Res Sci Educ
DOI 10.1007/s11165-007-9047-8
Teaching Chemical Equilibrium with the Jigsaw
Technique
Kemal Doymus
# Springer Science + Business Media B.V. 2007
Abstract This study investigates the effect of cooperative learning (jigsaw) versus
individual learning methods on students’ understanding of chemical equilibrium in a
first-year general chemistry course. This study was carried out in two different classes in the
department of primary science education during the 2005–2006 academic year. One of the
classes was randomly assigned as the non-jigsaw group (control) and other as the jigsaw
group (cooperative). Students participating in the jigsaw group were divided into four
“home groups” since the topic chemical equilibrium is divided into four subtopics
(Modules A, B, C and D). Each of these home groups contained four students. The groups
were as follows: (1) Home Group A (HGA), representing the equilibrium state and
quantitative aspects of equilibrium (Module A), (2) Home Group B (HGB), representing the
equilibrium constant and relationships involving equilibrium constants (Module B), (3)
Home Group C (HGC), representing Altering Equilibrium Conditions: Le Chatelier’s
principle (Module C), and (4) Home Group D (HGD), representing calculations with
equilibrium constants (Module D). The home groups then broke apart, like pieces of a
jigsaw puzzle, and the students moved into jigsaw groups consisting of members from the
other home groups who were assigned the same portion of the material. The jigsaw groups
were then in charge of teaching their specific subtopic to the rest of the students in their
learning group. The main data collection tool was a Chemical Equilibrium Achievement
Test (CEAT), which was applied to both the jigsaw and non-jigsaw groups The results
indicated that the jigsaw group was more successful than the non-jigsaw group (individual
learning method).
Keywords Chemical equilibrium . Jigsaw technique . Cooperative learning
Chemistry education is becoming increasingly popular and important as it seen as a means
of improving scientific thinking, providing students with more experience of forming
K. Doymus (*)
Kazim Karabekir Education Faculty, Department of Primary Science Education,
Ataturk University, 25240-Erzurum, Turkey
e-mail: [email protected]
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explanations and interpretations of their environment and with the capability of finding
solutions to problems. In recent years, research has focused on identifying and characterising students’ understanding of and difficulties with many topics in chemistry education.
Chemical equilibrium, among these topics, is one of the most difficult in chemistry
education (Huddle and White 2000; Paiva et al. 2002; Sandberg and Bellamy 2004).
Teaching chemical equilibrium takes up a large part of the chemistry curriculum. One of the
main objectives of chemistry education is to enable students to understand chemical
equilibrium as a dynamic equilibrium in which two semi-reactions, direct and inverse, take
place (Campanario and Ballesteros 1991). It is also desirable that students learn to use the
mass action law and Le Chatelier’s principle to predict the result of the possible variations
in variables (pressure, volume) involved in chemical equilibrium (Tyson et al. 1999).
Another main objective is that intermediate level students learn how to compute
equilibrium concentrations from initial concentrations of chemical species involved in a
given reaction. To do so, students are generally taught to write the Kc formula with the
dissociation rate as an unknown. Typical problems are carefully chosen to obtain easily
solved first grade or, at the most, second grade equations. The numerical values of Kc and
initial concentrations are also chosen in such a way that, if necessary, its powers are small
and can be ignored with regard to initial concentrations. Students sometimes do not
understand completely when this can and cannot be done. Even though they are able to
solve numeric problems successfully, many students have alternate conceptions about
chemical equilibrium (Van Driel 2002). The situation is even worse: these alternate
conceptions can also be identified in some pre-service science teachers (Campanario and
Ballesteros 1991).
To help students understand chemistry, researchers have suggested a variety of
instructional approaches, such as adapting teaching strategies based on the conceptual
change model (Krajcik et al. 1988), integrating laboratory activities into class instruction
(Johnstone and Letton 1990), using concrete models (Copolo and HounshelL 1995), and
using technologies as learning tools (Barne and Dori 1996; Kozma et al. 1996). In
chemistry education, however, learning methods are as important as teaching strategies.
Used a lot, among the learning methods, is cooperative learning (Eilks 2005; Hennessy and
Evans 2006; Wu et al. 2001). Cooperative learning facilitates this process by assigning
students to small groups in which they work together to increase their own and one
another’s learning. Student achieves more, improve their social skills, and increase their
capacity to work productively together (Colosi and Zales 1998).
Cooperative learning is viewed as a tool for preparing students to work in teams as
required in various employment settings, in the home, and in the community when there is a
need to combine energies and work towards a common goal (Bolling 1994; Bowen 2000;
Eilks 2005; Gardener and Korth 1996; Gillies 2006; Hennessy and Evans 2006; Levine
2001; Lin 2006; Mergendoller and Packer 1989; Prince 2004; Prichard et al. 2006).
Cooperative learning is a process by which students work together in groups to master
material initially presented by the instructor Slavin (1995). Johnson and Johnson (1999)
pioneered the concept of cooperative learning in business and economic education. Other
definitions of cooperative learning include descriptions such as classroom environments
where students interact with one another in small heterogeneous groups while working
together on academic tasks (Parker 1984).
In addition to cooperative learning, collaborative learning is an umbrella term for a
variety of educational approaches involving joint intellectual effort by students, or students
and teachers together (Delucchi 2006). Usually, students are working in groups of two or
more (Tao and Gunstone 1999), mutually searching for understanding, solutions, or
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meanings, or creating a product. Collaborative learning activities vary widely, but most
centre on students’ exploration or application of the course material, not simply the
teacher’s presentation or explication of it. Collaborative learning represents a significant
shift away from the typical teacher centred or lecture-centred milieu in college classrooms
(Hawkes 1991; Summers et al. 2005). In collaborative classrooms, the lecturing/listening/
note-taking process may not disappear entirely, but it lives alongside other processes that
are based in students’ discussion and active work with the course material (Brewer and
Klein 2006). Teachers who use collaborative learning approaches as well as cooperative
learning approaches tend to think of themselves less as expert transmitters of knowledge to
students, and more as expert designers of intellectual experiences for students – as coaches
or mid-wives of a more emergent learning process (Summers 2006).
When examining the various types of cooperative learning, the literature is fairly
consistent in regard to the models and methods of cooperative learning instruction.
Research by Sapon-Slevin (1990) identifies three broad epistemological orientations, or
meaning systems for the types of cooperative learning: transmission, transaction, and
transformation. Research on major approaches to cooperative learning reveals eight
classroom approaches: (1) Student Teams and Achievement Divisions (STAD), (2)
Teams-Games-Tournaments,(TGT) (3) Learning Together (LT), (4) Jigsaw (JIG), (5)
Jigsaw II (JIG II), (6) Group Investigation (Gl), (7) Team Accelerated Instruction (TAI), (8)
and Cooperative Integrated Reading and Composition (CIRC) (Mergendoller and Parker
1989).
The strategy that is recommended most for social and science studies is the Jigsaw
series (Slavin 1990). The rationale behind this strategy is that in social studies there may
not always be one answer to a question. Other strategies (such as STAD and TGT) usually
are looking for only one correct answer and are therefore best suited to the math and
sciences. There are currently three types of Jigsaw strategies available for teachers to use
in their classroom: (a) Jigsaw developed by Aronson (1978); (b) Jigsaw II developed by
Slavin (1987); and (c) Jigsaw III developed by Stahl (1994). Jigsaw and Jigsaw II differ
only in the fact that team competition is allowed in Jigsaw II. The basic parts of the
strategies are the same. In the jigsaw technique, each student prepares a part of the
assignment out of class. Returning to the group, each student peer teaches the information
to the rest of the members. All groups in a class may cover the same topic, or different
groups may have different parts of the topic. Groups are subsequently reorganised to peer
teach the material (Grasha and Yangarber-Hicks 2000). The jigsaw technique can enhance
cooperative learning by making each student responsible for teaching some of the
material to the group. In this technique, students are members of two different groups, the
“home group” and the “jigsaw group.” Initially, students meet in their home groups, and
each member of the home group is assigned a portion of the material to learn as an
“expert” (Doymus et al. 2004; Slavin 1991). The home groups then break apart, like
pieces of a jigsaw puzzle, and the students move into jigsaw groups consisting of
members from the other home groups who have been assigned the same portion of the
material. While in the jigsaw groups, the students discuss their particular material to
ensure that they understand it. Students then return to their home groups, where they
teach their material to the rest of their group (Colosi and Zales 1998). In prior researches,
jigsaws were formed from cooperative groups. In this study, jigsaw were formed from
both cooperative groups subjects of relative unit.
This study investigates the effect of cooperative learning (jigsaw) versus individual
learning methods on students’ understanding of chemical equilibrium in a first-year general
chemistry course.
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Materials and Methods
Sample
The sample of this study consisted of 68 undergraduates from two different classes enrolled
to a general chemistry course during the 2005–2006 academic years at Ataturk University.
One of the classes was defined as the non-jigsaw (control) group (n=36) and received
individual learning method, while the jigsaw (experimental) group (n=32) was taught by
cooperative learning (jigsaw). No pre-test was necessary, because all undergraduates
enrolled to the university had passed a university entrance examination and all the students
were similar to each other in terms of science academic achievement. In Turkey, there is a
centralised university entrance examination system which is highly competitive. Each year
almost two million students take this examination and only ten percent of them can get a
place in a university. The minimum and maximum marks to enter all universities in Turkey are
200.4 and 391.2 respectively. Students’ minimum and maximum marks in this study are 272.6
and 289.1 respectively. As seen from this range of marks it could be accepted that students
participated in this study as having the similar academic achievement. In addition, the students
came to the department where this research was conducted had been taught the same curriculum
in high school. In this curriculum, chemical equilibrium, dissolution, reaction rates,
thermodynamics, acids and bases, and etc. are the titles covered by the chemistry course.
Instruments
The main data collection tool was a Chemical Equilibrium Achievement Test (CEAT),
which was applied to both the jigsaw and non-jigsaw groups. The CEAT was developed by
the author and two chemistry teachers. The CEAT was divided into four modules. Each
module was composed of four multiple-choice questions and one open-ended question.
Open ended questions of modules are given as an appendix. Multiple-choice questions were
piloted with undergraduates from two classes of college chemistry. Item analyses were
performed for each question and confusing or vague questions were rewritten before the test
was used in the study. The open-ended questions were evaluated according to quality
analysis. The reliability coefficient (Cronbach alpha) for the multiple-choice questions was
0.78. The maximum score for the multiple-choice questions was 20. Also, for the validity
of CEAT developed, opinions of the chemistry lecturers and researchers on the subject have
been taken into consideration. Researchers have pointed out that the gains of CEAT related
to the subjects of equilibrium have been high towards measurement.
Procedure
The jigsaw (experimental) group students were randomly divided into two parts (16
students + 16 students). Figure 1 represents one of these parts (16 students). The other part
was organized in the same way as the first.
The students in this part were divided into four “home groups” since the topic chemical
equilibrium is divided into four subtopics: Modules A, B, C and D. Each of these home
groups contained four students.
These modules are as follows:
Home Group A (HGA) Representing the equilibrium state and quantitative aspects of
equilibrium (Module A). The students in HGA prepared the subjects ‘Equilibrium in
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Fig. 1 Subtopics (modules) of
the topic chemical equilibrium
and home groups representing
these modules. Each code, A1,
A2, A3 etc. stands for an individual student from a group
The equilibrium state and
quantitative aspects of
equilibrium
(Module A)
A1
A3
A2
A4
HGA
The equilibrium constant
and relationships involving
equilibrium constants
(Module B)
Altering Equilibrium
Conditions: Le Chatelier’s
principle
(Module C)
Calculations with
equilibrium constants
(Module D)
B1
B3
B2
B4
HGB
C1
C3
C2
C4
HGC
D1
D3
D2
D4
HGD
chemical systems,’ ‘Equilibrium constant expressed in pressures,’ ‘Equilibrium constants
and heterogeneous equilibrium’ and ‘condition of dynamic equilibrium’ and presented these
subjects to the class.
Home Group B (HGB) Representing the equilibrium constant and relationships involving
equilibrium constants (Module B). The students in HGB prepared and presented the
subjects ‘calculation of the value of equilibrium constant,’ ‘calculation of equilibrium
concentrations’ and ‘prediction of the direction of reaction.’
Home Group C (HGC) Representing altering equilibrium conditions: Le Chatelier’s
principle (Module C).
The students in HGC prepared and presented the following subjects to the class: ‘effect of
changing the amounts of reacting species on equilibrium,’ ‘effect of changes in pressure or volume
on equilibrium,’ ‘effect of temperature on equilibrium’ and ‘effect of a catalyst on equilibrium.’
Home Group D (HGD) Representing calculations with equilibrium constants (Module D).
The students in HGD prepared and presented the following subjects to the class: ‘significance
of the magnitude of equilibrium constants,’ and ‘calculations with equilibrium constants.’
Each home group studied their subjects on their own out of class. Then each group was
given 30 min to present their work to the class and 20 min for discussion with the class.
During this discussion, the home group answered the questions asked by the class. The
home groups then broke apart, like pieces of a jigsaw puzzle (Goodwin et al. 1991), and the
students moved into jigsaw groups consisting of members from the other home groups who
were assigned the same portion of the material. Then the students in the home groups,
following the presentation of all subtopics in the chemical equilibrium, formed jigsaw
groups containing JA, JB, JC and JD, with one student from each of the home groups (see
Fig. 2). In these jigsaw groups, the teacher asked them to familiarize themselves with their
subtopic. They prepared summary reports and then each jigsaw group prepared a teaching
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Fig. 2 Forming of jigsaw groups
from home groups
A1
A3
A2
A4
HGA
B1
B3
B2
B4
HGB
C1
C3
C2
C4
HGC
D1
D3
JA
A2 B2
C2 D2
JB
A3 B3
C3 D3
JC
D2
D4
HGD
A1 B1
C1 D1
A4 B4
C4 D4
JD
strategy for its members to use to explain their subtopic to the rest of the class. Each jigsaw
group presented their own topic to the class for 30 min, and then discussed the related
topics for 20 min.
The students then went back to the home groups. These home groups then consisted of
one student from each jigsaw group, and these students were called “expert students.” The
experts were then in charge of teaching their specific subtopic to the rest of the students in
their learning group.
In the non-jigsaw (control) group; the subjects of chemical equilibrium were taught by
researcher using individual teaching methods. Individual teaching may be defined as a
teaching application stressing on the use of tools so as to provide the skills an interests of
each students. In individual learning, the researcher planed the activities of the presentation
the subjects which would be taught during the lesson, in a report not by a classical teaching
presentation but by giving assignments to students on the subjects of chemical equilibrium,
and by providing internet addresses and workbooks in order to construct the information to
be presented to them. In this process, student’s performances were observed and the studies
were directed according to the feedbacks taken from them. Individuals were also informed
that they could earn bonus points in their course if they achieved 90% or better on the endof-lesson test.
Once the teaching was completed to subjects of chemical equilibrium during 5 weeks, the
CEAT was applied to both the jigsaw and non-jigsaw groups as a post-test. Following the
presentation of the subject chemical equilibrium, the data obtained were evaluated by SPSS.
Findings and Discussion
The post-test data obtained from multiple-choice questions in all the modules of the CEAT
and the independent t-test analysis of these data are given in Table 1. Also, Students
responses given to the open ended questions of both modules were qualitatively analysed.
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Table 1 Results of independent t-test analysis of multiple-choice questions of all modules of the post-test of
the CEAT
Module A
Module B
Module C
Module D
Group
n
Mean
SD
t
p
Jigsaw
Non-jigsaw
Jigsaw
Non-jigsaw
Jigsaw
Non-jigsaw
Jigsaw
Non-jigsaw
32
36
32
36
32
36
32
36
14.84
8.64
17.34
7.08
14.80
7.78
8.75
5.42
4.49
3.83
4.01
3.02
5.75
3.26
4.40
1.40
6.149
0.001
11.996
0.001
6.132
0.002
4.105
0.001
Similar responses were gathered under the some heading. The number of the students gave
this particular responses were given in parenthesis next to the expression.
Module A
Module A, given in Table 1, showed that the students in the jigsaw group were more
successful than those in the non-jigsaw group (t (66)=6.149, p<0.05). In general, one area
identified as a source of students’ difficulties was the subtle differences between physical
and chemical systems that are at equilibrium. Many teachers and textbooks use a reversible
physical system such as the dissolution of sodium chloride in water to introduce the
equilibrium concept (Tyson et al. 1999). This solution is often used as a starting point
because students have considerable experience with this type of reaction both at home and
at school. However, the results indicated that students’ experience and understanding of this
type of reaction were in direct conflict with how they were expected to interpret the reaction
in terms of an equilibrium mixture. Furthermore, some responses given to the open-ended
question in Module A of both jigsaw and non-jigsaw students are given in the following.
Jigsaw group:
Physical Equilibrium (PE):
Without changing molecules of matter, only state changes (19).
It is an equilibrium established as a result of physical change at macro level between
water and vapour (8).
Chemical Equilibrium (CE):
It is occurs by changes in molecules of matter, forming new molecules, and the
equilibrium established between these molecules (21).
It is an equilibrium that is established between Vforward =Vreverse (7).
It is an equilibrium established as a result of chemical change at micro level (2).
Non- jigsaw group:
Physical Equilibrium (PE):
It is change of matter from one state to another without changing the molecular
structure (12).
It is an intra-molecular event (8).
It is the balance of a vector (8).
Chemical Equilibrium (CE):
It is a form of new matter by breaking of bonds between molecules (8)
It is an intermolecular event (10).
Equilibrium of a reaction is liquid and liquid’s vapour in a closed container (6).
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When the responses given concerning physical and chemical equilibrium to the openended question of module A are examined, it is clear that the responses of the jigsaw group
are contained more correct answers without alternate conceptions about physical and
chemical equilibrium when compared to the non-jigsaw group. The possible reasons for this
success can be the self-confidence of students in the jigsaw group as well as refreshment of
information and elimination of alternate conceptions during the group work. On the other
hand, the responses of the non-jigsaw group include many alternate conceptions and this
reveals that students had difficulties in understanding physical and chemical equilibrium, or
they did not understand it at all.
Module B
According to the data for Module B given in Table 1, the achievement of the jigsaw group
is higher than that of the non-jigsaw group (t (66)=11.996, p<0.05). The World Chemistry
Olympics and nearly all other chemistry examinations include problems about chemical
equilibrium. Most of these problems require the calculation of equilibrium constants at
given (not necessarily explicitly) equilibrium concentrations of the reacting species, or of
the concentration(s) of certain compound(s) of interest. However, most students cannot
grasp the impact that the equilibrium constant has on the distribution of reaction systems.
Students from HGB help other students to understand equilibrium constants. The
responses of students to the open-ended question of Module B show that the jigsaw group
students understood the topic of equilibrium constants well, indicating that jigsaw is an
efficient teaching technique.
Jigsaw group:
In a reaction that is in equilibrium, amounts of products and reactants are equal,
otherwise, no equilibrium is possible (8).
Amounts of products and reactants don’t need to be equal, if Vforward and Vreverse are
equal, then the reaction is in equilibrium, the amounts don’t need to be equal (16).
In a chemical equilibrium Vforward and Vreverse should be equal and the reaction
continues at microscopic level (8).
Non- jigsaw group:
At equilibrium, concentrations must be equal, not the amounts of matter (11).
If amounts of matter are not equal, the equilibrium breaks and chemical reaction
continues until equilibrium is reached (9).
If a gas is formed in the products side of the chemical reaction, then the reaction is
not at equilibrium and for that matter should be equal (7).
Amounts of matter in chemical equilibrium can be both equal and unequal (6).
Module C
In the data of Module C, given in Table 1, the achievement of the jigsaw group is higher
than that of the non-jigsaw group (t (66)=6.102, p<0.05). In module C, within the context
of Le Chatelier’s principle, the reason for the success of the students in the jigsaw group is
the cooperative learning (jigsaw technique), which is an active learning strategy (Bodner
1986; Johson and Gott 1996). Additionally, many studies have been conducted to assist
students to overcome their difficulties in learning Le Chatelier’s principle by elimination of
conceptual mistakes (Sandberg and Bellamy 2004), and some were conducted using
animation or simulation methods. In the present work, the jigsaw technique was used in
order to teach the mentioned principle more effectively. One of the reasons why students
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understood the principle is that students in HGC prepared and presented the altering
Equilibrium Conditions:
Students in HGC prepared and presented the altering Equilibrium Conditions: Le
Chatelier’s principle subjects in class, and then jigsaw groups formed from HGC represented the same subject in class.
In the jigsaw technique, students support each other and that raises self-confidence. The
success of the jigsaw group can be seen from the answers of this group to the open-ended
question of Module C.
Jigsaw group:
Pressure effects
N2ðgÞ þ O2ðgÞ $ 2NO2ðgÞ ð8Þ
SO2ðgÞ þ 1=2O2ðgÞ $ SO2ðgÞ ð6Þ
N2ðgÞ þ 3H2ðgÞ $ 2NH3ðgÞ ð8Þ
Pressure has no effect
I2ðgÞ þ H2ðgÞ $ 2HIðgÞ ð22Þ
Non-jigsaw group:
Pressure effects
SO2ðgÞ þ 1=2O2ðgÞ $ SO3ðgÞ ð5Þ
PCl5ðgÞ $ PCl3ðgÞ þ Cl2ðgÞ ð8Þ
Pressure has no effect
Cðk Þ þ H2 OðgÞ $ COðgÞ þ H2ðgÞ ð10Þ
Module D
Mean scores for Module D in Table 1 were decreased in both the jigsaw and non-jigsaw
groups. Despite these decreases, the success of the jigsaw group was higher than that of the
non-jigsaw group (t (66)=4.105, p<0.05). In this module, the reason for the lower
achievement of the jigsaw group than in other modules may be the students’ lack of
complete comprehension of the basic concepts such as (1) being able to write the
equilibrium expressions, Kc, for a given balanced chemical reaction involving homogeneous equilibrium, (2) being able to write the equilibrium expressions, Kc, for a given
balanced chemical reactions involving heterogeneous equilibrium, (3) being able to write
the equilibrium expressions, Kp, for a given balanced chemical reaction involving
homogeneous equilibrium, (4) being able to write the equilibrium expressions, Kp, for a
given balanced chemical reactions involving heterogeneous equilibrium, (5) being able to
use given concentrations of reactant(s) and product(s), and determine the numerical value of
the equilibrium constant Kc or Kp for a reaction, (6) knowing the significance of very large
(or small) equilibrium constants, and (7) being able to determine the equilibrium constant
expression and the equilibrium constant for situations where chemical equations are
reversed, multiplied through by constant coefficients, or added together (Keeports 2005). In
this work, this was the part of chemical equilibrium with which students struggled most.
The main reason for this is that students cannot comprehend the seven items mentioned
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above. The students’ answers to the open-ended question of this module show that the
jigsaw group students are successfully understood this topic and use the concepts of this
part much better.
Jigsaw group:
Equilibrium constant affects temperature, pressure, amount of matter and catalyst(6)
Equilibrium constant affects only temperature, for concentration changes with the
change in temperature (10)
Non- jigsaw Group:
Equilibrium constant affects temperature, pressure, amount of matter and catalyst (14)
Although HGD presented topics such as ‘Significance of the magnitude of the
equilibrium constant’ and ‘calculations with equilibrium constants,’ jigsaw groups formed
from each student of HGD again presented the same subjects to the class. Therefore, it
appears that the concepts that students were facing difficulty with in understanding were
reduced markedly by the jigsaw.
Conclusions
According to this research, many students have difficulty understanding chemical
equilibrium and think that the forward reaction goes to completion before the reverse
reaction commences, or that at equilibrium no reaction is taking place, and so ‘nothing
happens,’ providing a detailed overview of students’ conceptual difficulties with
equilibrium (Harrison 2003; Van Driel 2002). Data obtained in the present study indicated
an easier understanding chemical equilibrium in students that used the jigsaw technique.
When the technique was applied, it appeared that the responsibility the students took may
have positively impacted their learning.
However, most of the students in the non-jigsaw group did not know the factors
affecting the equilibrium constant. It is obvious that they find it difficult to separate the
factors affecting the equilibrium constant and the factors affecting the equilibrium system.
Additionally they have difficulties in understanding what chemical equilibrium is and how
equilibrium systems form. Moreover, they think that equal amounts of matter, rather than
the equality of Vforward and Vreverse is necessary for equilibrium of a reaction. In jigsaw
group students, these kinds of incorrect statement are much lower in number. It is possible
that the students helped each other to reduce alternate conceptions.
Appendix
Open ended questions of modules
Module A;
Q1. Please explain physical and chemical equilibrium by giving examples to each.
Module B;
Q2. Are the total amount of reactants and products are equal at equilibrium?
Module C;
Q3. Please write two equilibrium reactions that one of them can not be affected by
pressure and the other one proceed towards products by the effect of pressure.
Module D;
Q4. What are the factors effecting equilibrium constant? Please explain by giving examples.
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