The study investigated 408 secondary school students' understanding of solution concentration and the dissolving process at the particulate level. Students completed a test on these concepts involving drawing submicroscopic representations. They achieved an average score of only 43%. Most students had misconceptions about particle arrangements in solutions and how concentration is represented at the particulate level. Very few students could correctly draw submicroscopic representations of ionic substance solutions or saturated versus diluted molecular crystal solutions. The study identified many common student misconceptions about basic solution chemistry concepts at the particulate level.

1. Assessing 16-Year-Old Students’ Understanding
of Aqueous Solution at Submicroscopic Level
Iztok Devetak & Janez Vogrinc & Saša Aleksij Glažar
# Springer Science + Business Media B.V. 2007
Abstract Submicrorepresentations (SMR) could be an important element, not only for
explaining the experimental observations to students, but also in the process of evaluating
students’ knowledge and identifying their chemical misconceptions. This study investigated
the level of students’ understanding of the solution concentration and the process of
dissolving ionic and molecular crystals at particulate level, and identifies possible
misconceptions about this process. Altogether 408 secondary school students (average
age 16.3) participated in the study. The test of chemical knowledge was applied and the
analysis of four selected problems related to drawing SMRs in solution chemistry is
presented. Selected students were also interviewed in order to gain more detailed data about
their way of solving problems comprised in the knowledge test. The average achievement
on solution chemistry items was only 43%. It can be concluded from the results that
students have different misconceptions about arrangements of solute particles in the
solution and presentation of its concentration at particulate level. Students show quite low
achievement scores on the problem regarding drawing the SMR of ionic substance aqueous
solution (7.6% correct answers) and even lower ones on the problem regarding drawing the
SMR of diluted and saturated aqueous solutions of molecular crystal (no completely correct
answers). It can be also concluded that many different misconceptions concerning the
particulate level of basic solution chemistry concepts can be identified. In the conclusion
some implications for teaching to reach a higher level of understanding of solution
chemistry are proposed.
Keywords Chemical misconceptions . Drawing submicrorepresentations . ITLS model .
Particle level . Solution . Chemistry
Introduction
Educational strategies in chemical education should lead to knowledge with understanding
and should include macroscopic, submicroscopic and symbolic levels of chemical concepts.
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DOI 10.1007/s11165-007-9077-2
I. Devetak (*) :J. Vogrinc :S. A. Glažar
Faculty of Education, University of Ljubljana, Kardeljeva ploščad 16, Ljubljana, Slovenia
e-mail: iztok.devetak@pef.uni-lj.si

2. The macroscopic component—concrete or sensor representation of chemical concepts—is
represented by experimental activity. Observations made at macroscopic level are explained
by the submicroscopic one (abstract particulate level). Symbolic levels of chemical
concepts [symbols of elements, chemical formulae and equations, mathematical equations,
graphical representations such as submicrorepresentations of particulate level of matter
(SMR), different models, schemata, etc.] are used by scientifically literate people to easily
communicate about the phenomena at abstract level. This level is the hardest one for
students to understand, especially without understanding of the submicroscopic level of
chemical concepts. Reasonable understanding of the phenomena is established when all
three levels of the concept cover each other, supported by visualisation elements, in a
specific way in students’ working memory. These relationships are presented in the
Interdependence of Three Levels of Science concepts model (ITLS; Fig. 1).
The Interdependence of Three Levels of Science concepts (ITLS) model draws on
different theories, such as Paivio’s dual coding theory, (Paivio 1986), Mayer’s SOI model
of meaningful learning (Mayer 1996) upgraded by Johnstone (Johnstone et al. 1994),
cognitive theory of multimedia learning (Moreno and Mayer 2000) and Mayer’s theory of
effective illustrations (Mayer 1993). The dual coding theory assumes that there are two
cognitive subsystems, one specialized for the representation and processing of nonverbal
objects or events, and the other specialized for dealing with language (Paivio 1986). The
three processes of the selecting relevant information (SOI); Organizing information in a
meaningful way to the learner; Integrating the new information with the learner’s prior
knowledge) model the prime cognitive processes in the learner that are needed for sense
making and support constructivist learning to the extent that they promote active cognitive
processing (Mayer 1996). Mayer’s theory of effective illustrations and cognitive theory of
multimedia learning builds on the implementation of simple illustrations to help direct the
student’s attention to specific elements and guide the students to build their own internal
connections among the parts. These activities help students to build a “runnable mental
model” by which students acquire knowledge and proceed toward meaningful knowledge
(Mayer and Moreno 2001). According to Mayer and Moreno (2001), when constructing
meaningful knowledge we should follow the multiple representation principle. This means
that it is better to present an explanation in words and pictures than only in words. From
Macro
level
Symbolic
level
Submicro
level
Mental
model
Visualization methods
Reality
Representation of the reality
Fig. 1 Model representing interdependence of three levels of science concepts—ITLS model (Devetak 2005)
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3. this perspective, learning science is also strongly connected with building knowledge
through understanding and concepts linking in students’ long-term memory by interpreting
multi-modal representations of science phenomena (Ainsworth 1999; Dolin 2001; Russell
and McGuigan 2001; Lemke 2004) and that students who recognized relationships between
different representations demonstrated better conceptual understandings than students who
lacked this knowledge (Prain and Waldrip 2006). In order to achieve better understanding
of science concepts students should be able to translate one representation into another one
and co-ordinate their use in representing scientific knowledge (Ainsworth 1999). Russell
and McGuigan (2001) argue that learners need opportunities to generate various
representations of a concept, and to recode these representations in different modes, as
they refine and make more explicit their understanding. In the process of science learning
teacher should therefore incorporate students’ “rich pool of representational competence” in
creating lessons that are motivating for students (diSessa 2004, p. 298), but diSessa also
points out that the quality of the representation ought to be evaluated according to its
purpose. Waldrip et al. (2006) argue that in order to maximize the effectiveness of designed
representational environments, it is necessary to take into account the diversity of learner
background knowledge, expectations, preferences, and interpretive skills.
SMRs are one representational mode in the ITLS model. SMR that are emphasised in
this paper are defined as pictorial elements that could be presented in 2-D or 3-D static or
dynamic representations of particle behaviour. These SMRs have a vast explicative power,
because they direct students towards specific elements that support construction of the
knowledge network in students’ long-term memory that leads students to learn new
concepts with fewer misunderstandings and incomplete interpretations. It is also important
to lay stress on the meaning of SMR in students’ formative and summative knowledge
assessment. SMRs help the teacher to identify students’ inaccurate or incomplete
understanding of chemical concepts and, after analysing them, to plan an adequate
educational strategy to avoid further formation of misconceptions anchored in students’
long-term memory (Devetak et al. 2004). Research studies in science education in the last
two decades have emphasised using different educational strategies to overcome the gap
between all three levels of chemical concepts using different forms of SMRs (Gabel 1999;
Lee 1999; Treagust et al. 2003; Bunce and Gabel 2002; Chittleborough et al. 2002;
Harrison and Treagust 2002; Eskilsson and Hellden 2003). The basis of the correct
comprehension of chemical concepts is an understanding of the structure of matter. It is
therefore recommended that teaching of science phenomena to students aged from 10 to
12 years should originate in macroscopic observations and gradually continue to particle
interaction explanations, and finally these explanations ought to translate into the symbolic
representations (Papageorgioua and Johnson 2005). Misconceptions of solution chemistry
at submicroscopic level are generally the outcome of misconceptions of the states of matter
and transitions between them, mixtures and pure substances and their particulate structure.
Students aged 11 to 13 years, as well as university students, perceive the process of
dissolving as melting (Lee et al. 1993; Ebenezer and Gaskell 1995; Williamson and
Abraham 1995; Ebenezer and Erickson 1996; Valanides 2000). Lee et al. (1993) reported
that even 12-year-old students believe that the solute literally disappears while dissolving,
and they do not understand that the solute was disintegrated into such small particles (ions
or molecules) that it can not be seen any more. Valanides (2000) came to similar
conclusions by conducting interviews with pre-service science teachers about dissolving
sugar, sodium chloride and ethanol in water. Eleven out of 20 students thought that sugar
melts in water; 13 of them suggested that sugar would not pas through filter paper during
filtration. Eight students described dissolving as a chemical reaction, because new chemical
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4. bonds are formed between sugar and water particles, and a new substance is formed—sweet
water. Prieto et al. (1989) found that students can not relate the process of dissolving with
the particles; it seems that students maintain the mental model of the continuity of the
solution which is perceived at the macro level until the age of 11 or 13. Similar findings
were reported by Butts and Smith (1987); some 16- and 17-year-old students believe that,
after dissolving, the sugar disappears, which they also graphically illustrated. Longden et al.
(1991) reported that 11- and 13-year-old students demonstrate more misconceptions about
solution chemistry at macro than at submicro level. Forty-nine percent of 11- and 62% of
13-year-old students correctly drew the SMR of the solution, but only 40% of 11- and 42%
of 13-year-old ones correctly described the process at macro level. The results also show
that students were successful in drawing SMR. It can be summarised that the number of
misconceptions was statistically significantly diminished from 11- to 13-year-olds, although
these students had not been formally introduced to solution chemistry at particulate level in
school. However, more recent research (Papageorgioua and Johnson 2005) indicates that by
applying better teaching/learning strategies, students aged 11 and above can better
understand the process of dissolving at the particle level.
Based on the previous research findings, the purpose of conceptual change is an
important aspect in science education. Conceptual change occurs when during the learning
process the new information to be learned comes in conflict with the learners’ prior
knowledge usually acquired on the basis of everyday experiences. In these situations, a re-
organization of prior knowledge in students’ long-term memory is required, this means that
a conceptual change emerges (Abell and Roth 1995; Duit and Treagust 2003; Limón 2002;
Pintrich and Sinatra 2003; Vosniadou 2003). If conceptual change is not adequate or does
not occur, the misconceptions or alternative conceptions are formed. These misconceptions
are usually very resistant to change during the future education process to which the learner
is exposed (Herron 1996).
Purpose
This study investigated the level of secondary students’ (average age 16.3 years)
understanding of the process of dissolving of ionic and molecular crystals in water at
particulate level, and identifies possible misconceptions about this process. This topic was
chosen because some of the previous researches show numerous problems regarding
students’ understanding of dissolving at particulate level (Prieto et al. 1989; Longden et al.
1991; Butts and Smith 1987; Lee et al. 1993; Valanides 2000). According to the Slovenian
educational system, the concept of solution chemistry is introduced in grade 5 (age 10) of
the lower primary school at macroscopic level and it is upgraded in grade 7 (age 12). In
grade 9 (age 14) of the lower secondary school the topic is introduced at submicroscopic
level and in grade 1 (age 15) of the higher secondary school upgraded with calculations of
different concentrations of the solution.
Research Questions
The questions asked in this study are:
1. What is the achievement of secondary school students’ in solving the SMR problems
about dissolving ionic and molecular crystals in water?
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5. 2. How do students illustrate their understanding of the concepts, such as: concentration
of water solutions, hydratisation, and dissolving at submicroscopic level by using
SMR?
3. What are the most frequent incorrect or incomplete drawings of SMR about dissolving
ionic and molecular crystals in water at submicroscopic level among secondary school
students?
Methodology
Sample
A total of 408 secondary school students (60.9% females; 39.1% males) participated in the
study. All students attended second year of the general type of secondary school
(gymnasium). The curriculum of the Gymnasium is common to all students. The students
attended the fourth year of chemical education during the period that testing was conducted
(2 years in higher primary school—age 13 and 14 and 2 years in secondary school—age 15
and 16). On average, the students participating in the study were 16.3 years old, with
standard deviation 5.7 months. The chemical concepts comprised in the test of science
knowledge were not instructed using SMR by the teachers who had taught the students
participating in the study.
Instruments
A paper and pencil chemical knowledge test (CK) was used, which includes 19 items on
four different topics: (1) pure substances and mixtures (four items), (2) chemical reactions
(six items), (3) aqueous solutions (four items) and (4) electrolyte chemistry (five items).
Students had to elaborate their solutions in eight items of CK. Items regarding the ITLS
model were classified in four groups: (1) submicro level (five items), (2) connecting
submicro and symbolic level (three items), (3) connecting macro and submicro level
(seven items), and (4) connecting all three levels of chemical concepts—macro, submicro
and symbolic level (four items). To assess students’ conceptual understanding of water
solutions on the nature of dissolving ionic and molecular crystals at particulate level, four
items (no. 9, 10, 11, and 12) on aqueous solutions in the CK test were used. Students had
to draw the adequate SMRs to illustrate their ideas about dissolving (see Appendix for
sample items).
An individual and semi-structured interview was used to obtain qualitative date about
students’ opinions of solving SMR problems. The interview protocol had two parts. In the
first part students were asked to describe the chemistry lessons from the perspective of
using SMRs and what other educational strategies teachers use (five questions). In the
second part, students described according to their opinions the specific decisions made
when solving particular SMR problems (e.g. Why did you draw this scheme [the
interviewer pointing to the student’s specific drawing in the CK] in such a way? Could you
explain your ideas about it, please? or What does this particle arrangement stand for?).
Students’ CK was used to conduct this part of the interview. Some explanations for
identified misconceptions on CK were acquired from the transcribed data. These were used
to throw light upon students’ ideas expressed in their SMRs.
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6. Research Design
The research was a non-experimental, cross-sectional and descriptive study (Bryman 2004).
The CK was administered to two university chemistry and one chemical education
professors. Their responses provided scientifically correct answers and validation for the
instrument. After the instrument was developed regarding the purpose of the study, a pilot
study was conducted with 77 students. The CK showed satisfactory measuring character-
istics (i.e. internal consistency reliability—Cronbach’s alpha was 0.80; discriminate indexes
for every item between 0.21 and 0.80 were all statistically significant—p<0.01). Students
spent 60 min solving the CK. The CK was optimised according to the pilot study, and seven
items were excluded (unsatisfactory difficulty indexes: 0.03–0.22) when preparing the final
instrument. Items were arranged regarding the difficulty index (from simple to more
difficult) and context (from items that include one level of concepts to items that include all
three levels of concepts regarding the ITLS model) in the final version of the CK. After the
modification, the instrument was applied on the research sample in a group and under
normal examination conditions in the middle of the school year. Descriptive statistics
(frequencies, mean values, and standard deviation) were obtained for illustrating students’
achievements on the CK. The 5% cut off was used in presenting the most frequent SMRs.
The decision was made according to the statistical significance of results. It tells us
something about the degree to which the result is “true” in the sense of being
“representative of the population”: 5% is customarily treated as a “border-line acceptable”
error level (Field 2000; Hinton 2004).
A sample of students was interviewed 5 days after the CK was applied. The sample
consisted of 42 students, selected on the basis of their achievement on the CK. One student
was drawn from each group of performance—high, intermediate and low in each testing
group. Interviews were audio taped (with the interviewees’ consent) and then transcribed
for analysis. Interviews were used to elucidate the students’ strategies and misconceptions
used to solve the CK problems.
Results and Discussion
Results of Students’ Success in Solving Solution Chemistry SMR Problems
It can be concluded from the statistical analysis that secondary school students show
average achievements in chemical knowledge of the tested basic chemical concepts
(Table 1). Students achieved on average 49% of all points possible on the CK. Kurtosis and
skewness show that the data are distributed normally.
Table 1 Descriptive statistics for CK
Maximum
points
possible
Students’
minimum
points
Students’
maximum
points
Average
points
Standard
deviation
Kurtosis Skewness
Total CK score 43.5 1 40.25 21.21 6.47 0.036 −0.089
Solution chemistry problems score 10 0 8.50 4.30 1.78 −0.616 −0.306
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7. In solving four problems regarding solution chemistry at particulate level, secondary
school students obtained on average only 4.30 out of 10 points (SD=1.78). The average
achievement score for these items was only 43%, which is even less than the average score
on the whole test.
For the purposes of this paper only four problems regarding solution chemistry were
selected from the CK. Problems no. 9 and 10 include concepts that refer to water solution
concentrations, and problems no. 11 and 12 refer to the understanding of dissolving ionic
and molecular crystals in water. All problems required students to draw a correct SMR.
Students were more successful in solving problem no. 9 and 10 in comparison with
problem no. 11 and 12 (Fig. 2).
In problem no. 9 Students had to present three different concentrations of the same water
solution at particulate level. The solute particles were presented by circles, water molecules
were omitted for clarity. The concentration of the first solution was defined, the second
solution was two-times more concentrated than the first solution, and the third solution was
one third of concentration of the first solution. All three solutions had the same volume.
When solving the problem, students had to think about two variables (the correct number of
solute particles and their arrangement in the solution).
To solve problem no. 9 correctly it is fundamental that students understand the text and
have some basic mathematical knowledge on proportions and proportional reasoning
abilities. The correct number of particles in the student SMR varied from the first to the last
part of the problem (part 1, 90.7%; part 2, 76.2% and part 3, 69.9%). Those students who
45.6
47.3
7.1
18.1
75.3
6.6
0.7
79.2
20.1
0
83.6
16.4
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
ProblemNo. 9 ProblemNo. 10 ProblemNo. 11 ProblemNo. 12
correct incorrect or incomplete no answer
Fig. 2 Students success in solving aqueous solutions problems
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8. gave the wrong number of particles in the first part had probably not read the text carefully,
while those who gave wrong answers in the second or third part had weak mathematical
knowledge on proportions, or do not have adequately developed proportional reasoning. On
the other hand, some students who gave the correct number of particles in the solutions,
made a wrong SMR of it (incorrect arrangement of the solute particles). The results
(Fig. 3a) show that almost 66% of the students gave a correct SMR in the first part of the
problem, 51% in the second and 50% in the third one.
Also in problem no. 10 composed from three parts, students had to present the
concentration of solutions at particulate level. To solve this problem adequately, students
had to take into account two variables: concentration of solute and volume of the solution.
In all three items students had to compare the concentration of solutions in two beakers
(beaker A and beaker B). The volume of solution in beaker A is half of the volume of
solution in beaker B. The concentration of the solutions in the items is different. In the first
item the concentration of solution is the same in both beakers; in the second the
concentration of solution in beaker A is half of the concentration in beaker B; in the third
item the concentration of solution in beaker A is one third of the concentration in beaker B.
Water molecules were omitted for clarity.
Compared with problem no. 9, the results in this task were much poorer. As shown in
Fig. 3b, just a little above 51% of the students solved the first part of the task correctly. The
toughest part was part 3, where students had to determine the concentration of the solution
in beaker A with two thirds lower concentration of the solution than in beaker B (20.6% of
correct answers).
In problem no. 11 students had to present an SMR of particles in aqueous solution of
potassium bromide with optional solution concentration. Water molecules were omitted for
clarity. Students were required to complete a legend to explain what the individual drawn
particles mean. To keep the scheme clear, they were asked not to draw the SMR of water
molecules. Students had to possess knowledge about the concept of ions, the nature of the
ionic bond, the structure of ionic crystals, dissolving of ionic crystals, and the arrangement
65
27
7,1
50,5
41,2
8,3
49,3
41,9
8,8
0 10 20 30 40 50 60
%
Correct
Incorrect
No answer
Correct
Incorrect
No answer
Correct
Incorrect
No answer
Correct
Incorrect
No answer
Correct
Incorrect
No answer
Part
one
Part
two
Part
three
Task
part
Problem No. 9
51,7
41,7
6,6
47,3
43, 9
8,8
20, 6
67, 4
12
0 10 20 30 40 50 60 70
%
Problem No. 10
7.6
70.8
21.6
2.9
76.3
20.8
0 10 20 30 40 50 60 70 80 90
%
SMR
Legend
Task
part
Problem No. 11
0.5
82. 8
16. 7
0
79.7
20.3
0 10 20 30 40 50 60 70 80 90
%
Scheme
A
Scheme
B
Task
part
Problem No. 12
Correct
Incorrect
No answer
Correct
Incorrect
No answer
Correct
Incorrect
No answer
Part
one
Part
two
Part
three
Task
part
Correct
Incorrect
No answer
Correct
Incorrect
No answer
Fig. 3 Detailed analysis of success in solving separate parts of SMR problems
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9. of ions in the solutions in order to correctly solve the problem. A correct SMR was given
only by 7.6% students, while in 70.8% of the answers the scheme was wrong. There were
21.6% of students who did not draw anything (Fig. 3c).
Problem no. 12 required an SMR of an aqueous solution of the saccharose with optional
concentration (scheme A) and a saturated aqueous solution of saccharose (scheme B).
Students had to draw the most realistic SMR of the solution with water molecules included.
Students need to understand the structure of molecular crystals, the process of dissolving
this type of crystals in water, the difference between unsaturated and saturated aqueous
solution, and the arrangement of solvent and solute particles in the solutions to correctly
solve this problem.
Of all the 11 problems in the test, this one gave the poorest results; none of the students
gave a correct SMR of saturated saccharose solution in box B (Fig. 3d).
For concrete problems see Appendix.
Alternative Conceptions Identified in Analysing Solution Chemistry SMR Problems
The analysis of students’ SMRs in problem no. 9 shows the most common misunderstand-
ing about solute particle arrangement in the solution (Fig. 4): 12.5% of the students made
ordered representations of the solute particles in the solution in the first part of the problem,
17.4% in the second and 13.0% in the third part.
It can be concluded from the results that students had more problems estimating the
correct number of particles in the second and in the third part of the problem: they just
focussed on counting the particles, not paying attention to their arrangement in the solution.
The following transcript of the interview with student no. 207 confirms this conclusion:
I: Why did you make an ordered arrangement of the solute particles?
207: Well, they are distributed throughout the whole vessel…
I: But why did you arrange them in an ordered manner outing them in one corner?
207: I thought that drawing them in such a way would make counting of the particles
easier…
I: But how are they arranged in the vessel?
207: Well, yes…throughout the whole volume of the beaker and they are unordered…
According to the interview they drew the ordered arrangement of the solute particles
because they just focused on the counting the particles and not on their arrangement, but if
Part 1 Part 2 Part 3
An ordered structure of the particles of the solute in the
solutions.
Part 1 Part 2 Part 3
The particles of the solute arranged at the bottom of the
place where the SMR of the solution should be presented.
Fig. 4 Students’ SMRs showing some alternative conceptions of solution chemistry solving the Problem no. 9
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10. the student is directed by discussion with the interviewer he/she shows some understanding
of the particle distribution in the solutions.
The second most frequent mistake (on average 5% of all mistakes) occurred when
students presented the solute particles at the bottom of the place where the SMR of the
solution should be drawn (Fig. 4). It can be argued that students placed the solute particles
on the lower part of the place reserved for the SMR of the solution because they assume
that the square represents the vessel where the SMR of the solution should be drawn, but
they do not understand the arrangement of the particles in the solution, or else they just
draw the particles in a way that would make the counting easier.
Other mistakes are varied and occurred in less than 5% of cases which are not presented
here. In total the percentage of these mistakes is the following: in part 1, 3.4%; part 2,
2.9%, and part 3, 2.7%.
Based on the results it is difficult to conclude that students do not understand the concept
of solution and how to present it at the qualitative level. The reasons may be that, while
drawing, they were more focussed on counting the particles. It is possible to infer that those
students who did not solve the problem are unable to imagine the solution at the submicro
level (part 1, 7.1%; part 2, 8.3% and part 3, 8.8%). The percentage of students who did not
make any SMR tends to grow from the first to the third part of the task, together with the
level of difficulty.
In addition to the mistakes related to particle distribution, or drawing irrelevant elements
in their SMR, the students also gave incorrect representations of the solution concentration.
The correct solution to SMR problem no. 10 should show that particles are presented in
a correct numerical ratio and should be randomly arranged.
During the interview the students were asked if they had any difficulties understanding
the task when the scheme, showing SMR of the solution in a beaker, was presented to them.
Their most frequent response was that they had no difficulties, whatsoever. It was found
that students better understood the schemes showing SMR of the solution in a beaker, than
the schemes showing the particles of the substances in a magnified part of a solution in a
circle. Drawing particles directly into the scheme of the beaker may mislead students to
think that there were only, for example, six particles in the beaker. According to the results
of the interviews, the majority of the students do not think in such a way. It can be
concluded that students at this age have adequate ideas about the number of particles in the
solution. Some transcripts from the interviews with students that underline the above
statements are presented below.
Part of the interview with student no. 380:
I: Would it be better for you if the particles in the scheme were presented in beakers,
or would you prefer to see a magnified part of the solution [showing both options]?
380: Well, I think it would, this is more confusing [pointing to magnified part],
because there are more lines and circles. I think that a scheme which is not so
crowded is clearer, in a beaker it seems better, but then everyone should know what
the real size of the particles is. I think it depends on the individual, and perhaps the
teacher should show both ways.
I: Would it be more confusing if there were only three particles in the beaker?
380: This is what I am saying, it could be a problem, but you can see that these are not
three particles if you can visualise a beaker, and a solution, and you know that there
are not three particles in it because you cannot see the dividing line. If there were three
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11. particles in such a large volume you could see the dividing line between them, there
would be a kind of border line where one could see three particles. If the particles are
small and packed together, then you see this is a substance, it makes it look coherent.
Part of the interview with student no. 210:
I: Would it be better for you if we gave you a scheme showing a beaker into which
you would draw particles, or would you prefer to see a magnified part of a solution
[showing both possibilities]?
210: I don’t know, the beaker, I think, so that we put one particle…that, yes, [pointing
to the scheme with the magnified part of the solution]…well, this too, it is clear, it
could be also this, I prefer the beaker…
I: Don’t you find it confusing if two levels are mixed, where we can see the beaker but
we cannot see the particles?
210: Oh, yes…well, for me it is easier to remember if I present it as a whole [pointing
to the scheme with a beaker] here it looks as if broken into small pieces, [pointing to
the scheme with magnified part of the solution]…you need to keep in mind that there
are two levels and this is better for initial presentation…no…but then to imagine it,
the beaker is more helpful, at least to me. It looks as a whole...
I: Wouldn’t you imagine then that there are only three particles in there?
210: No, not at all…
The results of the analysis of the SMR regarding the number of particles in different
solution concentrations were the following: part 1, 71.3%, part 2, 66.2%, and part 3, 29.7%.
This result is in agreement with the level of demand of each task. In solving the first part of
the task there were 20.3% of students who drew less particles of the solute in solution B
than in solution A. They did not consider the fact that the volume of solution B was only a
half of the volume of solution A. There were only 1.5% of students who thought that there
should be more particles in a smaller volume than in the larger volume of the solution with
equal concentration. In solving the second part of the task 19.6% of students made wrong
representations by half reducing the number of particles in solution A than in solution B.
They did not consider that the volume of solution A was twice the volume of solution B. In
solving the third part of the task, 47.1% of students made the same mistake, drawing more
particles in solution A than in solution B. There were 10.5% of the students who confused
solutions A and B and put one third of the concentration of solution A in solution B.
These results show that in defining the solution concentration, approximately 30% of
students forget to take into account the volume of the solution (just one variable—the
volume). In subsequent tasks, where the students had to deal with two variables (volume
and concentration), the percentage of correct SMRs significantly dropped (part 2 by 33.6%,
and in part 3 by 70.3%). This leads to the conclusion that students have difficulties in
proportional thinking when solving such tasks.
Students also had problems understanding the instructions, particularly with the
wording: “the concentration of the solution in beaker A is a one-third of the concentration
in beaker B”. They were not sure whether it was meant that they should draw in beaker A
two thirds or one third of the particles drawn in beaker B. To calculate the number of
particles in beaker A, they should apply the mathematical equation CB
3 2, where CB is the
number of particles in beaker B and is a multiple of integer 3. In this task in particular, it
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12. was evident how little applicative mathematical knowledge students possess to solve
chemistry problems.
These results indicate that using mathematical equations only, without previous
knowledge of chemical concepts, does not help in making chemistry calculations correct.
As in the previous task, the arrangement of particles in this task was similar: students
arranged particles of the solute in aqueous solution in an ordered manner. More than 20%
of the students made this mistake (part 1, 20.3%; part 2, 21.6% and part 3, 23.8%). The
reason why the percentage of mistakes in this task is higher than in the previous one is that
students were focussing more on counting and giving the correct number of particles while
neglecting the correct arrangement of the molecules of the solute in the solution.
It is interesting to note that, compared to task 9 (Fig. 4), there were fewer students who
gave an incorrect representation of the solution, drawing particles at the bottom of the
beaker (part 1, 1.5%; part 2, 1.0% and part 3, 1.0%). The reason might be due to different
spatial representations (task 9—square; task 10—beaker). From a later interview it became
clear that students are more familiar with the image of a beaker which they use during
chemistry classes.
There were other mistakes which were less frequent (less than 5% cases), and together
represent approximately 5.9% of all mistakes (part 1, 3.6%; part 2, 5.1% and part 3, 5.4%).
The analysis of students’ SMRs in problem no. 11 shows that typical mistakes can be
described as follows:
1. the particles in aqueous solution are molecules of potassium bromide
1.1 size of atoms in the molecule was correct (Fig. 5a) 23.8%
1.2 size of atoms in the molecule was incorrect (Fig. 5b) 22.3%
1.3 wrong number of potassium and bromine atoms in the molecule 13.8%
–there were two atoms of bromine to one atom of potassium (Fig. 5c) 10.7%
2. other mistakes (frequency less than 5.0% for each mistake) 14.0%.
Students had to give the legend to explain the particles which they had presented in the
SMR using a formula, and/or give the name of each drawn particle. Particles were
explained correctly by only 2.9% of students. Incorrect presentation of particles in the
legend was given by 76.3% of students, while no legend was given by 20.8% of students.
Typical mistakes of the legend can be grouped as follows:
Symbol of the element is given 43.0%
Name of the element is given 13.5%
Name of compound—potassium bromide was given 12.1%
Compound formula—KBr was given 6.6%.
These mistakes indicate that students did not read the instructions carefully enough, and
that they believe that the name of the atom and the ion of the element are the same. This
Fig. 5 Typical mistakes in the
potassium bromide aqueous solu-
tion SMRs
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13. means that teachers should emphasize the importance of correct naming of the atoms, ions
and molecules of substances and present to students examples of typical mistakes. Teachers
should, for that matter, talk to those students who show different difficulties in
communicating in terms of the names of compounds, in order to develop students’ system
of distinguishing between the meanings of different concepts. Teachers should show to the
student that it is important to use correct particle names. For that reason teachers should
also be very careful and consistent in communication during school lessons with students. It
is possible to speculate that, according to the recall of their knowledge, students know that
potassium bromide is an ionic substance, but they need teachers’ intervention to accurately
illustrate the particles of an ionic substance in aqueous solution. Part of the interview with
student no. 365 illustrates these conclusions:
I: You have drawn molecules of potassium bromide in the solution. Why?
365:…I don’t know…
I: What type of compound is potassium bromide?
365: Well, it’s ionic, isn’t it…
I: What happens if we put soluble ionic compounds in water?
365: Well, they go apart…they split…potassium should be particularly…and
bromine…
I: When I say potassium, what do you think of?
365: I don’t know, a metal, I think…
I: Is there a metal in the solution?
365: Potassium ions…
I: What kind of particles of potassium are in the solution?
365: Yes, there is…[laughing]…
I: Why did you not draw ions separately then?
365: I don’t know, I was not careful enough…It didn’t come to my mind…
An SMR of sodium chloride solution is presented in almost every course textbook,
therefore it was expected that students would know what the particles in an aqueous
solution of sodium chloride are, and transferring the knowledge to a similar solution of
ionic compound (potassium bromide) should not represent a particular problem. However,
the results of this test and the answers from the interview show that the students have
difficulties in understanding ionic bonds, particles in ionic crystals, and that if they learn the
SMR of potassium chloride it is learned by heart and they have difficulties in applying this
knowledge to other similar situations. Part of the interview with student no. 30 is presented
to show students’ acts of thinking during solving such SMR problems:
I: What type of substance is potassium bromide?
30: Ionic.
I: Is it soluble in water?
30: Yes, it is.
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14. I: What happens to soluble ionic compounds, when added to water?
30: They dissolve.
I: What does that mean?
30: That means that potassium bromide molecules are distributed in the solution.
I: Are ionic compounds made of molecules?
30: No, they consist of ions, the molecules ... they are only in water.
I: What does an aqueous solution of sodium chloride contain?
30: Ions.
I: What makes you think that potassium bromide solution is any different? Aren’t
these two substances similar?
30: Oh, yes, yes, ions are in the solution.
I: How should you draw them in the scheme correctly?
30: Ions separately.
I: Would you remember better if similar schemes were used in classroom for
presenting solutions of ionic substances?
30: Yes, definitely.
From the answers above we can infer that secondary school students (age 16 years) have
problems in differentiating particles of substances: i.e. atoms, ions and molecules. They have
difficulties in inferring the type of bond in simple binary compounds from the position of
elements forming compounds in the Periodic table. They are also weak in comparing the size
of atoms and ions of elements to define the size of particles in ionic compounds. The most
frequent mistake is that students believe (46.1%) that the particles of ionic compound in their
aqueous solutions are molecules. This is in agreement with the findings of Smith and Metz
(1996), who report that 37% of their tested students answered that there are molecules of
ionic compounds in aqueous solutions. They also concluded that the same answer was
given for aqueous solutions of strong bases. A large number of students are unable to
transfer the knowledge from the teacher’s presentation of one example and use it again in
solving tasks with similar examples. This shows that a lot of students can reproduce the
knowledge but are not able to use it independently for solving similar problems.
Analysis of SMR problem no. 12 shows that no students indicated particles of
undissolved solute (particles not distributed in solvent) that usually is the characteristic of a
saturated solution; they only showed particles distributed in solvent (Fig. 6; scheme B).
In most representations of the saturated solution, students gave only a large number of
closely packed saccharose molecules (71.3%). Such schemes would represent only a more
concentrated solution compared to the representations in box A. After analysing these
schemes it is not possible to infer whether the students really know the difference between
saturated and unsaturated solutions. Their representations are probably the result of
previous teacher explanations that the particles of the solute in unsaturated solutions stand
wider apart, while in saturated solutions they are more closely packed. Tables 2 and 3 show
the examples of students’ SMRs which we present in order of magnitude of occurrence. It
needs to be noted that in some SMRs more than one mistake was made.
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15. In nearly 80% of students’ SMRs the particles of the solute and the solvent were drawn
too far apart. More than 23% of students tried to show the hydration ring around the
saccharose molecule; however their perceptions of the hydration ring differ from student to
student. This indicates that teachers stress the meaning of hydration ring (particles of solute
around the particles of solvent) but students do not understand exactly what it means.
Compared to unsaturated solutions, the particles of the solute and the solvent in the
saturated solutions are too spaced out. Students also presented the saturated solution
without molecules of the undissolved solute, or, illustrated the saturated solution only by
drawing more molecules of the solute in relation to the number of molecules in scheme A.
Also in scheme B, similar problems were observed in drawing hydration rings as in
presenting the unsaturated solution in scheme A.
Table 2 Most frequent types of students’ SMRs of the unsaturated saccharose aqueous solution (scheme A)
Fig. 6 A correct SMR of
saccharose aqueous solution
(scheme A) and saturated
aqueous solution with the
same solute (scheme B)
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16. Students’ perception of saturated and unsaturated solutions could be further verified by
the interview results. Part of the interview with student no. 154:
I: How do you perceive the dissolving of sugar in water?
154: Well, a solution is as if…there is a substance, there are also some other particles,
which are not part of this substance, and then the substance in which the particles are
dissolved, surrounds the particles, if they are polar….
I: How do you perceive this solution at the particle level?
154: Probably, everything is…I don’t know….
Table 3 Most frequent types of students’ SMRs of the saturated saccharose aqueous solution (some
examples were compared with the SMR of the unsaturated solution)
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17. I: Why didn’t you draw it then?
154: [laughing]…I don’t know….
I: How about saturated solutions?
154: Well, a saturated solution is, it means…particles of the solvent are around the
substance which has been dissolved, and if we add some more substance into it, then
particles of substance do not get surrounded by the solvent….
I: Does that mean that you thought you were running short of the solute particles?
154: I don’t know, I guess so….
Part of the interview with student no. 384:
I: How do you perceive the solution of sugar in water?
348: There are water molecules, and in between there are molecules of saccharose….
I: What are the spaces between the particles in the solution?
348: I guess water molecules are closer together than the saccharose molecules….
I: How would you draw this?
348: Not quite close together…I think that water molecules and saccharose
molecules…because they are in motion, they probably hit one another….
I: How about a saturated solution?
348: Yes, and there is a solid substance at the bottom…and more saccharose
molecules in the solution, and an equal number of water molecules.
Part of the interview with student no. 16:
I: Why did you draw particles in such a nice order?
16: Particles are not ordered, I don’t know…but it is easier to count them in this
way….
I: Do you think the particles in the solution are in such order?
16: I guess they are not. I don’t know….
I: Would it be helpful if the solutions were explained to you by a scheme; on the level
of particles?
16: Yes, of course, it would help, I would better understand….
Based on the results from the interviews we can infer that some students know the
difference between saturated and unsaturated solutions at the macroscopic level, but they
have problems presenting the knowledge in a scheme at the submicro level. This may be
ascribed to the general situation at schools where teachers, when presenting the topic on
solutions, put too much emphasis on calculating the concentrations of solutions and
preparing solutions, even though this is not emphasised by the national curriculum.
Students have fewer problems with calculations, but they do not understand the difference
between the solution with different concentrations of the same substance and they are
unable to illustrate the solution concentration at the particulate level. This problem has been
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18. pointed out by other researchers too (Heyworth 1999). Similarly, Haidar and Abraham
(1991) report that 68% of the 17-year-olds included in their study had misconceptions about
the solutions at the particulate level.
Conclusions and Implications for Teaching
It can be concluded from the results, that the average achievement in solution chemistry
items was lower (43%), compared with the average overall success on the CK (49%).
Results of the analysis of four selected items indicate that students have most problems in
representing the particulate level of the solution of the ionic crystal (potassium bromide)
and molecular crystals (saccharose) in water.
The most common misconceptions of aqueous solutions detected in item analysis could
be classified into nine major groups (the percentage of students with a specific
misconception is shown in brackets: (1) particles of the solvent and solute are too far
apart in the solution (79% of students); (2) misconceptions of saturated solution (70% of
students); (3) misconceptions about the concentration at submicro level (up to 67% of
students); (4) ion name written as a name of the element or its symbol (48% of students);
(5) incomplete understanding of the concept of electrolyte dissociation (46% of students);
(6) misconceptions of the ratio between the number of solute and solvent particles in the
solution (25% of students); (7) ordered structure of the particles of the solute in the
solutions (15% of students); and (8) particles of the solute arranged at the bottom of
the place where the SMR is shown (5% of students).
The results can be summarised by answering the research questions.
The first research question is connected with the achievement of secondary school
students’ in solving the SMR problems about dissolving ionic and molecular crystals in
water. Students’ understanding of dissolving solid substances at submicroscopic level is
weak. They have difficulties in drawing and explaining SMRs to show specific character-
istics of aqueous solutions of ionic or molecular crystals. Students have poor ability to use
their knowledge (particles in aqueous solution of sodium chloride) in a new situation
(particles in aqueous solution of sodium bromide).
The second research question relates to students’ abilities to correctly illustrate their
understanding of the concepts, such as: concentration of water solutions, hydratisation, and
dissolving at submicroscopic level by using SMR. Students represented more misconcep-
tions of the concentration of the solution at the particulate level in the case of more
complicated calculations of the solute particle number (students’ problems with using
mathematical operations during solving chemistry problems) and comparisons of different
concentrations. Students also expressed misconceptions regarding particle arrangement in
the solution. They frequently drew particles of the solute in the ordered structure in the
solution and not randomly arranged.
The last research question—“What are students’ the most frequent incorrect or
incomplete drawings of SMR about dissolving ionic and molecular crystals in water at
submicroscopic level among secondary school students?” is related to the common
misconceptions in secondary school students mental models of dissolving ionic and
molecular crystals at submicroscopic level. The most frequent misconceptions (73.7% of all
SMRs) regarding solutions of ionic substance was the wrong particle (molecule) written in
the solution instead of separate ions, and the size and/or the amount ratio between
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19. potassium and bromine particles in the SMR was incorrect. Students also show many
different inconsistencies regarding the explanations of the drawn particles with their names
in the legend. It can be also concluded that students do not understand the submicro
structure of saccharose aqueous solution. They do not represent undissolved solute in the
saturated solution, and they draw the molecules of water and saccharose too far apart.
Implications for Teaching
The analysis of the results shows that the problem in understanding solutions at the particle
level is due to the pre-knowledge on topics such as: states of matter (particles in different
states of matter), types of particles (atom, molecule, ion) and chemical bonds (properties of
substances related to types of chemical bonds). It is important that teachers evaluate
students’ understanding of these chemical concepts related to the concepts to be upgraded
in the future lessons. If teachers conclude that students’ understanding of specific concepts
is not sufficient, they have to provide enough time to consolidate the knowledge to prepare
the basis for further concepts development in students’ mental model of specific science
phenomena.
The analysis of the selected problems regarding understanding the concentration of the
aqueous solutions and understanding of the dissolving of the ionic and molecular crystals at
submicroscopic level shows that teachers, when presenting concepts at the macroscopic
level, do not explain the concepts at the submicroscopic level. It is also important to point
out that teachers should not just drill students for making calculations on the topic of
solution chemistry, but they also have to introduce to them the conceptual problems (the
concentrations of the solutions at submicroscopic level) that include the particulate level of
chemical concepts.
The incorporation of SMRs, in educational process in the chemistry classroom at all levels
of education, according to the ITLS model is important from the perspective of learning
theories (e.g. Paivio’s dual coding theory, Mayer’s SOI model of meaningful learning,
cognitive theory of multimedia learning and Mayer’s theory of effective illustrations). Using
the ITLS model helps students to develop a deeper understanding of the concepts, mentally
organising them into a coherent cognitive structure, and interpreting them with relevant
existing knowledge, and it is also reflected in the ability to apply what was taught to new
situations—developed problem solving ability (Mayer and Moreno 2003). Before making
such attempts, the teacher should be aware, that it is also important for students to be
familiar with SMRs, so that they do not have problems reading them, but simply apply the
concepts knowledge to a new situation presented by the particulate level. It is also
important to emphasise the meaning of legends in such problems, so that students use
proper particles presented in the legend or that students accurately present particles that
they draw in an SMR with proper chemical symbols or names of the particles. Students’
misconceptions or incomplete understanding could be avoided if teachers combined those
two levels. This would be a common way of upgrading student knowledge which would
lead to a better comprehension of chemical concepts, which is a precondition for
understanding new ones that students come across in their advanced chemical education.
The results from the interviews with students show that they would better understand the
solutions if the concepts were explained at the submicro level. It is important to emphasise
that teacher should direct the discourse with students when developing their mental model
of solution chemistry. Teachers should be very precise in using correct concepts and
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20. adequate descriptions of the phenomena. They ought to combine the written and oral
evaluation to gain a more entire picture of students’ knowledge. During this process
teachers should pay attention to students’ expressions when describing specific phenomena.
It is also important to lay stress on the item text when evaluating especially lower (concrete)
cognitive levels of knowledge (i.e. knowledge, comprehension and application) or
evaluating the chemistry knowledge of students who display difficulties in chemistry
learning. Teachers should in this case use only one variable for the student to consider when
solving the specific task (e.g. one variable to consider is arrangement of particles and
another one is the correct concentration of the solution presented by the number of solute
particles).
It can be concluded that chemistry teachers, when presenting chemistry concepts, should
more frequently combine the three levels: macro-, submicro-, and the symbolic level and
more efficiently link the students’ pre-knowledge with the new topics, keeping in mind that
some topics are repeated later at higher levels of education, therefore suitable upgrading of
knowledge is necessary. Upgrading knowledge and linking the contents should be in the
forefront of teaching, not only in chemistry but also in science teaching in general.
In the end it is important to emphasize that to achieve the complex goals of modern
chemistry instruction, where focus is on gaining a deeper understanding of concepts,
developing the sensitivity needed to perceive problem situations, and problem-solving
strategies, quality teacher training is crucial. The teacher's role is no longer just to transmit
knowledge, but to organize a modern cognitive-constructivist model of instruction. To be
able to do so, the teacher needs a pre-service education based on a modern constructivist
approach, where the student's conceptions play a key role (Valenčič-Zuljan 2007). Teachers
also need to be offered permanent in-service development to support them practically in
organizing instructions in which learners will play an active and responsible role (Kalin and
Valenčič-Zuljan 2007).
Appendix
Problem No. 9
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21. Res Sci Educ

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