A4,

assist the student to

establish (and, if appropriate,

to link to relevant existing

knowledge/experience) :

(¡) that in the case of the

exploding carts, the ex-

panding spring exerts forces

on the carts placed at either

end of the spring, and that

these two forces are equal in

magnitude.

(ii) that, in the case of the

exploding carts, equal forces

from the spring acting on

carts of different mass result

in different cart velocities

after explosion,

(iii) that, in the case of ex-

ploding carts, when one cart

has a mass considerably lar-

gar than the other this situa-

tion is in some ways

anal-

ogous to a gun firing a

bullet. (Of the limitations to

the analogy, the most im-

portant to be drJwn out

here is that the relative mass

differences for gun and

bullet are much greater than

for the carts.)

A6.

Return to qualitative

problem.

After successful

solution of the problem as

asked,

use strategy B below if

appropriate.

To establish the separation of

all masses involved in an ex-

plosion;

to establish that

smaller mass pieces move

more quickly than larger mass

pieces.

To establish that a mass ex-

ploded away from a

"rigid"

body results in a force on

that rigid body.

To establish the generaliz-

ations needed in order to be

able to analyze and solve the

original qualitative problem.

Direct observation

This step is similar to Step A1

(b) (see Footnote a) in that

the production rules to be

applied will vary from subject

to subject, depending both on

each individual's existing

knowledge and beliefs, and

on each individual's interpre-

tations of steps A1 to A4.

Downloaded by [Monash University Library] at 02:15 10 February 2014

COGNITIVE RESEARCH AND INSTRUCTIONAL DESIGN

Appendix B (continued)

Strategy B Outline of strategy to be used for responses to the qualitative problem of the form "speed

of bullet very much greater than speed of gun and in opposite direction"

(i.e.,

correct answer to

questions asked).

Steps in the Strategy Purpose of Steps

Commentary on Steps

B1 Ask student if they can

be more precise about

the relative values of the

bullet and gun speeds.

B2 Repeat subsidiary ques-

tions (i) and (ii) from the

qualitative problem.

To establish that the ratio

of speeds is the inverse ratio

of the weights/masses in-

volved.

If this is not forth-

coming,

go to strategy A,

beginning at A4. If some such

statement is produced, go to

B2.

To elicit a statement of

Newton's Third Law and to

have the student authorita-

tively link this law to the

gun/bullet phenomenon.

Collins (1977) Rule 4:

for prior factors.

Ask

See commentary on Step A5.

Numbers of other rules

(e.g..

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 the

pistol?"

(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 indicate

the position of carts before the explosion so that a reference is available for considering

post-explosion effects.

If friction effects provide an interfering concept, move further by using an air track for explosions

and then returning to trolleys.

Downloaded by [Monash University Library] at 02:15 10 February 2014

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Die Bedeutsamkeit von Beispielen für das Lernen neuer (physikalischer) Konzepte ist lerntheoretisch Konsens (Fischer et al. 2003). Richtig eingesetzt, sind Beispiele in der Lage, die Abstraktheit bzw. Komplexität physikalischer Inhalte zu verringern, indem sie Anknüpfungspunkte an die Erfahrungen und somit an das bestehende Wissensnetz der Lernenden bieten (Kalyuga et al. 2010, Kircher et al. 2015, Schecker et al. 2018). Gleichzeitig ermöglichen Beispiele es durch ihre Verankerung in konkreten Kontexten einen für die Schüler*innen relevanten und interessanten Lebensweltbezug herzustellen (Muckenfuß 1995, Habig et al. 2018). Der Einsatz von Beispielen unterstützt so sowohl den kognitiven als auch affektiv-emotionalen Verstehensprozess. Aufgrund dieser Eigenschaften scheinen Beispiele gerade auch für Lernende mit geringerem Vorwissen von hohem Nutzen zu sein. Bezüglich einer optimalen Positionierung des Beispiels (vor oder nach der Regel) beim (Physik)Lernen gibt es jedoch sich entgegenstehende Befunde. Kulgemeyer (2018) spricht sich für die Reihenfolge Regel-Beispiel zum Erlernen von deklarativen Wissen (Faktenwissen) aus und verweist dabei auf Seidel et al. (2013), Champagne et al. (1982) und Korthagen & Kessels (1999), die alle Effekte zugunsten dieser Reihenfolge feststellen konnten. Demgegenüber steht der Ansatz der Basismodelltheorie (Oser & Baeriswyl 2001), der die Strukturabfolge (prototypisches) Beispiel - Konzept bei der Begriffs- bzw. Konzeptbildung vorsieht. Diese Vorgabe gründet sich v.a. auf den lerntheoretischen bzw. lernpsychologischen Ausarbeitungen von Aebli (1981; 1983) und Smith & Medin (1981) und beschreibt, dass durch das geführte Durcharbeiten eines einzigen – für das Konzept prototypische – Beispiel wesentliche Züge des Konzeptes aufgezeigt werden können, die dann in den vernetzten und verallgemeinerten Konzeptbegriff münden. Zwischen diese beiden Ansätze stellen sich die Studien von Kokkonen et al. (2021) sowie van Hout und Mettes (1976), die den Einfluss der Strukturabfolge im physikalischen bzw. ingenieurstechnischen Kontext überprüft haben und keine Effekte zugunsten der einen oder anderen Abfolge feststellen konnten. Aufgrund der uneindeutigen Forschungslage bezüglich der Reihenfolge der Strukturierungselemente in Bezug auf das Erlernen physikalischer Konzepte stellen wir die Forschungsfrage auf: Welchen Einfluss hat die Reihenfolge der Strukturierungsschritte „prototypisches Beispiel“ und „Regel/Konzept“ auf den Lernerfolg? Wir gehen davon aus, dass die Reihenfolge der Strukturierungsschritte sich auf den Lernerfolg der Lernenden auswirkt. Dabei nehmen wir an, dass das Vorwissen als moderierende Variable agiert, wobei die Richtung der Wirkung offen bleibt.

COMPRENDIENDO LOS PARADIGMAS DE KUHN A LA LUZ DE LA CIENCIA COGNITIVA

Article

Dec 2020

Alexander Bird

Frameworks for Comprehending Discourse

Article

Full-text available

Sep 1977

Thirty physical education students and 30 music education students read a passage that could be given either a prison break or a wrestling interpretation, and another passage that could be understood in terms of an evening of card playing or a rehearsal session of a woodwind ensemble. Scores on disambiguating multiple choice tests and theme-revealing disambiguations and intrusions in free recall showed striking relationships to the subject’s background. These results indicate that high-level schemata provide the interpretative framework for comprehending discourse. The fact that most subjects gave each passage one distinct interpretation or another and reported being unaware of other perspectives while reading suggest that schemata can cause a person to see a message in a certain way, without even considering alternative interpretations.

The Notion of Schemata and the Educational Enterprise: General Discussion of the Conference

Chapter

Sep 2017

Richard C. Anderson

Sciences of The Artificial

Book

Jan 1996

Herbert A Simon

In The Structure of Scientific Revolutions

Book

Thomas S. Kuhn

Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies

Mapping a Student's Causal Conceptions From a Problem-Solving Protocol

Article

John Clement

INTRODUCTION The problem of how to describe t.he structure of B student's current concep tions in I!l given area is 8 fundamental one for researchers who Beek to develop 8 theoretical foundation for cognitively oriented instruction . Recent develop ments in the physics leaching community, for elample, have emphasized cogni lively oriented approaches to teaching and the need for understanding the cognitive processes tbat underlie one's ability to "do" physics. Ideally, we would Ilke to have 8 picture of the kinds of knowledge structures and reasoning processes that are present in beginning students and that ate present in experts. Detailed descriptions of experts' knowledge structures, including those tacit knowledge structures not represented explicitly in the curriculu.m, would pre· sumably belp to define more clearly what is to be learned by the student. Detailed descriptions of beginning students' preconceptions and misconceptions would have value not only 8S a sophisticated evaluation tool, but would also make it more possible to take ccmroon preconceptions and misconceptions into 8.ccounl during instruction. This paper attempts to show that it is possible to st.udy systematically certain types of beginning students' conceptions in physics; specifically, causal concep· tions in mechanics. The paper examines the conceptions 8 freshman student uses to understand a simple physicol system involving the horiz.ontal motion of 8 cart launched scross 8 table, The task given to the student does Dot ask him to find 8. long series of adions which will solve a problem. Rather he is Bsked for a prediction and explanation of the effects on the system resulting from a single action. Protocols of 8uch explanations are particularly interesting because they tend not to be limited to formal, deductive arguments, but to include informal arguments that reflect the structuring of the subject's physical intuitions. The methodology used in this study involves two phases: obtaining problem· solving protocols via taped interviews, and analyzing these protocols to produce a model of the conceptions that Wlderlie the student's responses in the in. krv.iew. Several considerations are important t.o the success of this U!chnique. An Import.ant consideration daring the interview process is the attempt to en.

Factors Influencing the Learning of Classical Mechanics

Article

Dec 1980

The study described in this paper investigates the combined effect of certain variables on student achievement in classical mechanics. Our purposes are (1) to describe the preinstructional knowledge of mechanics, mathematical skills, and reasoning skills of a sample of college physics students, (2) to correlate these variables with the student's success in learning classical mechanics, and (3) to develop an hypothesis about the relationships between these variables and student achievement in mechanics. We also offer some proposals for improving the teaching of classical mechanics.

Elements of physics

Article

May 1979

Correlation between mathematical skills and success in physics

Article

May 1977

A pre-course test of algebraic and trigonometric skills has been correlated with performance in introductory physics without calculus. For 200 students in two sections it was found that mathematical abilities at the beginning of the course weakly correlate with performance in the course. A repeat of the test at the end of the course indicates that mathematical skills alone are not sufficient to guarantee success in physics, but that unless the student has the mathematical skills, the performance in the physics will be poor.

Cultivating the Capacity for Formal Reasoning: Objectives and Procedures in an Introductory Physical Science Course

Article

Sep 1976

A. B. Arons

Experience in a physical science course for preservice elementary teachers, inservice elementary teachers, and other nonscience majors has led to the identification of certain specific factors and procedures that seem to assist the attainment of the formal operational level of intellectual development on the part of students who are initially at a concrete or transitional stage.

A course in physics of human motion

Article

Nov 1975

A course in elementary mechanics especially designed for students of athletics and dance is described. The course has been taught for two years at the University of Minnesota. Innovative features include a gymnasium laboratory utilizing an inexpensive photographic technique for analysis of human motion. The order of presentation and the selection of topics, as well as the illustrative examples, are all unconventional in an elementary mechanics course. Student response is described. © 1975, American Association of Physics Teachers. All rights reserved.

Cognitive research and the design of instruction

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