Proc. Natl. Sci. Counc. ROC(D)
Vol. 12, No. 3, 2002. pp. 91-99
Using Cognitive-based Dynamic Representations to Diagnose
Students’ Conceptions of the Characteristics of Matter
*
**
MEI-LING CHIU , MEI-HUNG CHIU , AND CHIA-YEN HO
**
*Affiliated Senior High School
National Taiwan Normal University
Taipei, Taiwan, R.O.C.
**Graduate Institute of Science Education
National Taiwan Normal University
Taipei, Taiwan, R.O.C.
(Received October 17, 2002; Accepted April 9, 2003)
ABSTRACT
Numerous studies have shown that learners at different levels and ages have difficulties understanding
science concepts. Such difficulties are revealed by students’ alternative conceptions generated during instruction.
The reasons for these difficulties have some common features, such as students’ complex, abstract, and inconsistent
intuition about those science concepts. In chemistry, this also holds true for many fundamental concepts (e.g.,
the structure and motion of atoms and molecules; the behaviors of particles in gas, liquid, and solid states). To
understand the knowledge structure held by the tenth graders involved in this study, we first conducted openended and semi-structured interviews, followed by a paper-and-pencil test covering the arrangements and behaviors
of particles in three states (solid, liquid, and gas). We followed this with more interviews to hear their explanations
for each answer for the sake of developing multiple-choice test items based on the learners’ understanding of
chemistry. Using the results from the first stage, we designed a software program with dynamic representations
to help us investigate what representative knowledge the learners had of chemistry concepts and how they explained
the concepts. The students were tested individually in a computer lab. Each student worked at his or her own
computer and answered the questions so as to best reflect his or her understanding. The findings revealed that
the students were able to identify the static structures of particles in three states. They were also able to distinguish
the differences in particles’ motion between the solid and gas states. However, about 15 percent of the students
believed that particles in a solid are static. In addition, more than half of the students believed that the motion
of particles in a liquid was the same as that in a solid. Reasons for their choices were also examined. Implications
for learning and instruction are discussed.
Key Words: dynamic representation, matter, conception
I. Introduction
Active constructing and restructuring of knowledge
plays an essential role in learning. Students generate their
understanding via the interaction between their existing
knowledge structure and new information that might have
representations of concepts that are different from their
original ones. The gap between the existing and the new
knowledge framework creates the difficulties in learning
science. This is more obvious in the learning of abstract
concepts in chemistry. Johnstone (1991) considered that
chemistry instruction should include macroscopic,
microscopic, and symbolic levels. Of these, the microscopic level is the essence of chemistry teaching. However,
studies focusing on the concept of “basic” particles (e.g.,
Ben-Zvi, Eylon, & Silberstein, 1986, 1988; Gabel, 1993;
Johnson, 1998; Novick & Nussbaum, 1978, 1981) revealed
that despite a great deal of instruction emphasizing particle
theory, many pupils (at all ages) consistently showed that
they had difficulties or incomplete understanding of basic
particle theory. For instance, Stavy (1990) showed that
even when seventh and eighth graders were taught the
concepts of particles in their science curricula, only about
15% of eighth and ninth graders who had studied under
the same curricula were able to use the composition and
arrangement of particles to explain phase changes. Seventh
graders were completely unable to explain phase changes.
Since Craik (1943, cited in Johnson-Laird, 1989) first
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M.L. Chiu et al.
proposed the concept of mental models to refer to a special
kind of mental representation, many researchers have given
definitions of mental models (e.g., Gentner & Stevens,
1983; Norman, 1983; Vosniadou, 1994). Although the
definitions vary, the idea underlying mental models involves its intrinsic descriptions of observations or byproducts of actual interaction between one’s understanding
and a stimulus. Research has shown that there is a close
relationship between one’s mental models and concrete
representations (such as physical models, simulation, or
symbols). In this study, we were mainly interested in
investigating students’ mental models of the behaviors and
structure of particles in solids, liquids, and gases using
dynamic representations shown on computers.
interviewed the students about particles using open-ended
questions to obtain original responses. Second, we developed multiple-choice items based on the data drawn from
the students. Third, we conducted a paper-and-pencil test
using the drawings from the students. Once the test was
completed, we interviewed the students again to verify the
answers. Whenever needed, we interviewed the students
to obtain more in-depth explanations of their answers to
validate multiple-choice items. The merit of this design
was that the test items were primarily chosen based on the
students’ drawings or explanations of their understanding
of particles. These multiple research methods were iteratively used in this study.
2. Subjects
Research Questions
(1) What were the misconceptions that tenth graders
held about the particulate nature of a substance in
different states?
(2) What characteristics of those misconceptions were
in nature?
II. Description of the Research and
Methodology
This study was part of a larger project that investigated
how students at different levels understood chemistry
concepts in terms of their mental models. The main purpose
was not to “assess” the students’ performance, but rather
to “diagnose” their alternative conceptions of particles. In
this study, we tried to develop test items based on students’
alternative frameworks that we considered to be grounded
on constructive learning. The detailed and design processes
are described below.
Forty students were tested using pilot items in our
instrument. After the pilot test, we modified the test items
and then ran the experiment. Thirty-nine tenth grade
students (15 − 16 years old) in Taipei city were required
to complete a set of test items dealing with the states of
matter: solid, liquid, and gas. The test took the students
about 15 − 20 minutes to complete. These subjects had
learned some concepts related to the three states of matter
in the 8th and 9th grades along with fundamental concepts
about particles. However, they were never taught or tested
using dynamic representations of particles in school. The
majority of them stated that they had never seen this type
of dynamic test item before.
3. Instrument
The development of the diagnostic materials involved
several phases, and is described below.
A. The First Phase: Interviewing
1. Research Design
The tools used in the early stage of this study were
mainly interviews, drawings, paper-and-pencil test items,
and computerized test items. For this type of study, many
researchers in science education believe that a drawing is
a convincing way to illustrate what the students have learned
in chemistry. However, this study intended to extend this
approach to computerized simulation to investigate the
students’ understanding of particulate theory. To accomplish this goal, we employed a two-tier testing technique
proposed by Treagust (1995) to obtain the students’ knowledge structure by asking them to answer open-ended
questions and make diagrams to show their mental images
or representation of particles. The students were required
to make drawings, use Styrofoam, and think aloud about
their images of particles during the interviews. First, we
To understand tenth graders’ preconceptions about
the behaviors and structures of particles in three states
(solid, liquid, and gas), we interviewed 10 students individually using open-ended questions. The students were
required to draw graphs showing their mental images, use
Styrofoam balls to represent the three states of particles,
and think aloud while they were interviewed.
B. The Second Phase: Paper-and-Pencil Test
Responses to the interview questions were used to
form multiple-choice items for a paper-and-pencil test.
These items were considered to be student-oriented items
that were different from traditional multiple choice test
items. Once the items were constructed, an entire class
of 40 students was tested. The students were asked to select
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Dynamic Representations as Diagnosing Tools
Fig. 1. Question 1-1 in the test.
Fig. 3. Question 3-1 in the test: Which of the following graphs shows
the atomic arrangement of a liquid vaporizing to form a gas in
a closed container?
Fig. 2. Question 2-1 in the test.
the most appropriate answer to each question and then give
explanations for their choices. The data obtained from the
students were analyzed and developed into two-tier test
items: the first tier for their image representations and the
second tier for their explanations.
C. The Third Phase: Development of Diagnostic Software
Using Two-Tier Test Items
Based on the drawings obtained from the initial
interviews and the student responses from the paper-andpencil test, we developed a computerized test package
focusing on the students’ mental models of particles. This
computerized test package was specifically designed to be
unlike the common static representations of particles. Rather,
it dynamically revealed the characteristics of particles.
Therefore, all the responses students could choose from
were dynamic.
In total, there were 12 test items divided into three
sets. All three sets were intended to reveal students’ factual
understanding and the reasons for their conceptions. The
three sets are given below:
(1-1-1) Which of the following graphs best represents
the motion of particles in solid state at a particular temperature? Please click one.
(1-1-2) The one you have chosen is shown below. Please
explain your answer.
(1-2) Is there anything between the atoms? Why?
(1-3) If there is another solid metal that consists of
the same materials at the same temperature,
would the atoms be arranged in the same way?
Why or why not?
(2-1-1) Which of the following graphs shows the atomic
arrangement of a solid melting to form a liquid
(assuming that the volume remains constant)?
Why?
(2-1-2) Your choice is shown below. Please explain
your answer.
(2-2-1) Which of the following graphs best represents
the movement of particles in a liquid?
(2-2-2) Your choice is shown below. Please explain
your answer.
(3-1-1) Which of the following graphs shows the atomic
arrangement of a liquid vaporizing to form a
gas in a closed container?
(3-1-2) Your choice is shown below. Please explain
your answer.
(3-2-1) Which of the following graphs best represents
the movement of particles in a gas?
(3-2-2) Your choice is shown below. Please explain
your answer.
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M.L. Chiu et al.
Table 1. Average Scores of the Students on Items Related to Solid,
Liquid, and Gas Concepts
State
Number of question
mean
s.d.
solid
1-1
1-2
1-3
average
2-1
2-2
average
3-1
3-2
average
2.79
2.10
2.74
2.55
3.18
2.05
2.61
2.77
3.36
3.06
1.49
1.50
1.74
0.16
1.27
1.61
0.20
1.35
0.84
0.13
liquid
gas
Table 2. Correlation Coefficients for the Students with Respect to the
Total Scores and the Solid, Liquid, and Gas Item Scores,
Respectively
Solid
solid
liquid
gas
Total
1.000
0.157
(0.339)
1.000
0.063
(0.702)
.181
(.270)
0.738**
(0.000)
0.687**
Liquid
Gas
(1.000)
(.000)
.489**
(.002)
** Correlation is significant at the 0.01 level (2-tailed).
( ) Standard deviation.
student conceptions about particles. After conducting the
paper-and-pencil test items with class A consisting of 40
students, we modified the test items and developed a software
program designed to use dynamic representations of particles to test the students. To show the dynamic movements
and structures of particles, we used FLASH, a computer
application tool, to present particles’ motions in the three
states. This application tool allowed students to make their
own choices and then explain their selections. Once the
program was tested and modified, two chemists from the
Department of Chemistry reviewed it for external validity.
Then, we modified the software again and tested it on 39
tenth graders in class B individually in a computer lab. Each
student worked alone at his or her own computer. Both
qualitative and quantitative data were collected. Although
the responses from the first tier were quantitative data, they
were based on qualitative interview data that could be
considered to more authentically reflect of students’ understanding of particles.
III. Results
The following analysis has been based on three
perspectives: statistical performance, mental models, and
explanations of the states of matter.
1. Students’ Performance
Fig. 4. Pictorial representations of students’ conceptions of the motion
of particles.
D. The Fourth Phase: Expert Validation
After the prototype learning materials were developed,
two professors from the Department of Chemistry of National
Taiwan Normal University reviewed the software and gave
very positive feedback. We also asked them to check the
accuracy of the contents of the learning materials. The
package was then modified according to their feedback.
We also deleted choices from the package deemed inappropriate because they were chosen by no one or very few
students.
4. Procedure
As described in the previous sections, our main task
was to develop cognitive-based test items to diagnose
Table 1 shows the average scores of the students on
items related to solid, liquid, and gas concepts. The average
scores for solid, liquid, and gas were 2.55 (s.d. = 0.16),
2.61 (s.d. = 0.20), and 3.06 (s.d. = 0.13), respectively. After
making pairwise comparisons (Least Significant Difference),
we found that there were significant differences between
solid and gas (p = 0.014), and between liquid and gas (p
= 0.044). To our surprise, the students on average had the
highest scores for particles in the gas state, which we
considered to be more complex and abstract.
Table 2 shows the correlation coefficients for the
students on items related to solid, liquid, and gas concepts.
The total scores were significantly correlated with the
scores for the solid, liquid, and gas items; however, the
solid, liquid, and gas item scores were not significantly
correlated.
Tables 3 and 4 show that although many of the
students chose the correct figure (Item B in Fig. 1) to
represent the motion of particles in the solid state, their
explanations for their choice varied in terms of type and
quality. Pictorial representations of their mental models are
shown in Fig. 4.
Tables 5 and 6 show the responses to Question 12, which asked, “Is there anything between the atoms?”
Table 6 reveals that 9 out of 22 students, who believed that
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Dynamic Representations as Diagnosing Tools
Table 3. Responses to Question 1-1*
Question 1-1: Which of the following graphs best represents the motion of particles in solid state at a particular temperature? Please click one.
Choice
Correct reasons
Sub. No.
A
Vibrate all the time at the same place (Fig. 4(a)).
Vibrate at the same place, but cannot be seen (Fig. 4(b)).
19
2
Choice
Partially correct reasons
Sub. No.
Low temperature, low energy, vibrate little vibration (Fig. 4(b)).
Low temperature, low energy, vibrate little vibration (Fig. 4(b)).
Irregular action, very little vibration small (Fig. 4(b)).
Irregular action, very little vibration small (Fig. 4(b)).
Not in same direction (Fig. 4(a)).
4
1
2
1
1
Incorrect reason
Sub. No.
Still (Fig. 4(c)).
Still (Fig. 4(c)).
NA
6
1
1
B
B
A
A
B
B
Choice
A
B
B
*datum was missing.
Table 4. Summary of the Correctness of Students’ Answers to Question
1-1*
Atoms are motionless
in solid state
little vibration
total
Correct
Partially correct
Incorrect
Total
2
3
6
11
19
21
6
9
2
8
27
38
Space exists between atoms
Nothing exists among atoms
Depends
Total
*One data was missing.
Table 5. Responses to Question 1-2
Is there anything
between the atoms?
Yes
No
√
√
√
√
√
√
√
√
√
√
√
√
√
Correct or partially correct reasons
With attractive force (Fig. 5(b))
Vacuum
Partially correct reasons
Electrons (Fig. 5(a))
Some force (Fig. 5(b))
No space to hold anything
Connected with each other
Others
Incorrect reasons
The atom is the smallest unit.
Space
Others
Table 6. Summary of the Correctness of Students’ Answers to Question
1-2
Sub. No.
6
3
2
1
3
3
3
4
1
2
2
1
6
there was nothing between the atoms, also believed that
of an attractive force existed between the atoms. The rest
of the students (n = 13) believed that there was no space
between the atoms.
Correct
Partially
correct
Incorrect
Total
0
9
6
10
9
3
9
16
12
15
22
2
39
Question 1-3 tested a simple concept about whether
or not another block of the same material (metal) would
have the same atomic arrangement at the same temperature.
Table 7 shows that a majority of the students believed that
as long as the same metal was at the same temperature,
it would have the same atomic arrangement. However, it
was peculiar that several students believed that identical
metal blocks at the same temperature would have different
arrangements of atomic particles.
Similar to Question 1-3, Question 2-1 (Fig. 2) asked
the students to choose the picture that best represented the
atomic arrangement of a liquid (Tables 9 and 10).
Finally, Tables 11 and 12 show the students performance on questions regarding particles in a gas (Fig. 3).
Figure 7 presents models of their understanding. Again,
students who chose the same figure that best represented
their conception of particulates in gas, often offered different explanations for their choices (Fig. 8).
IV.Discussion and Concluding Remarks
− 95 −
From a previous study (Chiu, Chou, & Liu, 2002),
M.L. Chiu et al.
Table 7. Responses to Question 1-3
Question 1-3: If there is another solid metal that consists of the same material at the same temperature, would the atoms be arranged in the same
way? Why or why not?
Correct
Choice
Reason
Sub. No.
Yes
Yes
Yes
Yes
Same material, same arrangement (Fig. 6(a)).
Same substance (Fig. 6(a)).
Same temperature, same material.
Other.
8
7
9
2
Choice
Reason
Sub. No.
Yes
Yes
No
The atomic arrangement is fixed (Fig. 6(a)).
Low energy, stable.
Different but similar (Fig. 6(c)).
1
1
1
Choice
Reason
Sub. No.
No
No
No
No
Different arrangement and different spaces between atoms (Fig. 6(b)).
Random (Fig. 6(d)).
Different materials (Fig. 6(b)-(d)).
Other.
2
2
2
2
Partially correct
Incorrect
Table 8. Summary of the Correctness of Students’ Answers to Question
1-3
Correct
Same arrangement of atoms
Different arrangement of atoms
NA
26
0
0
26
Partially
Incorrect Total
correct
2
1
0
3
0
8
0
8
28
9
2
39
(a)
(b)
Fig. 5. The pictorial representations of “things” existing among particles.
we knew that students tend to consider dynamic concepts
of chemical equilibrium to be MATTER or event-like rather
than constraint-based interaction, which is normally inconsistent with the students’ daily life experiences and
understanding. In our current work, we found that the
students believed that particles sink to the bottom of a
container in solid state and float in the middle of the
container when charging from the solid state to the liquid
state. We speculate that the students think of the particles,
as non-interacting substances. However, the particles are
actually interacting with each other, a concept which seems
to be poorly developed in students at the tenth grade level.
This result would be consistent with what we found in our
chemical equilibrium study and in other particle studies
carried out by M.T.H. Chi and her colleagues (Chi, 1992;
Chi, Slotta, & de Leeuw, 1994).
(a)
(b)
(c)
(d)
Fig. 6. Pictorial representations of the atomic arrangement of the same
metal at the same temperature.
Several significant findings were obtained in this
study. Question 2-1 gave five choices, each presenting a
previous student misconception. Some students thought
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Dynamic Representations as Diagnosing Tools
Table 9. Responses to Question 2-1
Question 2-1: Which of the following graphs shows the atomic arrangement of a solid melting to form a liquid (assuming that the volume remains
constant)? Why?
Choice
Correct reason
Sub. No.
C
C
C
C
Attractive force between atoms becomes weak; the atoms can vibrate (Fig. 7(a)).
The distance between atoms in a liquid is larger than that in a solid (Fig. 7(b)).
Same atoms but the arrangement of atoms is loose (Fig. 7(b)).
The energy of atoms increases, the speed of vibration increases, making the distance larger (Fig. 7(b)).
11
8
3
2
Choice
Partially correct reason
Sub. No.
C
C
C
C
E
D
A
C
Attraction force exists among molecules (Fig. 7(a)).
Same number of atoms, increasing the volume (Fig. 7(b)).
Same volume but different shape.
The distance between atoms increases (Fig. 7(b)).
Same number of atoms; since liquid can flow, it does not have a fixed shape (Fig. 7(b)).
The electrons become active when the temperature increases, so the volume increases, too.
Other.
Other.
2
2
1
1
1
1
1
2
Choice
Incorrect reason
Sub. No.
A
The liquid sinks to the bottom of the container when it is melted.
1
Table 10. Summary of the Correctness of Students’ Answers to Question
2-1
A
B
C
D
E
Total
Correct
Partially correct
Incorrect
Total
0
0
24
0
0
24
1
0
8
1
1
11
1
1
0
0
0
2
2
1
32
1
1
37
(a)
(b)
(c)
(d)
Fig. 7. Pictorial representations of the atomic arrangement in a liquid.
that atoms sink to the bottom of a container (choice A) when
something changes from the solid to the liquid state, or that
some float on the surface (B). However, when the choices
were incorporated into a dynamic software program, very
few students chose these items. Instead, more students
chose the option stating that atoms float in the middle of
the container when changing from the solid to the liquid
(regardless of the conservation of atoms). Similar results
were also obtained for Questions 3-1 and 3-2. In our
interviewing process, we found that the students had five
types of mental models of the arrangement and motions
of particles in a gas. However, the students tended to select
the same answer (e.g., A for Question 3-1) to indicate their
understanding. We wonder whether or not the different
representations offered triggered different mental models
held by the students, causing them to answer differently.
In our analysis, we found that some students, even
at the tenth grade, still believed that something exists
between and among atoms. This result is consistent with
Griffiths & Preston (1992). Also, we found that a common
alternative conception about the static state of particles in
a solid state was not revealed by our study as it has been
in other research. Again, we speculate that the students
had not only developed a more correct concepts of the
particle action, but they also were able to differentiate
between the movement of particles in liquid and solid states.
Having examined the textbook used in the chemistry
class at the tenth grade, we found that its pictorial representations were misleading, causing student misconceptions regarding how particles exist in different states. Due
to the limitations of two-dimensional representations on
paper, the dynamic interaction of the particles at different
temperatures could not be depicted in the textbook, making
it difficult for students to imagine how particles vibrate in
different states, particularly in the solid state. This is
consistent with the conclusion drawn by Stavy (1990).
Research has shown that learning about the particulate nature of matter is important and necessary in chemistry
(Krajcik, 1991). It is common to use multiple-choice paperand-pencil test items to study students’ scientific concepts.
− 97 −
M.L. Chiu et al.
Table 11. Responses to Question 3-1
Choice
Correct reason
Sub. No.
A
A
E
A
A
E
The total number of atoms stays constantis. Gas particles can move freely (Fig. 8).
Attractive force decreases, so the particles can fill the entire container (Fig. 8).
The distance between atoms increases (Fig. 8).
The distance between atoms increases (Fig. 8).
Attractive force decreases, so they can move more freely (Fig. 8).
Attractive force decreases, so they can move freely (Fig. 8).
8
6
4
3
2
1
Choice
Partially correct reason
Sub. No.
E
A
A
A
E
E
A
The space between molecules is large (Fig. 8).
Fills the entire container (Fig. 8).
The molecules separate from each other more (Fig. 8).
The molecules separate from each other more (Fig. 8).
The heat energy makes the atoms move away from each other.
The gas holds more energy than the liquid, so the interactive force among the atoms has less impact on the atoms.
The space occupied by the gas becomes larger, but the total number of atoms remains constant (Fig. 8).
4
2
1
1
1
1
1
Choice
Incorrect reason
Sub. No.
E
E
A
E
The restrained force disappears.
The gas has no fixed volume or shape.
Other.
Other.
2
1
1
1
Table 12. Summary of the Correctness of Students’ Answers to Question
3-1
A
B
C
D
E
Total
Correct
Partially correct
Incorrect
Total
19
0
0
0
5
24
4
0
0
0
6
10
1
0
0
0
4
5
24
0
0
0
15
39
Fig. 8. Pictorial representation of the atomic arrangement in a gas.
methodology, the dynamic graphs also shed some light on
the students’ mental representations of the particulate nature
of matter.
In this study, however, we made use of two-tier items to
diagnose students’ conceptions of the particulate nature of
matter based on their own points of view. We believe that
it is more meaningful and valid to identify students’ understanding of particles by showing them simulated representations of particles. We also believe that the students
chose pictorial presentations in a multiple-choice format
similar to those they provided when interviewed using
open-ended questions because the multiple-choice questions were designed based on the students’ original responses to the open-ended interview questions. The present
study also suggests that although the students may have
chosen the same answers to the open-ended and multiplechoice questions, they might provided completely different
explanations to the answer. The second-tier explanations
for each question revealed each student’s idiosyncratic
thinking about the particulate nature of matter. Besides the
Acknowledgment
This work was made possible in part by Grant NSC 90-2511-S003-092 provided by the National Science Council, R.O.C. We felt very
sorry to hear that the third author, Chia-Yen Ho, died in an accident during
the reviewing process. We would like to express our sincere memory
of her by sharing this paper with her.
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