effects of conceptual assignments and conceptual change discussions on students' misconceptions...

JOURNAL OF RESEARCH IN SCIENCE TEACHING VOL. 39, NO. 10, PP. 1001–1015 (2002)

Effects of Conceptual Assignments and Conceptual Change Discussions onStudents’ Misconceptions and Achievement Regarding Force and Motion

Ali Eryilmaz

Department of Science Education, Faculty of Education, Middle East Technical University,

06531, Ankara, Turkey

Received 31 May 2002; Accepted 25 June 2002

Abstract: The purpose of this study was to investigate the effects of conceptual assignments and

conceptual change discussions on students’ achievement and misconceptions about force and motion. The

study was conducted with 6 physics teachers and their 18 classes, consisting of 396 high school physics

students. The teachers administered the Force Misconception and Force Achievement Tests to their physics

classes as a pretest. The results obtained were used to match the 18 classes statistically. Students assigned to

the conceptual assignment protocol completed five conceptual assignments about force and motion.

Students assigned to the discussion method participated in conceptual change discussions. At the end of

the 8-week treatment period, the same tests were administered to all students as a posttest. The data were

analyzed by using multivariate analysis of covariance, followed by protected univariate F test and step-

down analysis. The statistical results showed that the conceptual change discussion was an effective means

of reducing the number of misconceptions students held about force and motion. The conceptual change

discussion was also found significantly effective in improving students’ achievement in force and motion.

� 2002 Wiley Periodicals, Inc. J Res Sci Teach 39: 1001–1015, 2002

Intuitive beliefs that students develop on their own before taking the first course in physics

have a special place among the sources of difficulties students come across in physics. Researchers

have used different names for this: Novak (1977) called them preconceptions, Driver & Easley

(1978) referred to them as alternative conceptions, Helm (1980) called them misconceptions,

Sutton (1980) preferred the term children’s scientific intuitions, Gilbert, Watts, & Osborne (1982)

called them children’s science, Halloun & Hestenes (1985b) called them common sense concepts,

and Pines & West (1986) called them spontaneous knowledge. In this article, ‘‘preconceptions’’ is

used to indicate all beliefs students have before enrolling in their first formal physics course,

whereas ‘‘misconceptions’’ refers only to those beliefs students have that contradict accepted

scientific theories. Students’ misconceptions are related to (a) key concepts such as mass, velocity,

acceleration, force, etc.; and (b) fundamental principles and models such as Newton’s laws,

conservation laws, and others.

Correspondence to: A. Eryilmaz; E-mail: [email protected]

DOI 10.1002/tea.10054

Published online in Wiley InterScience (www.interscience.wiley.com).

� 2002 Wiley Periodicals, Inc.

Mechanics is the most frequently studied subject in physics; in mechanics, force and

motion are the most widely discussed topics. The following paragraphs list common mis-

conceptions that were widely analyzed and discussed in the literature, and thus emphasized in

this study.

Students often confuse the position and velocity of an object. When two objects have the same

position, some students think that they have the same velocity as well. Some students confuse the

velocity and acceleration of an object. When two objects have the same speed, students think

that they have the same acceleration at that time (Rosenquist & McDermott, 1987; Trowbridge

& McDermott, 1980, 1981; Whitaker, 1983).

Impetus is conceived to be an inanimate motive power or intrinsic force that keeps things

moving. Impetus can be gained, lost, or reconstructed in a variety of ways varying from student to

student. Furthermore, some students believe in circular impetus that tends to move objects in

circles (Caramazza, McCloskey, & Green, 1981; Halloun & Hestenes, 1985b; McCloskey & Kohl,

1983).

Some students believe that the speed of an object decreases even though the net force acting

upon it is zero. Students have difficulty visualizing a frictionless world (Halloun & Hestenes,

1985b).

Some students share an idea that an applied force is necessary for the continuity of motion at a

constant velocity although a frictionless medium is assumed (motion implies force misconcep-

tion). It is found that such imagined forces are especially common in explanations of motion that

continues in the case of obvious opposing forces. In addition, some students believe that such a

force dies out or increases to account for changes in an object’s speed (Champagne, Klopfer, &

Anderson, 1980; Clement, 1982; Gunstone, 1987; Sadanand & Kess, 1990; Sequeira & Leite,

1991; Whitaker, 1983).

Students sometimes believe that there is a linear relationship between force and velocity

(instead of force and acceleration). Therefore, these students expect a constant velocity from a

constant force (Champagne et al., 1980; Sequeira & Leite, 1991).

Students often interpret the term interaction by a conflict metaphor. They see an interaction as

a struggle between opposing forces. It follows from the metaphor that victory belongs to the

stronger. In a conflict, the more forceful exerts the greater force. Here more forceful can mean

bigger, greater mass, or more active. Hence, they believe that greater mass implies greater force or

the most active one produces greatest force (Maloney, 1984; Minstrell, 1982; Sadanand & Kess,

1990; Sequeira & Leite, 1991). Students believe that centrifugal force is a distinct kind of force and

exists in a Newtonian frame of reference (Gunstone, 1987).

Students believe that a heavier weight causes a bigger acceleration in free fall (i.e., heavier

objects fall faster) or that gravity varies significantly over a few meters, whereas the variation is

actually about 1 part in 1013. Moreover, some students also believe that gravity does not act until

impetus wears down (Gunstone & White, 1981; Minstrell, 1982).

During or after developing measuring tools to assess students’ preconceptions, the re-

searchers began to find ways to remedy these misconceptions. Otherwise these beliefs may remain

intact in the face of normal everyday teaching (Brown & Clement, 1987; Clement, 1982; Halloun

& Hestenes, 1985a; Viennot, 1979). Constructivism (Von Glasersfeld, 1990) and the parallel

conceptual change strategy display a common emphasis by the researchers. The famous condi-

tions for conceptual change are as follows: (a) There must be dissatisfaction with existing

conceptions. Scientists and students are unlikely to make major changes in their concepts until

they believe that less radical changes will not work. (b) A new conception must be intelligible.

(c) A new conception must appear initially plausible. Any new concept adopted must at least

appear to have the capacity to solve the problems generated by its predecessors. Otherwise, it will

1002 ERYILMAZ

not appear as a plausible choice. Plausibility is also a result of consistency of the concepts with

other knowledge. (d) A new concept should suggest the possibility of a fruitful research program.

It should have the potential to be extended and open up new areas of inquiry (Posner, Strike,

Hewson, & Gertzog, 1982, p. 214).

In parallel with these conditions, some researchers applied them in different formats for

different purposes. Nachtigall (as cited in Van Hise, 1988) used it for training physics teachers; and

the Problem-Posing Physics program developed by Brouwer (1984) for training university

lecturers. These programs focus on a system designed to provide students with the cognitive

conflict necessary to help them assimilate conceptions of physics into their everyday life. The key

points of these programs are as follows. The programs (a) ensure that students are aware of their

preconceptions (Nachtigall), (b) allow students to make their own conceptions or hypotheses

explicit and test them, (Nachtigall & Brouwer), (c) confront students with situations where their

preconceptions cannot be used as explanations (Nachtigall), (d) let students become aware of this

conflict (Nachtigall), (e) help students to accommodate the new ideas presented to them

(Nachtigall), (f ) make students conscious of the fact that their new knowledge is more powerful

than their previous ideas by applying the model in familiar and new situations (Nachtigall &

Brouwer), (g) give students a feeling of progress and growth in mental power and help students

develop confidence in themselves and their abilities (Nachtigall), and (h) test scientific under-

standing both conceptually and quantitatively (Brouwer).

Some researchers suggested using conceptual assignments to establish the first four steps of

the conceptual change strategy explained above. Nevertheless, in the literature this is one area in

which few studies have been conducted. Stavy & Berkowitz (1980) noted the importance of

homework problems in creating the cognitive conflicts necessary for preparation of the conceptual

change.

There are a number of research studies in students’ misconceptions about force and motion

that cannot all be cited in the context of this article. One can summarize the results of these studies

as follows: (a) Students frequently have preconceptions about physics concepts that have been

acquired before the formal study of physics (Driver & Easley, 1978; Halloun & Hestenes, 1985b;

Helm, 1980; Novak, 1977; Pines & West, 1986; Sutton, 1980; Watts & Pope, 1989). (b) These

preconceptions often significantly differ in ways from those that students are expected to learn

in physics courses (Halloun & Hestenes, 1985b; Helm, 1980; Maloney, 1984). (c) The pre-

conceptions related to particular physics concepts show consistency across diverse samples of

average students, honor students, and even physics teachers (Eryilmaz, 1992; Peters, 1982). (d)

The most important factors that affect students’ achievement in physics are students’ pre-

conceptions, gender, level of cognitive development, and mathematics ability (Champagne

et al., 1980; Eryilmaz, 1992; Halloun & Hestenes, 1985a). (e) Although traditional instructional

methods have a significant effect on students’ misconceptions, it is far from being sufficient in

remediating students’ misconceptions that are persistent and highly resistant to change (Brown &

Clement, 1987; Clement, 1982; Eryilmaz, 1992; Halloun & Hestenes, 1985a; Viennot, 1979). (f)

Some of the most common suggestions to remedy students’ misconceptions include teaching

physics conceptually, and by conceptual discussion methods (Brouwer, 1984; Posner et al., 1982).

(g) Most studies reviewed lacked of internal validity. The most common threat was subjects’

characteristics. (h) None of the research studies reported the power or the effect size for their

studies.

These summary results suggest that there is a need for research to develop a treatment by using

the suggestions of previous studies to remedy these misconceptions and test the effectiveness of

the treatment while controlling threats to internal validity by using appropriate research designs

and statistical methods. This study aims to accomplish these goals.

STUDENTS’ VIEWS OF FORCE AND MOTION 1003

Method

Population and Subjects

The accessible population was high school students enrolled in physics courses in both public

and private high schools in Brevard County, Florida. The study sample drawn from the accessible

population was a sample of convenience. It included the students of Brevard County physics

teachers who volunteered to participate in a physics misconception workshop and the study. Six

physics teachers and their 18 physics classes, consisting of 396 high school students, were

involved in the study.

The study sample was composed of 11th- and 12th-grade students. The ages of subjects

ranged from 15 to 19 years, with a mean of 16.8 years; 59% of the students were male. In analyzing

students’ prior experience in physics, 16% of the students had previously completed at least one

physics course. Thirteen percent of the students passed and 2% had failed. Moreover, 1% of

students had previously taken more than one physics course and passed the last one.

Measuring Tools

There are two measuring tools in the study: Force Misconception Test (FMT) and Force

Achievement Test (FAT). The purpose of the FMT is to assess students’ misconceptions about

force and motion. It is a diagnostic test and wrong choices on the test are more informative than

correct choices. All questions in the test are conceptual. On the other hand, the purpose of the FAT

is to assess students’ achievement in force and motion. Therefore, the multiple choice distracters

in the FAT are not alternative conceptions as they are in the FMT. However, they include typical

students’ mistakes, which are more often due to deficient understanding rather than carelessness.

Most questions in the FAT are quantitative.

The FMTand FAT differ mainly in their purposes and contents. The other difference between

the tests is the procedure followed in the development of the tests. This is explained in the

following sections.

FMT. Several studies have been done to describe students’ misconceptions in mechanics

courses. Thus, many diagnostic tests and questions have been developed and validated

(Caramazza et al., 1981; Clement, 1982; Eryilmaz, 1992; Halloun & Hestenes, 1985a; Hestenes,

Wells, & Swackhamer, 1992; Maloney, 1984; Minstrell, 1982; Sadanand & Kess, 1990). From

the pool of questions, the researcher developed a diagnostic test that consisted of 18 multiple

choice items. Thirteen of these were taken from the Force Concept Inventory (FCI) developed

by Hestenes, Wells, & Swackhamer (1992); two items were taken from Halloun & Hestenes

(1985a); two items about circular impetus were taken from the study by Caramazza et al. (1981);

and the last one about centrifugal force and motion implies force misconceptions from

Clement (1982). The questions out of the FCI replaced the corresponding questions in the

FMT. It was found that distracters of these questions in the FMT attracted more students

than the corresponding questions in the FCI (Eryilmaz, 1992). Internal reliability of the test

was calculated by using Cronbach alpha. The value obtained for this reliability coefficient

was .70. This value indicates moderate or relatively high reliability for a diagnostic test.

Students’ force misconception scores consisted of the number of items correct on the force

misconception posttest. The higher score on the test indicates fewer misconceptions about

force and motion.

1004 ERYILMAZ

FAT. Some articles reviewed in this study used course grades as an indicator of students’

achievement in physics (Halloun & Hestenes, 1985a). Course grades may not reflect the

achievement of the students owing to the reliability and validity of the tests used in the course.

Therefore, the FAT with 31 multiple choice items was developed to assess students’ achievement

on force and motion concepts independent of course grades. The FAT is designed to assess

students’ conceptual as well as quantitative understanding of basic Newtonian concepts. The table

of specification and the table of test specification were prepared using the physics textbooks that

were in use in Brevard County (Resnick et al., 1992; Taffel, 1992; Trinklein, 1990; Zitzewitz,

1995). This test was administered to 46 senior students in a nearby high school as a pilot study.

Items possessing item difficulty <.1 or > .90 and discriminating power <.2 were discarded.

Hence, the FAT consisting of 18 multiple choice items was developed. Most of these questions

were either directly taken or were slightly adapted from the studies of previous researchers

(9 questions from the Mechanics Baseline Test developed by Hestenes & Wells (1992) and 6 from

Turkish University entrance examinations). The researcher developed three questions. The test

was checked by a physics professor and a high school physics teacher for face and content validity

by comparing the content of the test with the test specification. Possible achievement scores

ranged from 0 to 18. Students’ achievement scores consisted of the number of items correct on the

force achievement posttest. The higher score indicates higher achievement.

Internal reliability of the test was calculated using Cronbach alpha. The value obtained for this

reliability coefficient was .74 for the posttest. This value indicates relatively high reliability

for a researcher developed achievement test.

Design and Procedures

Physics teachers at senior high schools in the local area were invited to participate in this

study. Each physics class of teachers who responded positively to the invitation was randomly

assigned to one of the four groups shown in Table 1. Thus, each teacher used different treatments

with different classes depending on the number of classes she or he had. The experiment was a

2� 2 factorial design. The teachers participating in this quasi-experimental study were trained for

9 hours by the researcher to standardize the administrative procedures and the implementation of

the treatments.

The teachers administered the FATand FMT to all groups as a pretest to assess students’ initial

conceptual and qualitative understanding of basic Newtonian concepts during the second week of

the school term. Later, these data were used to match students statistically in different treatment

groups on prior knowledge. Throughout the experiment, the researcher observed the control and

treatment classes to ensure that all teachers followed the guidelines and procedures for treatment

verification purposes. Finally, during the 10th week of the school term the teachers again

administered the FAT and FMT as a posttest. These data were used to analyze the effect of the

treatment on students’ conceptual and quantitative understandings of basic Newtonian concepts.

All tests were scored using a computer program previously developed by Eryilmaz (1992).

Table 1

Factorial design of the experiment

Assignments

Conceptual Quantitative

Conceptual Change Discussion Yes Group 1 Group 2No Group 3 Group 4


Variables of the Study

There were eight variables in the study. Students’ gender and age, students’ prior experience

with physics, students’ prior knowledge about force and motion, teacher, and methods of instruc-

tion were independent variables. Students’ misconceptions about, and students’ achievement in

force and motion were dependent variables.

Students’ pretest scores on the FAT and FMT were highly correlated to each other. Hence,

they were summed to yield students’ prior knowledge about force and motion. The methods of

instruction had four levels: conceptual change discussion, conceptual assignments, quantitative

assignments, and conventional lecturing. Three contrast-coded variables were used to represent

these groups. Prior experience with physics was operationally defined as a student’s response to

the following question: Have you taken any course in physics before this one? (a) No, I did not take

any course before. (b) Yes, I took one and failed. (c) Yes, I took one and passed. (d) Yes, I took more

than one and failed the last one. (e) Yes, I took more than one and passed the last one. Student’s

responses were coded 0, 1, 2, 3, or 4, respectively, for the purpose of analysis.

Treatments

Assignment Protocol (Conceptual Assignments versus Quantitative Assignments). Some

students had 5 conceptual assignments and some students had 5 quantitative assignments on the

same topics. The conceptual assignments involve physical phenomena from real life related to force

and motion. Students were asked to perform and/or observe a phenomenon and then explain it.

However, the quantitative assignments do not involve an observation or explanation. Students

were asked to calculate some physical quantities (e.g., distance, time, speed, acceleration, net force,

normal force). All assignments were essay type questions. An example for the conceptual assig-

nments is as follows: Experience the following while you are sitting in a car, bus, or any other means

of transportation: (a) while you are constantly increasing your speed, (b) while you are slowing down

(e.g., applying the brakes), and (c) while you are traveling at constant speed in a vehicle going around

a corner. Then, answer the following three questions for each of the situation above. Are your

findings for the three situations in agreement? Why? (a) What do you experience? In other words, in

what direction is your body leaning? (b) What is the net force acting on the car and you? (c) Compare

the direction your body is taking with the direction of the net force acting on you.

An example for the quantitative assignments is as follows: It takes a 615-kg racing car 14.3 s

to travel at a uniform speed around a circular racetrack of 50 m radius. (a) What is the acceleration

of the car? (b) What average force must the track exert on the tires to produce this acceleration?

Students in the conceptual assignment groups had conceptual assignments in the 2nd, 4th, 5th,

7th, and 8th weeks of the fall semester. All the groups did not follow these dates exactly. They

varied slightly for some groups depending on the contents the students were studying at that time.

Students in the quantitative assignment groups had quantitative assignments in the same weeks.

All students were asked to turn in a brief answer to each assignment in 1 week. The assignments

turned in were evaluated regarding whether the students studied the assignments. If an assignment

was turned in and was related to the question asked, this student was assumed to have completed

the assignments. If not, the student was assumed not to have completed the assignment. In the

latter case the student was asked to redo the assignment.

Conceptual Change Discussion Protocol (Conceptual Change Discussions and Conven-

tional Lecturing versus Conventional Lecturing Alone). Students in the conceptual change

1006 ERYILMAZ

discussion groups had conceptual change discussions for about 20 minutes during the 3rd, 5th, 7th,

8th, and 9th weeks of the Fall semester. These dates were not followed exactly by all groups. They

varied slightly for some groups depending on the content that students were studying at that time.

The conceptual assignments were chosen as topics for the discussions for all groups. Discussions

were held according to the following guidelines that were provided to the teachers:

1. Use the conceptual question as an exposing event that helps students expose their

conceptions about a specific concept or rule.

2. Allow all students to make their own conceptions or hypotheses explicit (verbally and

pictorially).

3. Ask what students believe or think about the phenomena and why they think so.

4. Write or draw students’ ideas on the blackboard even if they are not correct.

5. Be neutral during the discussion. If one or some students give the correct answer, take

it as another suggestion and play the devil’s advocate.

6. Be patient. Give enough time to the students to think and respond to the questions.

7. Ask only descriptive questions in this part to understand what students really think

about the phenomena.

8. Try to get more students involved in the discussion by asking questions of each student.

9. Assist students in stating their ideas clearly and concisely, thereby making them

aware of the elements in their own preconceptions.

10. Encourage confrontation in which students debate the pros and cons of their different

preconceptions and increase their awareness and understanding of the differences

between their own preconceptions and those of their classmates.

11. Encourage interaction among students.

12. Create a discrepant event, one that creates conflict between exposed preconceptions

and some observed phenomenon that students cannot explain.

13. Let students become aware of this conflict; cognitive dissonance, conceptual conflict,

or disequilibrium.

14. Help students to accommodate the new ideas presented to them. The teacher does not

bring students the message, but she or he makes them aware of their situation through

dialogue.

15. Make a brief summary from beginning to the end of the discussion.

16. Show explicitly where oversimplification, exemplification, association, and multiple

representations have happened, if any. If not, give exemplification, associations with

other topics, and multiple representations for the topic.

17. Give students a feeling of progress and growth in mental power, and help them

develop confidence in themselves and their abilities.

Power Analysis

An essential and primary decision in the power analysis is determination of the population

effect size before the study. Cohen & Cohen (1983) offered the following suggested values: small,

ES¼ 0.20; medium, ES¼ 0.50; and large ES¼ 0.80 [ES¼ (Mean of the experimental group�Mean of the control group)/Standard deviation of control group]. Because the effect of the

treatment outlined above is unknown in the literature, even a small (0.20) or medium (0.50) effect

size in the study may have practical significance.

AType I hypothesis-wise error rate [the rate of rejecting a true null hypothesis (a)] of .05 and a

Type II error rate [the rate of failing to reject a false null hypothesis (b)] of .20 are set a priori to any

hypothesis testing. Sample sizes of 167 students were calculated by using Cohen’s power table for

a medium effect size. The sample of the study was 396 students; therefore, the statistical power of

the study is > 80% (1� b).


Results

Descriptive Statistics

Table 2 presents the pre- and posttest achievement and misconception scores of all students in

the study, according to two main effects. Although all groups showed mean increases in their

achievement and misconception scores from pretest to posttest, the means for students’ posttest

achievement and misconceptions scores were too low. The effect sizes vary from 0.45 to 0.78

(medium to high). Moreover, the mean values vary from 5.42 to 6.42 for the force achievement

scores and from 7.13 to 8.07 for the force misconception scores. The most apparent difference

evident from this table was between control and experimental groups. All of the experimental

groups’ effect sizes were greater than control groups’ effect sizes, with the sole exception of the

experimental group for conceptual assignments whose effect size was less than the control groups’

effect size for the misconception scores. Also, with two treatments together there is a large

difference in the effect size between treatment and control groups. The groups with two treatments

together have a much higher effect size as compared to the groups with a single treatment for

the achievement scores. However, these effect size calculations were not based on adjusted

means of students’ achievement. Therefore, the real effect size values are different from these

values. Overall, the variability in scores remained relatively stable from pretest to posttest.

Inferential Statistics

Determination of the Covariates. Five independent variables (age, prior experience with

physics, prior knowledge, teacher, and gender) were predetermined as potential confounding

factors to the study. Therefore, these variables were used as covariates to statistically equalize the

differences among the groups. Cohen & Cohen (1983) warned new researchers not to include

many variables in the covariate set. They noted, ‘‘We raised a red flag against such practices in

general MRC analysis. The ‘less is more’ principle holds with even greater force in Analysis of

Partial Variance (APV)’’ (p. 412). Therefore, they suggested that variables in the covariate set

should be a few, reliably measured, and highly correlated with the dependent variable. All

Table 2

Force Achievement Test score means, standard deviations, and effect sizes

Force Achievement Force Misconceptions

N

Posttest (Pretest) Posttest (Pretest)

M SD ES M SD ES

Conceptual AssignmentTreatment (G1 & G3) 203 6.26 (5.07) 3.02 (2.42) 0.49 7.75 (6.32) 2.89 (2.70) 0.53Control (G2 & G4) 193 6.07 (4.94) 2.93 (2.71) 0.42 7.82 (5.80) 2.89 (2.76) 0.73

DiscussionTreatment (G1 & G2) 207 6.42 (5.13) 2.75 (2.54) 0.51 8.07 (5.85) 3.05 (2.84) 0.78Control (G3 & G4) 189 5.89 (4.88) 3.18 (2.59) 0.39 7.47 (6.30) 2.67 (2.60) 0.45

Two treatments togetherTreatment (G1) 113 6.15 (4.97) 2.52 (2.11) 0.56 7.68 (5.79) 2.80 (2.70) 0.70Control (G4) 99 5.42 (4.59) 2.74 (2.36) 0.35 7.13 (5.56) 2.27 (2.29) 0.68

Note. N¼ 396; SD¼ standard deviation; ES¼ effect size; G1, G2, G3, and G4 are group numbers in Table 1.

1008 ERYILMAZ

predetermined independent variables in the covariate set have been correlated with the two

dependent variables (force achievement and force misconceptions). The results of these corre-

lations and their significance are given in Table 3. As seen in the table, all independent variables in

the covariate set have significant correlations with the two dependent variables except students’

age and teacher. Therefore, the age and teacher were discarded from the covariate set. The

significant IVs (prior experience with physics, prior knowledge, and gender) remained in the

covariate set for the following inferential analyses.

Missing Data. The issue of missing data was addressed before examining the inferential tests

used in this study. Initial data were gathered for 410 high school physics students. At the end of the

8-week treatment period, 396 high school physics students were posttested for force achievement

and force misconceptions. The loss of 14 students (3.4%) was due to a variety of reasons including

dropping the course at some point during the experiment, changing sections during the course of

the study, or being absent on the day of the posttest. The 14 students not completing the posttest

were dropped from the statistical analyses of the study as suggested by Cohen & Cohen (1983).

Thirty (7.6%) of the 396 students posttested did not complete the force achievement and

misconception pretests. Therefore, a dummy variable was created to represent this missing

independent variable (IV) data (0¼ data not missing; 1¼ data missing). The increases (I) in model

variance (R2) owing to the addition of the missing data dummy variable after three variables in the

covariates (students’ prior experience with physics, prior knowledge, and gender) were significant

for force achievement, F(1, 391)¼ 5.16; p� .05, and for force misconceptions, F(1, 391)¼ 9.50;

p� .05. Therefore, the missing data variable was retained as an independent variable, and missing

pretest values were replaced with the mean pretest scores of the entire study group.

Homogeneity of Regression. All analyses of partial variance designs [analysis of covariance

(ANCOVA) or multivariate analysis of covariance (MANCOVA)] have the assumption of homo-

geneity of regression. This assumption is that the slope of the regression of a dependent variable on

a covariate is constant over the different values of group membership. The increases (I) in

explained model variance (R2) due to the addition of the 12 interaction variables (after 7 variables

in the covariates and group memberships) did not result in significant variance change for force

achievement, F(19, 376)¼ 1.17; p > .05, and force misconceptions, F(19, 376)¼ 1.10; p > .05.

This means that the homogeneity of regression assumption can be retained for this model. In

other words, the interaction set can be discarded, and therefore excluded from further inferential

statistical analyses.

Table 3

Significance test of correlation between covariates and two dependent variables

Variables

Correlation Coefficient

Force Misconceptions Force Achievement

Age .030 .083Prior experience with physics .231* .338*Prior knowledge .626* .606*Teacher .063 .022Gender �.315* �.202*

Note. N¼ 396.

*p� .05.


The MANCOVA Model. A MANCOVA was conducted using force achievement and force

misconception scores as the dependent measures. It used students’ prior experience with physics,

prior knowledge, gender, and missing values of prior knowledge as the covariates. Conceptual

assignments, discussion and their interaction were used to determine group membership. As can

be seen from their respective multivariate Fs in Table 4, the covariates used in this study per-

formed the function for which they were intended. All accounted for a significant portion of model

variance. This provided good evidence that the participants were adequately matched by the

inclusion of these covariates. The table also shows a significant main effect for discussion, Wilk’s

L¼ .964; F(2, 387)¼ 7.11; p< .05; and nonsignificant effects for conceptual assignments, Wilk’s

L¼ .995; F(2, 387)¼ .94; p > .05, and treatments’ interaction, Wilk’s L¼ .990; F(2, 387)¼1.89; p > .05.

Follow-up Analyses. Two models were used as follow-up analyses subsequent to the

significant omnibus MANCOVA presented above. These are protected univariate F tests and step-

down analysis. These follow-up procedures were taken to investigate the unique importance of

each dependent variable in the model. Readers should note that in the follow-up procedures

described below, only the discussion effect was subject to investigation because it was found to be

significant in the omnibus test.

Protected Univariate F Tests. Tabachnick & Fidell (1989) suggested that univariate tests

should be performed at an alpha level adjusted for the number of tests to be performed to control

Type I error rates adequately. Therefore, in the following analysis, alpha was taken as .025 (i.e.,

.05/2). Two follow-up univariate ANCOVAs for the dependent variables showed that the effect of

the discussion on both force achievement, F(1, 388)¼ 6.86; p¼ .0092, and force misconceptions,

F(1, 388)¼ 11.39; p¼ .0008, were significant at the adjusted alpha. Examination of covariate-

adjusted means showed that the directions of these effects were in favor of the discussion groups in

both cases. The discussion groups showed significantly higher achievement, mean¼ 5.99, and

fewer misconceptions, mean¼ 7.55, when compared with their control groups, means¼ 5.36 and

6.78 for achievement and misconceptions, respectively. These statistics therefore provided a

support for the hypothesis that, when prior experience with physics, prior knowledge, and gender

have been controlled, students experiencing conceptual discussions and conventional lecturing

Table 4

Multivariate analysis of covariance of Force Achievement and Force Misconceptions

Source of Variance Wilk’s L Num. df Den. df Multivariate F

CovariatesPrior experience with physics .978 2 387 4.26*Prior knowledge .620 2 387 117.35*Gender .965 2 387 6.89*Missing data IV .970 2 387 5.90*

Group membershipsConceptual assignment .995 2 387 0.94Discussion .964 2 387 7.11*C. assignment�Discussion .995 2 387 1.02

Note. N¼ 396.

*p� .05.

1010 ERYILMAZ

will have higher force achievement and fewer force misconceptions compared with students

experiencing conventional lecturing alone.

Step-Down Analysis. Haase & Ellis (1987) stated that the limitation in using univariate F

tests as the follow-up procedure is that it ignores any correlation between dependent variables.

This may give a greater degree of importance to a single dependent variable than truly warranted.

Step-down analysis as described by Tabachnick & Fidell (1989) was used as a second follow-

up procedure to test this. Priorities of dependent variables for the study were important in this

analysis. Therefore, two step-down analyses were performed, one with force achievement as

the dependent variable of highest priority and one with force misconceptions as the depen-

dent variable of highest priority. Step-down F tests were performed at an alpha level of .025

(i.e., .05/2).

In the first step-down F test, the force achievement scores were analyzed with the force

misconception scores acting as an additional covariate so that any variance overlap between the

force misconceptions and achievement was taken into consideration. The effect of the discussion

method was not significant, F(1, 387)¼ 2.76; p¼ .0973. This indicates that the effect of the

discussion method on the force achievement after accounting its effect on the force miscon-

ceptions was not significant. In other words, the students’ achievement was not significantly and

uniquely affected by the discussion method after its effect on the students’ misconceptions.

The second step-down F test was performed to assess the effect of the discussion method on

the force misconceptions beyond its effect on the force achievement. When force misconception

scores were analyzed with the force achievement scores acting as an additional covariate, the

effect of the discussion method was still significant, F(1, 387)¼ 37.41; p¼ .0074. This indicates

that the effect of the discussion method on force misconceptions after accounting its effect on

force achievement was also significant. In other words, force misconceptions were also signi-

ficantly and uniquely affected by the discussion method after its significant and unique effect on

the force achievement.

Conclusions, Discussion, and Implications

The main purpose of this study was to evaluate the effects of conceptual assignments and

conceptual change discussion method on improving students’ achievement and remedying

students’ misconceptions about force and motion. To accomplish this goal, the FATand FMTwere

developed and validated, five conceptual assignments were developed to allow students to observe

and think about some daily life phenomena, and conceptual change discussions were held for

students to talk about what they observed and what they inferred from their observations while

they were doing the conceptual assignments.

In summary, the following conclusions are offered. (a) The conceptual change discussion was

an effective means of reducing the number of misconceptions students held about force and

motion. (b) The conceptual change discussion was also significantly effective in improving

students’ physics achievement in force and motion. (c) Further examination of this treatment

effect through step-down F tests showed that although the force misconceptions were significantly

and uniquely affected by the discussion method after its significant and unique effect on the force

achievement, students’ achievement were not significantly and uniquely affected by the dis-

cussion method after its significant and unique effect on the students’ misconceptions. (d) Weak

evidence (in the form of nonsignificant treatment and interaction effects) was provided by the

study that the conceptual assignments and the combined effect of the treatments (the conceptual


assignments and the conceptual change discussions) were effective means of reducing the number

of misconceptions students held, and significantly improved students’ physics achievement in

force and motion. (e) A gender difference was observed in the misconceptions. Male students

had fewer misconceptions than female students in force and motion. This difference was not

manifested in the students’ achievement scores.

The experimental group for conceptual assignments had a smaller effect size than the control

on the misconception score noted in Table 2. The conceptual assignments allowed students to

observe and think about some daily life phenomena. In other words, this in itself reinforced

students’ misconceptions derived from years of personal experience. However, when conceptual

assignments are accompanied by conceptual change discussion, students’ misconceptions are

remediated.

Informal interviews with the teachers in the discussion groups revealed that these teachers had

two difficulties in applying the discussion method: determining and using exposing and discrepant

events. Teachers in Group 2 had difficulty initiating the conceptual change discussions because

their students did not do the conceptual assignments. Instead, they tried to imagine the phenomena

in the conceptual assignments and then discuss them. However, teachers in Group 1 did not have

this difficulty because their students had already completed the conceptual assignments. Second,

all teachers in the discussion groups (Groups 1 and 2) had problems of finding discrepant events for

each misconception. The teachers and the researcher believe that helping teachers in these

problems will improve the effect of the conceptual change discussion.

When the treatment effect translated to effect sizes, the follow-up results yielded ESs of

�0.23 for the force misconceptions and 0.18 for the force achievement. The students who

participated in the conceptual discussions (N¼ 207) reduced their level of force misconceptions

by 9 percentage points compared with the students who did not participate in the conceptual

discussions (N¼ 189). Along with the observed decrease in the force misconceptions, the results

of this study showed a 7-percentage point increase in the average achievement of the discussion

group students over their control group peers.

This leaves the question of the practical significance of the observed ESs for force achieve-

ment and misconceptions. As described before, a small or medium size treatment effect was

expected. The treatment ESs measured here approximately matched the small ES. Although these

results were of practical significance, the ES values are small. In general, the results confirm many

studies that indicate how resistant misconceptions are to change.

In comparing the results of this research with those of the previous studies, this research

supports the findings of previous studies that most students have misconceptions in physics.

Furthermore, the percentages of students’ misconceptions are relatively comparable with the

findings of the previous studies (Terry & Jones, 1986; Brown, 1989; Gunstone, 1987; Maloney,

1984).

Two previous studies addressed the effectiveness of the conceptual discussion method

(Nussbaum & Novick, 1982; McConney, 1992). Nussbaum and Novick improved and used this

conceptual discussion method to remedy misconceptions about particles of gases in their case

study. In his dissertation, McConney used almost the same conceptual discussion method to

remedy students’ misconceptions in biology. Both studies concluded that the conceptual dis-

cussion method is an effective means of reducing the number of misconceptions. The findings of

this study support their findings.

The finding of this research is in agreement with that of Eryilmaz’s (1992) study, that male

students have fewer misconceptions than female students in mechanics. However, the finding of

this research does not support the finding of Eryilmaz’s (1992) study that male students have

higher achievement in mechanics than female students. I could not find experimental research

1012 ERYILMAZ

studying the effect of conceptual assignments on students’ misconceptions and achievement in

mechanics. Hence, I have no results to compare with the results of conceptual assignments and

treatments’ interactions.

The internal validity of the study refers to the degree to which extraneous variables may

influence the results, and consequently the conclusions of the research. As outlined by Fraenkel

and Wallen (1996), the factorial design used in this study provides some control for the internal

validity threats of subject characteristics, mortality, instrument decay, testing, history, maturation,

and regression. However, location, data collector characteristics, data collector bias, attitudinal,

and implementer threats were not controlled by the design.

Many possible subject characteristics (prior experience with physics, students’ physics

preconceptions, students’ physics achievement, age, and gender) might affect students’ achieve-

ment in force and motion. Hence, they may be potential confounding variables in the study. Most

of these variables were included in a covariate set to match statistically subjects on these factors.

To control the mortality (loss of subjects) threat, absence of data was treated as a research

factor. Data collector characteristics and data collector bias were controlled by training the data

collectors (the teachers) to ensure standard procedures under which the data were collected. All

tests were scored by the computer program. This helped control the instrument decay threat to

internal validity. Exposure to a pretest might alter the subjects’ performance on a posttest.

However, presumably the pretest would affect both groups equally. Moreover, the experiment’s

duration (8 weeks) helped reduce the pretest effect on the posttest in this study.

One of the biggest threats to internal validity might be attitudinal effect (the way in which

subjects view the study). Having 8 weeks between the pretest and posttest helped reduce the effects

of these threats. Moreover, the study took place in regular school settings. Finally, the most

important threat to internal validity might be implementation because six different teachers

were responsible for the treatments. This was controlled by training the six teachers to standar-

dize the conditions, under which the treatments were implemented, and the researcher and a

graduate student followed up with observations throughout the study. Furthermore, the six

teachers were also treated as a covariate.

Confidentiality was not a problem in the study because the names or physical characteristics

of the students or teachers were not revealed in any form. Moreover, students’ numbers were used

instead of their names. In addition to this, all students were provided with consent forms. They

were told that even if they did not want to participate in the study, they needed to indicate so on the

consent form and return it. About 88% of students returned their positive consent forms. Only two

students returned their negative consent forms and they did not take the posttests. Therefore, these

two students’ data were discarded from the study. The remaining students’ data of about 12% were

included in the analysis based on two reasons. First, it is evident from the Department of Health

and Human Services revised regulations for research with human subjects (Fraenkel & Wallen,

1996, p. 40) that if students’ identities are anonymous in the study, there is no need for a consent

form from the participants. That is the case with this study. Second, these students did not return

the consent form with negative response. Therefore, their data were used in the analyses.

The accessible population was high school students enrolled in physics in both public and

private high schools in Brevard County, Florida. The subjects were not randomly selected from

the accessible population. They were the students of six physics teachers from 6 high schools

(5 public, 1 private) who volunteered for the physics misconception workshop provided by the

researcher. This constituted a 40% representation (6 of a possible 15) of the senior public and

private high schools in Brevard County. The use of a nonrandom sample of convenience some-

what limits the generalizability of this study’s findings. Brevard County is largely middle-class

and suburban. It constitutes 90% White, 8% Black, and 2% Asian, Pacific Islander, and others.


However, generalizations to similar populations of high school physics students are justified.

Considering the sample size (396 students), the results and conclusions found in this study can be

applied to the broader target population of middle-class, predominantly White and suburban, high

school physics students in the United States.

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