concepts of force

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Students’ concepts of forceas applied to related physicalsystems: A search for consistencyM. Finegold a & P. Gorsky aa Technion ‐Israel Institute of Technology, Haifa, IsraelVersion of record first published: 24 Feb 2007.

To cite this article: M. Finegold & P. Gorsky (1991): Students’ concepts of force as appliedto related physical systems: A search for consistency, International Journal of Science

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INT. J. SCI. EDUC., 1991, VOL. 13, NO. 1, 97-113

Students co nc ep ts of force as appliedto related physical systems: A searchfor consistency

M. Finegold and P. Gorsky, Techn ion-Israel Institute of Technology,Haifa, Israel

Recent attempts to categorize studen ts' conceptual understanding of physical phenomena into consistentand meaningful frameworks have had limited success. We report here on an analytic technique by meansof which we were able to identify what appear to be meaningful conceptual categories of students'understanding of force. However, we found only very limited support for two often-quoted alternativeframeworks, viz.: (a) if body is moving, a net force always acts on it in the direction of the motion, and (6)no forces act on objects at rest.

Introduction

Resu lts of a great deal of research over the past 15 years have shown that s tud en ts,prior to any formal instruction in physics, commonly adhere to well developed butscientifically incorrect beliefs about force. Many of these beliefs are held even afterostensibly successful courses in physics. Research efforts were also directed atcategorizing these beliefs into higher level conceptual categories and frameworks.Initial studies (e.g., Vien not 1979, G ilbe rt and Osb orn e 1980, Clem ent 1982, G ilber tet al. 1982, W atts 1983) identified framewo rks th at apparen tly accou nted for thedifferent beliefs. Gilbert and Watts (1983) summarized the most common frame-works as follows:

If a body is not moving there is no force acting on it.If a body is moving there is a force acting on it in the direction of the motion.Constant motion requires a constant force (p. 73).

To identify the frameworks, the researchers mentioned above all used a similartechnique described as follows by Watts (1983):

The frameworks described here come from no one pupil. They have been piecedtogether from the implicit and explicit conceptions used by the children during the

course of the interview... The frameworks form a composite picture based on ideasshared by a number of pupils. The need is to develop models of student understand ingthat are powerful enough to capture im portan t individual differences, yet not so specificthat the net product is the same number of models as there are pupils (p. 218).

Th is approach yielded valuable information ab out how students un derstan d th e lawsgoverning physical phenomena. It yielded no information, however, about howindividual students, with all their conflicting beliefs, apply these same laws todifferent objects in given systems.

0950-0693/91 $3-00 1991 Taylor & Francis L td.

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9 8 RESEARCH REPORTS

Other researchers have tried to identify c onc eptua l framew orks b ased on theresponse sets of individual s tuden ts. In an early study, C ham pagn e et al. (1980)noted that students failed to recognize th at the sam e physical laws apply to objects infree fall and objects sliding dow n an inclined plane. Chi et al. (1981) concluded that

the schemata of s tudents who have studied physics are based on physical objects(springs, inclined planes, etc) and not on physical laws. In an impo rtant s tudy,Hal loun and H estenes (1985 a, 1985 b) tested m ore than 4000 college stud ents inArizona and identified the beliefs adher ed to after the s tudy of physics and the extentto which they are held. In addition, they attempted to identify coheren t conceptualcategories and frameworks held by individual stu den ts. Th ey failed and concluded:'However, nearly every student used some mixture of concepts . . . and appeared tobe inconsistent in applying the same concept in different situa tion s' (1985a, p. 1058).

In other words, Halloun and Hestenes (1985 a) were unable to find consistent

conceptual categories within the frameworks employed by individual s tudents.Clough and Dr iver (1986) explored s tud ent s' use of concepts across a n u m b e r ofdifferent tasks, probing their understanding of pressure, heat and evolution. Th eyreported that stude nts were not consistent in applying alternative frameworks. M orerecently, Reif (1987) conducted a study in which he tried to account for inconsistentthought . He found that whe n stude nts who had already stud ied p hysics were asked toexplain some physical phe no m eno n, they invoked 'knowledge fragmen ts' instead ofgeneral knowledge. Reif comments:

In their attempts to apply a concept, novice students rarely invoke the definition of theconcept or other general know led ge ... Instead, they rely on various special knowledgeelements stored in memory, try to achieve one of these, and apply it without muchsubsequent reasoning (p. 316).

The purpose of our s tudy is to investigate the consistency, if any, with which forceconcepts are used by individual students in different, but closely related con texts.Clough and D rive r (1986) discuss the im por tance of this question, especially as itrelates to the extent to which outcomes of a study are dependent on the tool of inquiryused:

Many frameworks identified from interview transcripts would presumably then be littlemore than artifacts of the methodology, transient solutions devised in an interviewwhere an answer of some kind is a social imperative. It can be argued, however, that theuse of the same intuitive ideas across contexts which are different, but which scientistsconstrue similarly, would offer some support for the validity of student frameworks ascommonly available ways of thinking (p. 475).

Research design

Goals

The a ims of this research are:

1. T o determine the percentage of s tudents who are consistent in the ir beliefsabout the forces actin g on objects at rest and objects in mot ion.

T o determine the percentage of s tudents who consisten tly app ly the correctNewtonian laws and the percentage who consisten tly app ly alternativeframeworks such as those cited ab ove.

2. For those stu dents who appear to be inconsistent in their beliefs, to identifytheir categories of thought and to look for evidence of an underly ing logic intheir apparently contradictory beliefs.

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STUDENT S' CONCEPTS OF FORCE 99

In addressing these goals, we ask a series of questions about students' conceptualcategories concerning forces. Do students consistently include or exclude:

1. A gravitational force for the book and pendulum at rest?2. A force opposing gravity for the book and pendulum at rest?3. A net force acting in the direction of the movement of objects undergoing

periodic, linear and projectile motion?4. Forces opposing gravity for objects at rest and for the same objects in motion?

We will refer to these questions as research questions 1 to 4.

Participants

A total of 534 university students and high school pupils, 35 of whom wereinterviewed, completed the written test described subsequently.

— 333 university students (designated below as UNIV), 18 of whom wereinterviewed, who had recently completed an advanced or standard intro-ductory course in mechanics.

— 201 high school pupils (grades 10-12) from various urban and rural schoolsthroughout Israel, distributed as follows:

— 112 pupils (grades 11-12), 8 of whom were interviewed, who studiedphysics at an advanced level (designated below as ADV);

— 32 pupils (grade 11), 4 of whom were interviewed, who studied physics atan ordinary level (designated below as ORD);

— 57 pupils (grade 10), 5 of whom were interviewed, who had not studiedphysics (designated below as NO).

The test

We designed a ten-item test, to be administered to university and high schoolstudents, to elicit their beliefs about the forces acting on the following objects (seeAppendix A):

— A suspended pendulum bob at rest (Q l).

— An oscillating pendulum bob at three different positions, one of which is thelowest point on its path (Q2 a, b , c).— A book at rest on a table (Q3).— A book moving at a constant velocity on a smooth table (Q4).— A cannonball fired at a 45 ° angle at three positions, one of which is the h ighest

point on its path (Q5 a, b, c).— A ball thrown straight up (Q6).

The test was administered as a written task or as a written task accompanied by aninterview. For every item, the students or pupils were presented with a drawing of

the system and asked to use arrows to show each of the forces acting on the object inquestion and to name each force. T hose interviewed were also asked to explain theiranswers.

Test validity

We used Ebel's (1972) criteria for evaluating content validity: (a ) relevance,(b ) objectivity, (c) balance, (d ) difficulty, (e ) specificity. (A test shows specificity if a

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10 0 RESEARCH REPORTS

test-wise novice in the field covered by the test is generally unable to answerquestions correctly. To the degree that any test measures reading skills or generalintelligence, it lacks specificity.) Ebel (1972) recommends that the first four criteriabe evaluated by a panel of experts and that the fifth be evaluated on an experimental

basis.Panel members offered several suggestions (primarily regarding the wording ofthe questions) that led to changes in the test. One serious criticism concerned thelevel of question difficulty. Questions were perceived as being too simple and trivia l.However, on the basis of preliminary test results, this criticism was found to beunjustified. Regarding the relevance, objectivity, balance and difficulty of the finalversion of the test, panel members agreed that the test met the specifications.

In order to evaluate specificity, eight intelligent high school pupils (grades 9-12)who had not studied physics were asked to take the test. Six pupils answered all thequestions incorrectly while the other two declined to answer any of the questions onthe ground that they did not know the answers and had no basis for makingintelligent guesses. We conclude, therefore, that the test meets the criterion forspecificity described by Ebel (1972).

Test reliability

Two reliability measures were used. First, the reliability of the test questions ineliciting identical answers on different occasions and, second, the reliability of thescoring process.

For the test-re test reliability, a group of 20 pupils was retested one month afterthe initial test in order to determine if the same answers were given for both tests.The chi-square test was used to evaluate the relation between the two sets of answers.The chi-square statistic measures the discrepancy between observed and expectedfrequencies. It was found that for all ten questions, none of the discrepancies wasstatistically significant at the 5% level or less. It was concluded, therefore, that pupilsanswered questions similarly on both occasions.

For the reliability of the scoring process, 25 response sets were randomly chosenand marked by two experienced judges. Th e extent of agreement between judges, thekappa coefficient, was calculated. Kappa values for the 10 questions ranged from 0-82to 100.

Method of analysis

Test results were analysed using the data base capabilities of the Lotus 123 program.Data (student responses) were entered as follows:

I D

1

2

Q l

C

NF

Q2a

G + Fm

Fm

Q 2b

G

F m

Q 2c

G + Fm

F m

Q 3 . . .

C . . .

N F. . .

Q6

G + Fm

F M

5

Each row presents a Student Identification Number (ID) and a coded responseanalysis. For example, 'C signifies a correct answer, 'G' that only gravity was

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STUDEN TS' CONCEPTS OF FORCE 101

indicated in the response, 'Fm ' that only a non-scientific force in the direction of themotion was shown, 'G + Fm ' that bo th gravity and a non-scientific force were cited,and 'NF' that no forces at all were indicated. The program counts the types andfrequencies of errors. In order to identify and search for conceptual categories, data

queries were created that scanned the entire data base. Some examples of these dataqueries follow.

1. What percentage of pupils neglected the tension in the string for thependulum bob at rest (Ql) but included the tension for the pendulum inmotion (Q2a, Q2b, Q2c)?

2. What percentage of pupils included a force in the direction of the pendulumbob's motion as it rose and fell (Q2a, Q2c), but neglected such a force when thebob passed through its equilibrium point (Q2b)?

3. What percentage of pupils included a force in the direction of the cannonball's

motion as it rose and fell (Q5a, Q5c), but neglected such a force when thecannonball reached its maximum height (Q5b)?4. What percentage of pupils met the criteria for data queries 2 and 3 described

above.

One hundred and eighty data queries were initially listed. Some were extremelycomplex, analysing responses from all ten questions. Each query presents an a ttemptto identify students' patterns of thought, which may be consistent or inconsistent.For example, we found that very few respondees met the criterion for data query 4(see above) despite its symmetry. In trying to identify consistent student frame-works, we carried out the following procedures:

1. Define conceptual categories to account for different response sets and writethe appropriate data queries.

2. Analyse the output generated by the queries (the output consists ofpercentages of students whose responses match the different conceptualcategories).

3. Revise the categories and queries to account for the remaining data.

These steps were carried ou t iteratively until we had identified categories to account

for most of the response sets. All told, about 280 different queries were examined.

Research findings

Students' beliefs about the forces acting on objects at rest

To answer research questions 1 and 2 regarding the inclusion or exclusion of theforce of gravity and the forces which oppose it, we studied responses to questionsabout two systems at rest: a suspended pendulum bob and a book on a table. For eachone of these systems, the vast majority of all respondees indicated the correctNewtonian forces or no forces or gravity only.

Our next s tep was to check answers for consistency - was the same rule applied inboth systems? As seen from table 1, respondees, except for the high school pupils inthe ORD and NO groups, adhere to highly consistent beliefs for the two differentsystems at rest. Of particular interest is the finding that less than 10% of the pupilswho had not studied physics (NO) were consistent in the Aristotelian belief tha t noforces act on objects at rest. Gilbert and Watts (1983) pointed out that many

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102 RESEARCH REPORTS

T able 1. P ercen tage s of resp ond ees applying consisten t force arrays forboth systems at rest.

UNIVA D VO R DN O

Correct

939431

0

No Force

0009

Mg only

03

2568

Consistent

93975677

Mg = gravitational force.

researchers (e.g., O sbo rne 1980, H elm 1981 , W atts and Zylbersztajn 1981 , M instrell1982, Watts 1983) reported that the Aristotelian 'no force' belief is a 'commonalternative framework' among pupils who have not studied physics. Our findingssuggest, however, that the 'no force' belief is neither common nor an alternativeframework.

Among pupils who had not studied physics (NO), we found that only 9%responded that no forces act on the book at rest, while 17% of the same groupresponded that no forces act on the pendulum bob at rest. These findings led us toconclud e that the belief is not com m only h eld, at least amon g the pupils tested in ou rsample .

Acco rding to Engel and D rive r (1982), a framework oug ht to be a description of a

perspective from which a prediction of events can be made. That is, in order to beconsidered a framework, a belief, or set of beliefs, should make it possible for anobserver to predic t certain events. In th is case, the events to be predicted are pup ils 'respo nses to the quest ion : 'W ha t force or forces, if any , are acting on given objects atrest?'

Of the pupils in the N O gr oup w ho respond ed tha t no force acts on the p en du lumbo b at rest (17%), only slightly mo re tha n half (9%) cons istently applied th is belief inboth systems at rest , pendulum bob and book. We suggest, therefore, that theAristotelian 'no force' belief is not applied consistently and does not meet the

criterion of a framework as defined by Engel and Driver (1982). Altogether, morethan 90% of the pupils who had not studied physics recognized the presence of agravitational force acting on objects at rest on or near the earth's surface in at leastone system.

We next sought to identify the inconsistent beliefs held by the ordinary levelpupils (ORD) and those who had not studied physics (NO). Table 2 shows thepercentages of pupils who adhered to various inconsistent beliefs.

Column A shows the percentage of pupils who indicated the correct Newtonianforces acting on the pendulum bob at rest but indicated only a gravitational forceacting on the book at rest. Colum n B shows pupils w ho correctly identified the forcesacting on the book, but failed to identify th e upw ard force exerte d by the string on th epe nd ulu m b ob . Co lum n C shows pup ils w ho indicated a gravitational force acting onthe pendulum bob, but failed to note a gravitational force acting on the book.Column D shows pupils who noted a gravitational force acting on the book, butconcluded that neither gravity nor any other force acted on the pendulum bob.

A pparen tly no general law or laws (e.g., 'T h e total net force acting on a bod y atrest is zero' or 'gravity always acts on objects on or near the earth's surface') govern

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STUDENTS' CONCEPTS OF FORCE 103

Table 2. P ercentag es of two groups (ORD and NO) applying incon sistentforce arrays for both systems at rest.

PendulumBook

O R DN O

ACorrect

Mg only

130

BMg onlyCorrect

315

CMg onlyNo Force

014

DNo ForceMg only

04

Total

4423

Mg = gravitational force.

the think ing of these two grou ps; it app ears , as Reif (1987) poin ted o ut, that specificrules exist for specific situ atio ns: a force law for objects at rest on surfaces, for objectssuspended from strings, etc.

Students' beliefs about the forces acting on objects in m otion

Here, we seek to answer research question 3: does the motion of an object alwaysimply the presence of a net force acting in the direction of the movement? Thisquestion relates to objects undergoing periodic, linear and projectile motion. Tobegin, we identified the beliefs adhered to by the students for each of the threesystems examined. Next, we organized the different beliefs into more generalconceptual categories.

Students' beliefs about periodic motion: W e studied stu den ts' beliefs abou t the forcesacting on an oscillating pendulum bob at different points along its path. Ninedifferent arrays were identified, each of wh ich seems to show an interna l logic. M orethan 86% of all the respondee s (excluding the O R D group) adhered to one of the ninearrays described below. In arrays A to E, we see that the stu dents indicated the sam eforce configuration at each point along the pendulum bob's path.

A. T h e correct Ne wto nian forces.B. Co rrect N ew tonia n forces and a force in the direction of the motio n of the

pendulum bob.C. Grav ity only.D . G ravi ty and a force in the direction of the m otio n.E. On ly a force in the direction of the m otio n.

In arrays F to I, the motion force on the pendulum bob momentarily disappearswhen it reaches its equilibrium position.

F . Co rrect Ne w toni an forces at each of the three positions and a m otio n force atthe two positions above the equilibrium point.

G . G ravity at each of the three positions and a m otion force at the two p ositions

above the equilibrium point.H . A mo tion force at the two positions above the equilibrium point and gravityat the equilibrium point.

I. A mo tion force at the two positions above the equilib rium p oint and no forceat the equilibrium point.

Intervie w data revealed several explanations for the om ission of a mo tion force at theequilibrium point. For example, Uri, a 10th grade student who had not studied

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104 RESEARCH REPORTS

physics, said that some force was present within the pendulum bob as it oscillated.However, since this force periodically changed direction, it was cancelled at theequilibrium position. Fou r of the five pupils who had not studied physics (NO) andtwo of the four ordinary level pupils (ORD) also perceived force as an internal, ratherthan as some external entity acting on the object.

A more typical answer, common to pupils who had studied physics, drewconclusions about forces on the basis of assumptions concerning energy. Forexample, interviewees claimed that when the pendulum reached its equilibriumposition no potential energy was present and that therefore no force was acting.Ordinary level pupils were generally unable to distinguish between the concepts offorce and energy while the advanced students were able to identify their errors andreach more appropriate Newtonian conclusions.

Arrays D, E, H and I were representative only of pupils who had not studied

physics.Students' beliefs about linear translational motion: Our results indicate that m ore than82% of the respondees in each group adhere to some reasonable or logicallydefensible belief about the forces acting on objects in linear motion. The variousforce arrays designated by students for a book in motion on a frictionless table (Q4)were:

— The correct Newtonian forces (Mg + N).— The correct Newtonian forces and a force acting in the direction of the

movement (Mg + N + Fm).— The force of gravity and a force acting in the direction of the movement(M g + Fm).

— Only a force acting in the direction of the movement (Fm).

Students' beliefs about one- and two-dimensional projectile motion: We studiedstudents' beliefs about the forces acting on two objects in flight: a cannonball firedfrom a cannon (Q5a, 5b, 5c) and a particle projected straight up (Q6). Questions 5a, band c (Appendix A) elicit from the students their beliefs about the forces acting on acannonball at three points along its trajectory. Question 6 elicits students ' beliefsabout the forces acting on a particle as it moves upward.

For questions about a projectile moving upward or downward (Q5a, 5c, Q6)nearly all respondees selected one of the following three arrays, although notnecessarily in a consistent manner: gravity directed downward or a force in thedirection of the motion or both. For the cannonball at the height of its trajectory(Q5b), some students indicated that no force is acting.

Student responses were examined for consistency. Inconsistent arrays werecharacterized by contradictions. For example, different answers were given forquestions 5a and 6, or gravity was indicated in some answers in which the objectsare rising or falling, but not in all of them. We found that more than 75 of allrespondees adhered to one of the six consistent and logically defensible arrays shownin table 3 (arrays 2-6 show variations on the concept of an impetus force, Fm).

Objects in mo tion: studen ts' conceptua l categories

Here, an attempt is made to answer research question 3: do students consistentlyinclude or exclude a net force acting in the direction of the movement of objects

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STUDENT S' CONCEPTS OF FORCE 105

T able 3. C onsistent force arrays for projectile mo tion.

Arrays

1

23456

Q5a

G

G + FmG + FmG + FmG + FmF m

Q5b

G

G + FmGN FG + FmFm

Q5c

G

G + FmGGGF m

Q6

G

G + FmG + FmG + FmG + FmF m

Fm = a force in the direction of the motion; G = gravity; N F = No forces.

undergoing periodic, linear or projectile motion? Furtherm ore , evidence is sought toshow that students' individual beliefs may be categorized into coherent and

internally consistent conceptual frameworks. Table 4 presents students' beliefsabout the forces acting on the objects in each of the cases investigated. T he categoriesare as follows.

1

5-8

9-11

12-131415-16

The correct Newtonian forces are noted.A motion force is consistently included.A motion force acts on objects undergoing translational, but not periodicmotion.A motion force acts on all objects investigated except the pendulum bobat its equilibrium position.Motion forces appear only in oscillatory motion.Motion forces appear only in linear motion.Motion forces appear only in projectile motion.

Each of categories 2-4 is internally consistent. In each of them, the same rules areapplied to the objects regardless of the kind of motion involved. For example, incategory 2, forces that oppose the earth's gravitational force are correctly applied,and, in addition, a force in the direction of the motion appears in every case. Incategory 3, forces that oppose the earth 's gravitational force (N, T ) are consistentlyexcluded while a force always appears in the direction of the movement. However,categories 2-4, despite their logical appeal, are rarely applied (the percentages ofrespondees who adhered to each of the sixteen categories appears in Appendix B).

Each of categories 9-11 is also internally consistent. A force acting in thedirection of the motion appears in all cases except at the equilibrium point of theoscillating pendulum bob . For example, in category 11, except for the equilibriumpoint at which no force is indicated, the only force noted is a force acting in thedirection of the motion of the object. These categories too are not widely used.

We now consider the validity of the 'motion implies a fo rc e. .. alternativeframework. As cited previously, Engel and Driver (1982) define a framework as a

description of a perspective from which a prediction of events can be made. We havealready noted that categories 2—4 and 9-11 are generally not used by students . Asecond approach looked only for the consistent use of a motion force acting on theobjects. Here we ignore beliefs regarding gravity and opposing forces, using as acriterion for consistency only the presence of a motion force in every case or in everycase except that of the bob at its equilibrium point. Few additional students (2-5%)were found who met this criterion.

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Table 4. Consistent conceptual categories for periodic (Q2a, b, c), linear (Q4) and projectile motion(Q5a,b,c, Q6).

Conceptualcategory

123456789

10111213141516

Q2a

G + TG+T+FmG+FmFmG + TGG + TG + TG+T+FmG + FmFmG+T+FmG + FmG + TG + TG + T

Periodic motion

Q2b

G + TG+T+FmG + FmFmG + TGG + TG + TG + TGN FG + TGG + TG + TG + T

Q2c

G + TG+T+FmG + FmFmG + TGG + TG + TG+T+FmG + FmFmG+T+FmG + FmG + TG + TG + T

Linear— motion

Q4

G + NG+N+FmG + FmFmG+N+FmG + FmG + FmG+N+FmG+N+FmG + FmFmG + NG + NG+N+FmG + NG + N

Q5 a

GG + FmG + FmF mG + FmG + FmG + Fm

G + FmG + FmF mGGGG + Fm

Projectile motion

QSb

GG + FmG + FmFmG + FmG + FmG + Fm

Q5c

GG + FmG + FmFmG + FmG + FmG + Fm

impetus-likeG + FmG + FmFmGGGG + Fm


impetus-like

Q6

GG + FmG + FmF mG + FmG + FmG + Fm


Fm = a motion force; G = gravity; T = tension; N = normal; NF = no forces.

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We have noted previously research findings claiming that s tudents often use the'motion implies a force...' explanatory framework (Viennot 1979, Clement 1982,1983, Watts 1983). However, all of the researchers report on students working withsingle systems and not across different systems. In light of the above data, we suggest

that th is framework is not a good predictor of students' beliefs concerning objectsundergoing periodic, linear or projectile motion. This, we believe, is so both beforeand after the study of physics.

We now consider evidence showing that students do adhere, however, to logicaland meaningful conceptual categories. We content that each of categories 1-16 isinternally consistent and may be understood in terms of rules, some of which arescientifically acceptable. Having already discussed the consistent logical bases ofcategories 1-4 and 9 -11 , we now tu rn to the seemingly inconsistent and fragmentedcategories, 5-8 and 12-16 (table 4). Here, scientific and non-scientific beliefs co-exist.

Categories 12 and 13 consistently include correct forces acting on the five objectsundergoing translational motion. For the oscillating pendulum bob, however,students included a force acting in the direction of movement of the bob at the twopositions above its equilibrium point. Our interview data showed that some studentsdrew conclusions about forces on the basis of assumptions concerning energy.

Reif (1987) and Chi et al. (1981) point out tha t some students seem to be unable toapply scientific laws in their most general form and are influenced by the objects thatmake up the system. This finding is supported by our observation that studentswhose responses match categories 14—16 apparently had difficulty in understanding

the motion of bodies acted on by impulsive (short-term) forces. For example,category 14 includes a force acting in the direction of the motion of the book (Fm ),but does not include a force acting in the direction of the motion of the objects inflight. Category 15 shows a motion force for projectiles, but not for lineardisplacement. Categories 5-8 consistently apply a motion force for linear andprojectile, but not for periodic motion.

All of categories 1-16 indicate consistent, internal logic. More than two-thirds ofthe university students (UNIV) and the advanced high school pupils (ADV) usedone of these categories. We conclude, therefore, tha t these students may have usedconsistent and meaningful conceptual categories to describe the forces acting onobjects in motion.

The responses of nearly 70% of the ordinary level pupils (O RD) and 90% of thepupils who had not studied physics (NO) did not match any of the 16 categories. Weconclude, therefore, that their conceptual categories are neither logical normeaningful at least according to the rules applied in this study.

Since this research is based on written responses without back-up interviews, wecannot claim that students actually use such categories or the rules that seeminglyunderlie them . Only further research in which, for example, students are asked toexplain their responses, can justify such a claim. However, given the small number of

categories (11) used by more than tw o-thirds of the university students (UNIV) andadvanced high school pupils (ADV), it is reasonable to assume that these categoriesare indeed meaningful.

Students' concep tual categories concerning reactive forces: objects at rest andobjects in motion

Here, an attempt is made to answer research question 4: do students consistentlyinclude or exclude the forces opposing gravity for objects at rest and for the same

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1 0 8 RESEARCH REPORTS

objects in motion? Two objects were investigated, a pendulum bob and a book on atable. Tables 5 and 6 present the findings.

At least 75% of all the respondees in each group answered consistently for thesystems at rest and in motion. T hey either included or excluded forces opposing the

force of gravity (T and N). Inconsistencies appeared in the pendulum problems: 25%of the ordinary level pupils (ORD) and 14% of those who hadn't studied physics(NO) excluded tension for the system at rest and included tension for the system inmotion. A 10th grade student who had not studied physics, said, in support of hisclaim that the string exerted a force on the moving bob: 'When the bob is moving,something must be holding it up .' A parallel belief was not identified for the book inmotion. Table 7 shows how the reactive forces (N and T) were perceived in allsystems where such forces appeared.

Tab le 7 shows that 79% of the university studen ts (U NIV ) and the advanced levelhigh school pupils (ADV) adhered to consistent beliefs, either correct or incorrect.

T able 5. Beliefs regardin g the pr ese nc e of a force exer ted by the string onthe pendulum bob at rest and in motion (percentages of respondees).

Pendulumat

rest

including TUNIVADVORDNO

% excluding TUNIVADVORDNO

Pendulum

% including T

938446

0

24

2514

in motion

% excluding T

1102

48

2984

T able 6. Beliefs regard ing the pr ese nc e of a force exerte d by the table on abook at rest and in motion (percentages of respondees).

Book in motion

Book

atrest

% including NUNIVADV

ORDN O

% excluding NUNIVA D VO R DN O

including N

9087

444

2164

% excluding N

00

00

58

5093

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STUDE NTS' CONCEPT S OF FORCE 109

Table 7. C onceptual catego ries relating to forces that oppose gravity forboth system s, pendulum and book, at rest and in mo tion (percentagesof respondees).

Book at

rest andin motion

including NUNIVADV/ \ l ) 1 \\ t\

N O

excluding NUNIVADVORDNO

Pendulum (at including T

847925

0300

rest and in motion) excluding T

32

1928

006

61

However, the ordinary level high school pupils (ORD) and those who had notstudied physics (NO) were inconsistent in noting the reactive forces; theyexpe rienced difficulty in recognizing t he tens ion in the strin g as a force acting on thependu lum bob .

Conceptual frameworksT ab le 8 show s the percentages of stud en ts who answered all ten qu estions correctly;that is, percentages of studen ts who consistently applied N ew ton 's laws for objects atrest and for objects in motion.

In addition to the category in which the correct Newtonian forces wereconsistently applied, 15 different categories describing students ' understanding ofthe forces acting on objects in motion were identified. These categories were cross-tabulated with those describing objects at rest (beyond the identification of reactiveforces), and an even larger number of conceptual frameworks was identified. This

technique yielded almost as many models as there were students and provided nouseful information.

Summary of findings

Many students in the sample, both prior to and after formal instruction inphysics, adhere to scientifically incorrect beliefs about the forces acting onobjects at rest and/or in motion.Prior to learning phy sics, less than 10% of the pup ils tested consistently adhe red

to the Aristotelian belief that no forces act on objects at rest. After instruction,this belief was virtually non-existent.T h e 'm otion imples a net force' framework is not consistently applied, even bypupils who have not studied physics. We would expect such pupils to indicateconsistently some force acting in the direc tion of the m otio n of any mov ing objectsince they presum ably believe that a force sustains the mo tion. T hi s expectationwas not supported by the data.

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1 1 0 RESEARCH REPORTS

Table 8 Percentages of respon dees giving correct answ ers for allquestions.

Respondees ( )

UNIVA D VO RDNO

462900

— Apparently consistent and coherent conceptual categories were identifiedregarding the forces acting on objects in motion. That is, the response setsrecurred and appear to be logical. More than two-thirds of the universitystudents and advanced high school pupils adhere to one of 11 such categories.

— Frameworks probably exist in students' minds as repositories for physics subjectmatter; however, except for students who consistently apply a Newtonianframework, they do not provide a perspective from which studen ts' beliefs aboutphysical behaviour may be predicted.

Conclusions and implications for instruction

This study shows that, like their counterparts abroad, many Israeli students, afterstudying physics, either do not understand, or have great difficulty in applying,New ton's laws to drawings of systems. The difficulties described here and in otherresearch work seem to reflect a problem that pervades all of education, that of thedistinction between the particular and the general. As Reif (1987) pointed out, manystudents are unable to identify particular instances of general rules or laws, oftenbeing unable to identify the important elements in a system and to reach appropriateconclusions.

These difficulties are greatly aggravated in physics instruction due to theinterference resulting from students' prior knowledge. We need conceptual changestrategies that focus not only on eliminating non-science beliefs like motion forces,but which develop abilities to apply general rules to particular instances and toextract general rules from particular instances. Toward this end, we are currentlydesigning software simulations of physical situations not reproducible in thelaboratory. These simulations present the logical outcomes of non-scientific beliefssuch as a book falling through a table as an outcome of neglecting the reactive forceexerted by the table. In this way, we attempt to refute pupils' prior knowledge and tohelp them to grasp the general applicability of physical laws over a wide range oftopics and situations (Finegold and Gorsky 1988).

References

CHI, M., FELTOVICH, P. and GLASER, R. 1981, Categorization and representation of physicsproblems by experts and novices. Cognitive Science, Vol. 5, pp. 121-152.

CHAMPAGNE, A., KLOPFER, L. and SOLOMON, C. 1980, Factors influencing the learning ofclassical mechanics. American Journal of Physics, Vol. 48, pp. 1074-1079.

CLEMENT, J. 1982, Students' preconceptions in introductory mechanics. American Journal ofPhysics, Vol. 50, pp. 60-71.

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CLEMENT, J. 1983, Students' alternative conceptions in mechanics: A coherent system ofpreconceptions A paper presented at the Conference on Stud ents' Misconceptions inScience and Mathem atics, Cornell University, Ithaca, New York.

CLOUGH, E. and DRIVER, R. 1986, A study of consistency in the use of stude nts' conceptualframeworks across different task contexts. Science Education, Vol. 70, No. 4,

pp . 473-496.E E L R. 1972, Essentials of educational measurement (New Jersey: Prentice-Hall, 2nd edition).ENGEL, E. and DRIVER, R. 1982, Children s interpretations of scientific phenomena-analysis of

descriptive data. A paper presented at the British Educational Research AssociationAnnual Conference, University St. Andrews, Scotland.

FINEGOLD, M. and GORSKY, P. 1988, Learning about forces: Simulating the outcomes ofpupils' m isconceptions. Instructional Science, Vol. 17, pp. 251-261.

GILBERT, J. and OSBORNE, R. 1980, Identifying science students concepts: The IAI approach.In W. Archenhold (ed.), Cognitive Development Research in Science and Mathem atics(Centre for Studies in Science Education, University of Leeds, Leeds).

GILBERT, J., WATTS, M. and OSBORNE, J. 1982, Stud ents' conceptions of ideas in mechanics.Physics Educ, Vol. 17, pp. 62-66.

GILBERT, J. and WATTS, M. 1983, Misconceptions and alternative conceptions: Changingperspectives in science education. Studies in Science Education, Vol. 10, pp. 61-98.

HALLOUN, I. and HESTENES, D. 1985 a, The initial state of college students . American Journalof Physics, Vol. 53, pp. 1043-1055.

HALLOUN, I. and HESTENES, D. 1985 b , C ommon sense concepts about motion. AmericanJournal of Physics, Vol. 53, pp. 1056-1065.

H E L M H. 1981, Conceptual misunderstandings in physics. In Perspective 3, School ofEducation, University of Exeter, Exeter.

MINSTRELL, J. 1982, Explaining the 'at rest ' condition of an object. Physics Teacher, Vol. 20,pp. 10-14.

OSBORNE, R. 1980, Force: Learning in science project. Working paper No. 16. University ofWaikato, Hamilton, NZ.

R E I F F. 1987, Instructional design, cognition, and technology: Applications to the teaching ofscientific concepts. Journal of Research in Science Teaching, Vol. 24, pp. 309-324.

VIENNOT, L. 1979, Spontaneous reasoning in elementary dynamics. European Journal ofScience Education, Vol. 1, pp. 205-221.

WATTS, D. 1983, A study of schoolchildren's alternative frameworks of the concept of force.European Journal of Science Education, Vol. 4, pp. 217-230.

WATTS, D. and ZYLBERSZTAJN, A. 1981, A survey of some children's ideas about force. PhysicsEducation, Vol. 15, pp. 360-365.

CorrespondenceDr M. Finegold, Department of Education in Technology & Science, Technion-IsraelInstitute of Technology, Technion City, Haifa 32000, Israel.

Appendix A: test que stions

In the questions tha t follow:

— ignore the forces resulting from air pressure and air friction,— objects in motion are rigid and are not spinning.Draw arrows showing each of the forces acting on the objects in question and nameeach force. Do not show only the total net force.

Questions 1 and 2 describe a mathematical pendulum - a point mass suspended froma cord of negligible mass.

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112

1. A stationary pendulum bob.

RESEARCH REPORTS

2. The pendulum bob, at each of the th ree positions below, is moving from left toright. Draw and label each of the forces, if any, acting on the bob at all threepositions.

2a 2b: The bob is at itslowest point

2c

3. A book is at rest on a flat table :

4. A book is moving on a flat, frictionless table from left to right. The movementresulted from the release of a compressed spring and, at this moment, no physicalcontact exists between the spring and the book.

I I

5. A cannonball, shot from a cannon, follows the trajectory shown below. Draw andlabel each of the forces, if any, acting on the cannonball at the points labelled5a, 5b and 5c.

The ball is atits highest point

5b A

5a *

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6. A particle is thro w n straig ht up from po int A. Dr aw and label the force or forces, ifany, acting on the particle as it passes upward through point B.

D

Appendix B

Table 9. Students w hos e responses m atch ed the categories show n intable 4 (percentages).

Category

123456789

10111213141516

Total

UNIV

46000300730023305

72

ADV

29400503370020149

67

ORD

000006

13060000060

31

NO

0022000004200000

10

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