Using computer simulations in chemistry problem solving

Abstract

This study is concerned with the effects of computer simulations of two novel chemistry problems on the problem solving ability of students. A control–experimental group, equalized by pair groups (n_Exp = n_Ctrl = 78), research design was used. The students had no previous experience of chemical practical work. Student progress was checked twice, once 15 minutes after they had started looking for a solution, before the experimental group was exposed to the simulation, and again after completion of the test. The 15 minutes check confirmed the equivalence of the two groups. The findings both verified the difficulty of the problems, and indicated improved mean achievement of the experimental group (students who were shown the problem simulations), in comparison to the control group (students who solved the problem in the traditional way). Most students assumed that the major benefit of the simulations was to help them with the proper application of the equations. The effects of scientific reasoning/developmental level and of disembedding ability were also examined. The performance level for formal reasoners was found to be higher than that for transitional reasoners and that for transitional reasoners higher than for concrete ones. Field independent students were found to outperform field intermediate ones, and field intermediate students were found to outperform field dependent ones. Finally, in most cases the experimental group outperformed the control group at all levels of the above two cognitive factors.

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Introduction

Problem solving

Problem solving is a higher-order cognitive activity, hence a composite one, that involves various cognitive functions, not least of which is the retrieving from long-term memory of a certain amount of information and the holding and working with it in working memory; simultaneously, information derived from the problem statement must also be held and processed in working memory. According to psychology and cognitive science, the human information processing capacity is restricted (Miller, 1956; Simon, 1974) due to the limitations of working memory (Baddeley, 1992). We can only pay attention to a certain limited amount of information and perform a restricted amount of work on a task at any one time. Many researchers have dealt with the role of working memory capacity in problem solving in science (e.g.Johnstone and El-Banna, 1986; Roth, 1988; Johnstone et al., 1993; Tsaparlis, 1998; Tsaparlis and Angelopoulos, 2000; Stamovlasis and Tsaparlis, 2001, 2003, 2012; St Clair-Thompson et al., 2012). In addition, other psychometric variables, such as ‘scientific reasoning’ (previously referred to as ‘developmental level’ in the Piagetian sense) and ‘disembedding ability’ (degree of ‘field dependence/independence’) play an essential role in science problem solving (Niaz, 1991; Niaz et al., 2000; Tsaparlis, 2005; Overton and Potter, 2011).

Central and crucial for problem solving are also the number and quality of available relative operative schemata in long-term memory. Piaget considered a schema as an internal structure or representation, and operations as the ways in which we manipulate schemata. The operative schemata entering a problem constitute the logical structure of the problem. According to Niaz and Robinson (1992) (see also Tsaparlis et al., 1998), the logical structure of a problem represents the degree to which it requires formal operational reasoning.

At this point, it is necessary to distinguish between what have been termed ‘problems’ and ‘exercises’. Exercises can be carried out relatively easily by many students, as they require only the application of well-known and practiced procedures (algorithms) for their solution. The skills that are necessary for this are as a rule lower-order cognitive skills (LOCS). On the other hand, a real/novel problem requires that the solver must be able to use higher-order cognitive skills (HOCS) (Zoller, 1993; Zoller and Tsaparlis, 1997). Note that the degree to which a problem is a real problem or merely an exercise will depend on both the student’s background and the teaching (Niaz, 1995). Thus, a problem that requires HOCS for some students may require LOCS for others in a different context.

A thorough classification of problem types has been made by Johnstone (1993, 2001). In this work, we are interested in real/novel problems. Such problems, requiring both the development of appropriate strategies and HOCS, prove very difficult for inexperienced students. A number of researchers (Simon and Simon, 1978; Larkin and Reif, 1979; Reif, 1981, 1983) have studied the differences between expert and novice problem solvers. The basic differences were: (a) the comprehensive and complete schemata of the experts, in contrast to the sketchy ones of the novices; and (b) the extra step of the qualitative analysis undertaken by the experts, before they move into detailed and quantitative means of solution. According to Reif (1983), a ‘basic description’ of a problem is the essential first stage in problem solving:

“The manner in which a problem is initially described is crucially important since it can determine whether the subsequent solution of the problem is easy or difficult – or even impossible. The crucial role of the initial description of a problem is, however, easily overlooked because it is a preliminary step which experts usually do rapidly and automatically without much conscious awareness. A model of effective problem solving must thus, in particular, specify explicitly procedures for generating a useful initial description of any problem … The basic description summarizes the information specified and to be found, introduces useful symbols, and expresses available information in various symbolic forms (e.g. in verbal statements as well as in diagrams)” (pp. 949–950).

Experience, or a lack of experience, on the part of secondary students with realistic chemical and physicochemical systems, such as those involved in chemical problems is also relevant to this work.

Problem solving and practical work

In science in general, and chemistry in particular, problems are related to phenomena and experiments. To solve a problem, students must have the previous knowledge and actual experience to reconstruct the phenomenon or experiment represented verbally in the problem, to be able to generate an initial ‘basic description’ of the problem. This is not an easy task, especially for school pupils in many countries (including Greece) who, very often, lack involvement with experiments, and experience chemistry only through talk, chalk, and books. Even when experiments are performed by the students, they are usually of the recipe type and contribute little to problem solving and enquiry learning in the laboratory (Domin, 1999a; Johnstone and Al-Shuaili, 2001; Tsaparlis, 2009). A content analysis of 11 general chemistry laboratory manuals reported that the majority required the learners to operate predominantly at the three lower cognitive levels of Bloom’s taxonomy (knowledge, comprehension, and application), and ignored the three higher levels of analysis, synthesis, and evaluation (Domin, 1999b).

Problem solving ability can be enhanced by associated laboratory activities. Interestingly, Kerr (1963, cited in Johnstone and Al-Shuaili, 2001) listed among the aims for practical work that it should provide training in problem solving and Roth (1994) found that physics problem solving at the upper secondary level was improved by means of practical work. Bowen and Phelps (1997) reported that demonstrations tend to improve the problem-solving capabilities of the students because they help them switch between various forms of representing problems dealing with chemical phenomena (for instance, symbolic and macroscopic). Deese et al. (2000) found that demonstration assessments promote critical thinking and a deeper conceptual understanding of important chemical principles.

In previously published work (Kampourakis and Tsaparlis, 2003), a laboratory/practical activity, involving the well-known ammonia-fountain experiment, was used in order to find out if it could contribute to the solution of a demanding chemistry problem on the gas laws (this is the same as problem 1 in the present study). Furthermore, the extent to which the practical activity, together with a follow-up discussion/interpretation in the classroom, could contribute to the improvement of the problem-solving ability of the students was assessed. The subjects were from tenth and eleventh grade (16–17 year olds). It was found that students from the experimental groups achieved higher scores than those obtained by students from the control groups. The differences, although not large, were in many cases, statistically significant. Mean achievement was, however, low, and only a small proportion of the students considered that the practical activity had been relevant/useful to the solution of the problem. It was concluded that many students lacked a good understanding of the concepts that relate to the ideal-gas equation. In addition, as is the case with most Greek students, the students had no previous experience in working with chemicals and carrying out, or even watching, experiments. It seems possible that observing the chemical experiment so dominated their attention that little opportunity was left for any mental processing of what was going on and why. In addition, the experiment chosen involved many details (including the production of ammonia gas from the reaction of ammonium chloride with sodium hydroxide), and involved many physics and chemistry concepts. It therefore seems likely that an overload of students’ working memory took place, preventing significant improvement in their ability to solve the problem.

The present study

In this paper, we report a study that employed computer simulations to demonstrate two experiments that were relevant to the solution of two chemistry problems. The computer program guided students in using the simulation, in performing the experiment, and in dealing with the problem. One of the experiments was basically the same as the ammonia fountain experiment, used in the earlier Kampourakis and Tsaparlis study (with some modifications/refinements). The second experiment concerned the ignition of a sulfur and oxygen mixture. The problem associated with the first experiment was exactly the same as that described in the previous study, while a new problem was specifically designed for the second experiment. Both problems were based on the use of the ideal-gas state equation for the calculation of gas volume or gas pressure respectively, and concentrations of aqueous solutions (molarities) were also involved in the problems and the calculations.

The central research question being investigated (Research question 1) is as follows: Does watching a simulation on a computer screen while attempting to solve a problem have an effect on students’ ability to solve the problem? In addition, the study offers the opportunity to investigate further two important factors that are known to have an important effect on students’ problem solving performance:

(2) Is the ability of students to solve problems related to their scientific reasoning/developmental level?

(3) Is disembedding ability (degree of field dependence/independence) connected to students’ ability in problem solving?

Rationale

Computer simulations in science education

As stated above, one can pay attention to only a limited amount of information and can perform only a restricted amount of work on a task at any one time. If the amount of information processing exceeds one’s capacity, it will result in cognitive overload (or working memory overload) (Johnstone and El-Banna, 1986; Sweller, 1988; Sweller and Chandler, 1991). In the case of laboratory experiments to be performed by the students, instructions can be designed so as to reduce the cognitive load and hence the possibility of overload. Cognitive Load Theory, developed by Sweller (Sweller, 1988; Bannert, 2002), which employs information processing theory, paying attention to the inherent limitations of working memory, is of relevance here.

Richard E. Mayer’s cognitive theory of multimedia learning, which is based on the fact that paying attention to several tasks simultaneously will result in a portion of the working memory not being available for learning (Mayer, 1997, 2001; Mayer and Moreno, 1998), is of relevance to this study. Mayer’s theory discusses a number of design principles for efficient multimedia instruction. The modality principle states that materials which present both verbal and graphical information should present the verbal information in an auditory format, and not as written text (Moreno and Mayer, 1999). On the other hand, according to the split attention effect, students learn better from animation and narration rather than from animation, narration, and on-screen text (Mayer, 2001). Other principles include the spatial contiguity principle – “Students learn better when corresponding words and pictures are presented near rather than far from each other on the page or screen”; the temporal contiguity principle – “Students learn better when corresponding words and pictures are presented simultaneously rather than successively”; the coherence principle – “Students learn better when extraneous material is excluded rather than included”; and the individual differences principle – “Design effects are stronger for low-knowledge learners than for high knowledge learners, and for high-spatial learners rather than for low-spatial learners”.

Virtual interactive experiments performed on the computer appear to be a powerful tool (Lajoie, 1993; Josephsen and Kristensen, 2006). Research shows that a computer-based learning environment can reduce the time required for performing a task, and at the same time reduce the cognitive load. Careful design and instructions can then contribute to enhanced student learning (Lajoie, 1993; Lajoi et al., 1998, 2001; van Bruggen et al., 2002; Josephsen and Kristensen, 2006).

According to Oakes and Rengarajan [2002, cited in Akaygun and Jones (2013)], an animation is a multimedia presentation that is rich in graphics and sound, but not in interactivity, while a simulation is defined as an interactive and explorative representation. The authors maintain that it is not always possible to re-create in a simulation an accurate real-world environment; further, the more sophisticated a simulation, the more accurately it represents and describes the target phenomenon.

Computer simulations have been used in a variety of teaching situations especially as a substitute for, or complement to, the chemistry laboratory (Butler and Griffin, 1979; Akaygun and Jones, 2013). Early laboratory applications involved simulations of macroscopic laboratory procedures. Later simulations extended the emphasis to representing phenomena at the atomic and molecular level, as well as to simulating large and expensive laboratory equipment. Although animations and simulations are different in terms of their level of interactivity, both have been used as effective tools for chemistry instruction. For instance, a number of studies have found that students who received instruction that included computer animations of chemical processes at the molecular level were better able to comprehend chemistry concepts involving the particulate level of matter than those who did not (Williamson and Abraham, 1995; Sanger and Greenbowe, 1997a, 1997b; Burke et al., 1998; Sanger et al., 2000; Ardac and Akaygun, 2004, 2005).

A main feature of simulations is their dynamic information and character, which increases the information-processing demand, and thus may not contribute to improved learning in comparison with static pictures (Rieber, 1990; Lewalter, 2003; Lowe, 2003). Lewalter maintains that dynamic visuals may reduce the load of cognitive processing by supporting the construction of a mental model, but they may cause higher cognitive load because of their transitory nature. Focusing on one type of presentation component may result in missing information from a different presentation component, because of the split attention effect. This effect occurs not only when one has to attend to multiple presentation stimuli (such as combinations of picture and text), but also when attending to a single presentation that includes temporal changes (as is the case in an animation or a simulation). Control of the variables in a dynamic visual can reduce the split attention effect.

The effect of scientific reasoning and disembedding ability on problem solving

Two cognitive variables, scientific reasoning and disembedding ability, were also considered in this study. These were considered pertinent for the following reasons: research has shown that solving chemistry problems involves many of the attributes of formal reasoning in the Piagetian sense, hence the ability to reason scientifically might be expected to be reflected in successful problem solving. For instance, Niaz and Robinson (1992) reported that the developmental level of students is the most consistent predictor of success when dealing with the logical complexity of chemistry problems, so that the number of operative schemata entering a problem may be the main contributor to the difficulty of the problem, overidding its mental (or cognitive) demand (the latter is connected with working memory capacity). Tsaparlis et al. (1998) confirmed the findings of Niaz and Robinson in the case of chemical equilibrium problems, by manipulating the logical structure of these problems. On the other hand, disembedding ability separates signal from noise and has proved to be an important factor for performance in real/novel problems, in which the field effect plays a central role: field-dependent subjects find it difficult/are unable to separate an item from its context, whereas field-independent subjects are able to make this distinction and can therefore focus better on the relevant field or context. A continuum exists between these two categories, with an intermediate category of field-intermediate subjects.

In a study on non-algorithmic quantitative physical chemistry problems that have many of the features of novel/realistic problems (Tsaparlis, 2005), it was reported that functional mental capacity and disembedding ability played important roles and were definitely more significant than either scientific reasoning or working memory capacity. Note that the psychometric test for measuring mental capacity (the figural intersection test) involves disembedding ability in addition to information processing.

The effects of scientific reasoning and disembedding ability have also been examined in the area of acid–base equilibria, and were found to be important for student performance, with the latter ability clearly having the larger effect (Demerouti et al., 2004). Developmental level was connected with conceptual understanding and application, but less so where complex conceptual situations and/or chemical calculations were involved. Disembedding ability was important in situations requiring demanding conceptual understanding, and where this is combined with chemical calculations. Overton and Potter (2011) investigated students' success in solving, and their attitudes towards, context-rich open-ended problems in chemistry, and compared these to algorithmic problems. They found a positive correlation between algorithmic problem solving scores and mental capacity (as measured with the figural intersection test), while scores in open-ended problem solving correlated with both mental capacity and disembedding ability. St Clair-Thompson et al. (2012) compared further algorithmic and open-ended problems with respect to mental capacity and working memory capacity; for the algorithmic problems working memory was reported to be the best predictor, while for open-ended problems both working memory capacity and mental capacity were important. On the other hand, BouJaoude et al. (2004) found that among a number of cognitive variables (learning orientation, developmental level, mental capacity, but not including disembedding ability), developmental level had the highest power to predict student performance in conceptual problems.

Method

The study was carried out over two consecutive school years, 2001–2002 and 2002–2003. In the first year, 101 tenth-year students, who were attending an upper secondary school (lykeion/lyceum) in an urban district of Piraeus, Greece (school A) participated. The students were divided into four classes, and 82 students who had been matched by pairs (see below) were selected. These 82 students formed the two study groups I_A and II_A, each with n = 41. The intervention was carried out during two teaching sessions. The research activity was carried out over two weeks, with one study session per week and one standard teaching period separating them. Group I_A acted as the experimental group (EG) for problem 1 and control group (CG) for problem 2 and vice versa for group II_A.

In the second year, 120 tenth-year students, coming from a different urban upper secondary school also in the Piraeus district (school B) participated. These students were also divided into four classes, and 74 students who had been equalized by pairs were selected. These 74 students formed the two study groups, I_B and II_B, each with n = 37. One group of school B acted as EG and the other as CG. Because of lack of instructional time, only problem 2 was used in the second year of the study.

The first author was a teacher in both schools. A chemistry teacher acted as the second teacher in school A, while a physicist took on this role in school B. All three were experienced teachers, with the first two holding postgraduate degrees in chemistry education. In both schools and for both problems, each teacher taught one EG and one CG of students.

All students in both schools had the same experience in working with chemicals in the lab, and all had attended the same computer simulations. Matching by pairs of the two groups for each year of the study was carried out on the basis of the following parameters: (i) mean achievement in three tests plus a final in-term exam in the chemistry course; (ii) scientific reasoning (developmental level) of the students (see below). In addition each pair of students had similar mean achievement in two final in-term exams in the physics course; Table 1 contains details about this matching by pairs. Statistical comparisons using a Student t-test for independent samples and Pearson correlations demonstrate the equivalence of the groups.

Table 1 Description of the matched by pairs experimental and control groups of students for the two schools used in the study. Mean percentage achievement (with standard deviations in parentheses) in chemistry, physics, and in the Lawson test, plus statistical tests (t test and correlation coefficients)

	Chemistry	Physics	Lawson test
School A
Group IA	54.5 (21.5)	61.5 (17.0)	53.6 (20.0)
(n = 41)
Group IIA	54.5 (22.0)	62.5 (18.5)	54.0 (18.9)
(n = 41)
Tests for equivalence
t-Test (p-value)	0.16 (0.87)	0.20 (0.84)	0.38 (0.70)
Pearson r	0.97	0.76	0.86
School B
Group IB (experimental)	73.8 (16.8)	69.9 (22.0)	53.7 (20.8)
(n = 37)
Group IIB (control)	75.0 (17.4)	69.9 (20.4)	51.6 (18.9)
(n = 37)
Tests for equivalence
t-Test	0.97 (0.34)	0.02 (0.98)	1.03 (0.31)
Pearson r	0.97	0.79	0.81

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The testing procedure

At the outset, the students were informed about the research character of the teaching and testing methodology. The students were asked to solve a given problem each time. Testing took 35 minutes. For the EGs it took place inside the computer school labs, which were each equipped with 12 and 10 PCs for schools A and B respectively. The students wrote on special double copy paper. For both the EG and the CG, 15 minutes after the start of the test, the teacher asked the students to hand in one copy of their paper, with what they had written up to that time. This allowed for an evaluation of the students’ achievement up to that time. Following that, the students of the CG were allowed to continue their effort for 20 more minutes, after which the teacher collected their final papers. In the case of the EG, after the students handed in the copy with their work up to the 15th minute, they were instructed to use their PC to watch the problem simulation for 5–7 minutes. During this time, they were free to run and watch the simulation as many times as they wanted. Then, they were allowed to continue their effort in solving the problem for 15 more minutes, after which time their final papers were also collected.

The problems

Two problems were used. Problem 1 was taken from an official book for tenth-grade students, supplied by the Greek Ministry of Education, and was identical to the problem used in the Kampourakis and Tsaparlis (2003) study. Problem 2 was devised and constructed by the second author.

Problem 1: A vessel contained gaseous ammonia (NH₃) at a pressure p₁ = 2 atm, and a temperature of 27 °C. Part of the ammonia gas was transferred to a container containing water, where it dissolved completely to produce 2 L of a 0.1 M aqueous ammonia solution. If the pressure in the vessel is reduced to 1.18 atm, find the volume of the vessel.

The logical structure of problem 1 involves two main schemata: the ideal gas equation and concentration of aqueous solutions (molarity). The problem caused various difficulties to the students. In particular, they failed to connect the fall in the gas pressure with the ammonia solution that was formed. To make the problem as close as possible to a real problem (and not a traditional exercise), no further comments about the problem were provided, and the value of the ideal gas constant was not given, so the students needed to know or be able to calculate the value of the ideal gas constant in the proper units.

Most successful solvers applied the ideal gas equation twice, for both the initial and the final state of the ammonia gas in the flask: p₁V = n₁RT (1) and p₂V = n₂RT (2). From these two equations, they arrived at the relationship n₁/p₁ = n₂/p₂ (3). If n_s is the number of moles of ammonia dissolved in water, then n₂ = n₁ − n_s. Substituting into eqn (3) provides solution of the resulting equation for n₁. Finally, substitution of the value for n₁ into eqn (1) leads to the calculation of V. A much smaller proportion of students did not use the ideal gas equation, but instead started with the equation p₁/p₂ = n₁/n₂ (at constant V and T), and went on as mentioned above. A number of students (11 out of 41, 26.8%) made (eventually successful or unsuccessful) use of the difference between the two given pressures in their solution, which led to the relationship p₁ − p₂ = n_sRT/V. This alternative method of solution is easier and faster, so the students who employed it demonstrated a good conceptual understanding of the problem. Note that the existence of a pressure gauge in the experimental setting is likely to have contributed substantially to the idea to subtract the two pressures, a fact that was admitted by the students who employed this method.

The marking scheme for problem 1 is given in Appendix 1 (Table 6). Partial marks were allocated to the various steps in the solution procedure as follows: 10.0 + 2.5 = 12.5 marks for calculation of moles of ammonia gas dissolved in water; 11.25 marks each for eqn (1) and (2); 2.5 marks each for conversion of degrees Celsius to degrees Kelvin and for knowing or estimating the value of R; 20.0 marks for the relationship n₂ = n₁ − n_s; 22.5 marks for the algebraic manipulations that lead to a final expression for V; 10.0 marks for intermediate numerical calculations; finally, an additional 7.5 marks for the correct numerical result with proper units. Four experienced chemistry teachers independently marked fifteen randomly selected papers, according to the agreed marking scheme. The Pearson correlation coefficients between the four markers varied between 0.94 and 0.99.

Problem 2: A closed vessel with a volume of 4 L, at a temperature of 207 °C, contains a mixture of sulfur (S) and precisely the quantity of oxygen gas (O₂) required for complete combustion. The vessel is supplied with a piston and an exhaust gas valve. The mixture is ignited so that all the sulfur is burnt and all of the oxygen is consumed [S(s) + O₂ (g) → SO₂(g)]. By pressing the piston, all the combustion gas produced is transferred into a beaker containing 0.5 L cold water, where part of the gas is dissolved to give a solution with a concentration of 0.96 mol L⁻¹. The remaining gas is collected in an inverted test-tube, and was found to occupy a volume of 0.448 L at STP. Calculate the pressure in the closed vessel before igniting the mixture and compressing the piston.

Here again the value of the ideal gas constant was not supplied for the same reason as for problem 1. On the other hand, so as not to further increase the complexity of the problem, we included in it the relevant chemical equation. To solve this problem one has to consider the moles n₁ of SO₂ that were dissolved in water and the moles n₂ that were collected in the test-tube. The total amount of SO₂ is then n₁ + n₂. Next, the moles of O₂ which were present in the vessel before combustion have to be calculated from the reaction stoichiometry. Finally, the ideal-gas equation has to be applied to calculate the initial pressure in the vessel.

Problem 2 is more demanding than problem 1, having a more complex logical structure. In addition to the schemata of the solvation and the ideal-gas equation, it involves the extra schema of the stoichiometry of the chemical reaction (combustion of sulfur). A further complication arises from the fact that part of the gas produced is dissolved in water and the remainder is collected separately.

The marking scheme for problem 2 is given in Appendix 1 (Table 7). All student papers were marked by the first author, who was a chemistry teacher in school A and one of the two teachers in school B. Validity and reliability of the marking schemes was judged by having 40 papers (20 for each group, EG and CG) marked by another teacher chemist. The correlation between the two markings was high (r = 0.96).

The simulations

The simulations for the two problems are described in Appendix 2. The problems themselves provided the scenarios for design and construction of the simulations. For technical reasons, audio material was not included, so some of Mayer’s design principles for effective multimedia instruction were not employed (see Rationale). However, efforts were made to ensure that the simulations were clear and easy for the students to use, suitable for the students’ age and level of knowledge, and simple, without extra added information (‘noise’), which would have been irrelevant to the solution of the problems (Mayer’s coherence principle). Also, little time was required for the handling and watching of each simulation, and care was taken to ensure that the simulation did not reveal the solution. The duration of each simulation did not exceed 1.5 minutes, so that students could watch it several times within the 5–7 minutes available.

The same procedure and construction perspective was adopted for the simulations of both problems. Three screens were created; the one that appears first is the simulation of the experimental set-up, while the other two screens play supporting roles: one is descriptive/explanatory about the equipment and its connection with the problem; and the other provides functional help. When execution of the problem is initiated, the main page, which shows the experimental set up, appears. Navigation is horizontal, that is, there is ability to switch between the three screens: Description of the experiment; Restart the experiment; Help, by using three “buttons”, which are always present and active. Further details about the simulations are provided in Appendix 2.

Psychometric measures

In this study, scientific reasoning was assessed by means of the Lawson paper-pencil test, which included 15-open-ended-items, and tested the following reasoning modes: conservation of weight, displacement of volume, control of variables, proportional reasoning, combinational reasoning, and probabilistic reasoning (Lawson, 1978). The two schools involved in our study were matched by pairs in terms of scientific reasoning as follows: In the two groups, I_A (n = 41) and II_A (n = 41), of school A there was precisely the same number of students in each of the three developmental levels: 6 concrete, 23 transitional, and 12 formal reasoners. Similarly for the two groups, I_B (n = 37) and II_B (n = 37), of school B, there were 6 concrete, 21 transitional and 10 formal reasoners in each.

Disembedding ability was assessed by means of the Hidden Figures Test, which is a 20 minute test that was devised and calibrated by El-Banna (1987), and is similar to the Group Embedded Figures Test, GEFT, devised by Witkin (Witkin et al., 1971; Witkin, 1978). The two groups from school A were NOT matched in terms of this ability: in group I_A there were 21 field dependent, 14 field intermediate, and 6 field independent students while in group II_A there were 15 field dependent, 14 field intermediate, and 12 field independent students. On the other hand, the two groups from school B were matched, with each group having 6 field dependent, 20 field intermediate, and 11 field independent students.

Results

Table 2 gives data and statistical comparisons for student achievement during the first 15 minutes. For testing significance of differences of mean achievements between the two matched samples, we used the parametric paired Student’s t test (t-test for matched pairs) and the non-parametric Wilcoxon signed-rank test (W) (Cohen and Holliday, 1982). Since we were interested in testing whether one process was better or worse than the other, we employed two-tailed criteria. It is evident that during the first 15 minutes the two groups EG and CG did not differ in their treatment, as the use of the simulation was only introduced after their papers had been collected; therefore, the student achievement during the first 15 minutes provides a further check on the equivalence of the two groups. With the exception of school A for problem 2, the EG and the CG were equivalent statistically. The considerable improvement demonstrated by the CG students from school A, in the case of problem 2, might be attributed (a speculation) to the fact that the CG students for problem 2 had previously acted as the EG for problem 1, so they had attended the simulation program for problem 1. It was evident to these students (now forming the CG) that they were not going to use the computer this time, so they worked diligently on the problem, while the students from the EG were waiting to see the simulation program, and were less eager to begin work on the solution before that.

Table 2 Total percentage achievement (mean values with standard deviations in parentheses) at time 15 minutes after the start of the test (paired t-test and Wilcoxon signed-rank test)

School	Experimental group	Control group	t Value (p)	W Value (p)
a School A enters here through problem 1 and school B through problem 2.
Problem 1
A	16.3 (23.3)	13.4 (16.4)	0.91 (0.370)	0.51 (0.609)
	(n = 41)	(n = 41)
Problem 2
A	11.4 (12.7)	29.4 (27.5)	−4.93 (<0.001)	−4.23 (<0.001)
	(n = 41)	(n = 41)
B	8.65 (8.18)	10.5 (15.2)	−0.79 (0.44)	−0.71 (0.479)
	(n = 37)	(n = 37)
Problems 1 and 2^a
A + B^a	12.7 (18.0)	12.1 (15.8)	0.314 (0.755)	0.036 (0.971)
	(n = 78)	(n = 78)

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Achievement in solving the problems

Table 3 shows the achievement of the EGs and CGs for schools A and B, respectively, as well as for the sum of schools A and B, but with school A entering in the latter sum only through problem 1 (the reason will become clear below). Recall that school A did both problems, while school B tackled only problem 2. The table also contains data for the statistical comparisons (t and W values). As a matter of fact, students from the EG might have been handicapped by (i) the interruption of the solution process for the EG while they viewed the simulation and/or (ii) any misunderstanding that might have been introduced because of the simulation.

Table 3 Total percentage achievement (mean values with standard deviations in parentheses) in solving the two problems for the experimental and control groups (plus statistical comparisons)

School	Experimental group	Control group	t Value (p)	W Value (p)
a School A enters here through problem 1 and school B through problem 2.
Problem 1
A	32.1 (26.6)	23.1 (20.5)	2.12 (0.030)	2.32 (0.010)
	(n = 41)	(n = 41)
Problem 2
A	40.6 (26.5)	38.8 (32.7)	0.43 (0.700)	0.52 (0.600)
	(n = 41)	(n = 41)
B	36.4 (30.5)	26.4 (26.6)	1.81 (0.080)	1.73 (0.080)
	(n = 37)	(n = 37)
Problems 1 and 2^a
A + B^a	34.1 (28.4)	24.6 (23.5)	2.81 (0.006)	2.96 (0.003)
	(n = 78)	(n = 78)

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The following conclusions can be drawn from the data: in all cases, performance was low and below a 50% value. Achievement by the EG was higher for both problems. There were statistically significant differences in favor of the EG for the following cases: school A for problem 1 and sum of schools A for problem 1 and B for problem 2.

Achievement of school A was much higher for problem 2 (especially for the CG), and this can be attributed to the experience these students gained, both from solving problem 1 and from their practice with the simulation program. The considerable improvement displayed by the CG from school A on problem 2 (showing only a very small and statistically insignificant inferior achievement to that for the corresponding EG from school A) might be attributed to the fact that the CG students for problem 2 acted as the EG for problem 1, so they had previously experienced the simulation program for problem 1. While for problem 1 there is a statistically significant difference, in the case of problem 2 only for school B was the difference substantial and near statistical significance.

An important finding relates to the number of successful solvers, both in each problem, and with regard to the effect of the simulations. We identified students who achieved a mark over 80% in each problem as successful solvers. From a total of 41 students, there were 6 successful solvers of problems 1 (14.6%), of which 5 belonged to the EG and 1 to the CG. Also, from a total of 78 students, there were 23 successful solvers of problem 2 (29.3%), 11 belonged to the EG and 12 to the CG. Recall the effect of practice on the achievement of the CG from school A on problem 2.

It is of particular interest to examine the improvement of mean achievement from 15 minutes until the end of testing (see Tables 2 and 3). The highest positive effect of the simulation was noted in the case of school B for problem 2, in which case the EG improved its mean achievement from 15 minutes until the end of testing by 4.2 times (8.65 → 36.4), while the CG improved by only 2.5 times (10.5 → 26.4). On the other hand, the group from school A that acted as EG for problem 1 improved its mean achievement by about a factor of 2 (16.3 → 32.1) for problem 1, but much less (only 1.3 times) for problem 2 (29.4 → 38.8) when it acted as CG. This can be attributed to two factors: this group knew that as CG they were not going to watch a simulation, hence they worked steadily during the first 15 minutes, thus advancing their solution further (29.4), and, as a result, their further improvement by the end of time (38.8) was not particularly impressive. However, the fact that their overall achievement (38.8) is comparable to that of the corresponding EG (40.6) is impressive; their experience of working with the simulation for problem 1 could well have played a role. Finally, the group from school A that acted as CG for problem 1 improved its mean achievement by about a factor of 2 (13.4 → 23.1) for problem 1, but much more (3.6 times) for problem 2 (11.4 → 40.6) when it acted as EG. It is apparent that all groups got better with more time, but using the simulation was far more effective in most cases (except for the case of school A for problem 2). Note that all the above changes of score from time 15 minutes until the end of testing are statistically significant (p < 0.001), as judged by using the t test for dependent samples.

Turning to some qualitative aspects of the use of the simulations, discussions with the students after the intervention showed that most students initially assumed that the simulations did not help them in the solution of the problems but were useful in helping with the proper application of the equations. Further discussion revealed some interesting aspects of the students’ actions and attitudes, with several of them admitting that through the simulations they “cleared out something (in their minds)”. We quote below some of the most useful comments that were collected:

• Using the computer did not disturb them, but on the contrary they found it interesting.

• The instructions were clear.

• They had no problem using the quick instructions of the software, and they did not need practice.

• They did not assume that they were helped with the final solution of the problems.

• In the simulation of problem 1, the pressure gauge helped them realise that pressure changed.

• They received an overall help from the simulation of problem 2 because it was long and it was difficult for them to keep in mind the procedure.

• Some students protested that they had never before solved a similar problem before taking the test with problem 1.

Effect of scientific reasoning on the effectiveness of the simulation

Table 4 shows comparisons for students according to their levels of scientific reasoning (developmental level). For statistical comparisons, values of the paired t statistic as well as of the Wilcoxon signed-rank test are given, because the groups are matched by pairs. Recall that here all samples were matched by pairs in terms of levels of scientific reasoning, so we have equal numbers for each level for the EG and the CG. Formal students performed better than transitional, and transitional better than concrete students (except for the EG from school A for problem 2). In all cases (except for school A for problem 2), the difference is higher in the case of the formal students. Also, in most cases the EG students performed better than the CG students at all levels of logical thinking. However, due to the small samples, the differences are not statistically significant, except in the case of the formal students for the sum A (problem 1) + B (problem 2) and nearly so for the formal students of school A for problem 1.

Table 4 Total percentage achievement (mean values with standard deviations in parentheses) for the three levels of scientific reasoning, and statistical comparisons

Levels of scientific reasoning	Experimental group	Control group	t Value (p)	W Value (p)
School A (problem 1)
Concrete	15.0 (8.94)	6.7 (0.30)	1.494 (0.195)	1.355 (0.176)
	(n = 6)	(n = 6)
Transitional	27.6 (20.1)	23.8 (19.5)	0.840 (0.410)	1.326 (0.185)
	(n = 23)	(n = 23)
Formal	49.2 (34.9)	29.8 (22.9)	2.143 (0.055)	2.161 (0.031)
	(n = 12)	(n = 12)
School A (problem 2)
Concrete	34.2 (36.9)	13.3 (8.12)	1.176 (0.293)	0.841 (0.400)
	(n = 6)	(n = 6)
Transitional	31.9 (19.2)	29.4 (23.95)	0.422 (0.677)	0.770 (0.441)
	(n = 23)	(n = 23)
Formal	60.4 (24.4)	70.0 (27.3)	−0.846 (0.415)	−0.831 (0.406)
	(n = 12)	(n = 12)
School B (problem 2)
Concrete	25.3 (30.1)	20.3 (13.98)	0.430 (0.680)	0.339 (0.735)
	(n = 8)	(n = 8)
Transitional	33.8 (29.4)	26.0 (27.5)	1.069 (0.298)	1.083 (0.279)
	(n = 20)	(n = 20)
Formal	51.9 (30.6)	32.5 (33.9)	1.491 (0.174)	1.718 (0.086)
	(n = 9)	(n = 9)
School Α (problem 1) and B (problem 2)
Concrete	20.9 (23.4)	14.5 (12.4)	0.937 (0.366)	0.550 (0.582)
	(n = 14)	(n = 14)
Transitional	30.5 (24.7)	24.8 (23.3)	1.373 (0.177)	1.662 (0.096)
	(n = 43)	(n = 43)
Formal	50.4 (32.3)	30.9 (27.4)	2.620 (0.016)	2.748 (0.006)
	(n = 21)	(n = 21)

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Effect of disembedding ability on the effectiveness of the simulation

Table 5 shows a comparison of students according to their level of disembedding ability. For statistical comparisons, values of the parametric t statistic for independent samples as well as of the Mann–Whitney test (U or z for one or both samples >20–25) (U is a non-parametric counterpart for independent observations.) (Recall that in this case, the EGs and CGs were not matched by pairs in terms of levels of disembedding ability, except for school B (for problem 2) – but even for school B the equalization was in numbers of students per level, and not by pairs.) Field independent students outperformed field intermediate students (except for the EG from school A for problem 2), and field intermediate students outperformed field dependent ones [except for the CG from school A for problem 1, the EG from school B for problem 2, and for the sum (school A for problem 1 + school B for problem 2) for the EG]. Also, with one exception, the EG students outperformed the CG students at all levels of disembedding ability, but, due to the small samples, the differences are not statistically significant. In the case of school A for problem 2, the field independent students from the CG (n = 6) performed much higher than the corresponding students of the EG (n = 12), but their sample size was very small.

Table 5 Total percentage achievement (mean values with standard deviations in parentheses) and statistical tests (t-test for independent samples and Mann–Whitney U test) for the three levels of disembedding ability

Levels of disembedding ability	Experimental group	Control group	t Value (p)	U Value (p)
School A (problem 1)
Field dependent	27.6 (25.6)	22.3 (24.4)	0.628 (0.535)	0.988 (0.323)
	(n = 21)	(n = 15)
Field intermediate	32.5 (21.3)	18.6 (9.99)	2.217 (0.036)	2.700 (0.007)
	(n = 14)	(n = 14)
Field independent	46.7 (39.2)	29.2 (24.1)	1.18 (0.255)	1.42 (0.154)
	(n = 6)	(n = 12)
School A (problem 2)
Field dependent	31.0 (24.7)	21.4 (16.8)	1.387 (0.0174)	1.241(0.215)
	(n = 15)	(n = 21)
Field intermediate	48.6 (25.7)	48.2 (31.5)	0.033 (0.974)	0.500 (0.617)
	(n = 14)	(n = 14)
Field independent	43.3 (28.2)	78.3 (25.6)	−2.556 (0.021)	−2.204 (0.028)
	(n = 12)	(n = 6)
School B (problem 2)
Field dependent	39.2 (35.5)	18.3 (15.9)	1.312 (0.219)	1.203 (0.229)
	(n = 6)	(n = 6)
Field intermediate	28.1 (27.0)	25.9 (26.8)	0.260 (0.797)	0.461 (0.648)
	(n = 20)	(n = 20)
Field independent	49.8 (31.5)	31.6 (31.5)	1.353 (0.191)	1.776 (0.076)
	(n = 11)	(n = 11)
School Α (problem 1) and B (problem 2)
Field dependent	30.2 (27.8)	21.2 (22.0)	1.216 (0.230)	1.41 (0.158)
	(n = 27)	(n = 21)
Field intermediate	29.9 (24.6)	22.9 (21.6)	1.254 (0.214)	1.636 (0.102)
	(n = 34)	(n = 34)
Field independent	48.7 (32.3)	30.3 (27.3)	1.918 (0.063)	2.183 (0.030)
	(n = 17)	(n = 23)

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Conclusion and answers to the research questions

The two problems proved very difficult for the students in our sample. Student performance was disappointing (under the 50% mark) for both problems and both the experimental group (EG) and the control group (CG). This can be attributed to the involvement of various complex concepts, such as the ideal gas law equation, volumetric analysis, and, in the case of the problem 2, reaction stoichiometry. As a matter of fact, the concept of the ideal gas and the ideal gas law are even difficult for first and second-year undergraduate students (Kautz et al., 1999). In addition, our students had no previous practice with similar problems, had no experience in carrying out experiments, and were not even familiar with laboratory equipment. To ensure that the problems were not straightforward algorithmic exercises but had features of real/novel problems, we did not provide the value of the ideal gas constant for the students. Regarding our three research questions, our conclusions are as follows:

Research question 1. Does watching a simulation on a computer screen while attempting to solve a problem have an effect on students’ ability to solve the problem?

Our results showed improved mean achievement for the EG, that is for the students who used/viewed the problem simulations, in comparison to the CG, who solved the problem in the traditional way by thinking and writing on paper. This was more evident when the results for the two schools were combined (school A for problem 1 and school B for problem 2) to give a larger sample (sum A + B).

Achievement levels at school A were much higher for problem 2 (especially for the CG), and this can be attributed both to the experience these students gained from solving problem 1 and from their practice with the simulation program. The considerable improvement in problem 2 for the CG at school A might be attributed to the fact that the CG for problem 2 had previously acted as the EG for problem 1, so it had experienced the benefits of the simulation program for problem 1. An additional fact that supports the above speculation is that in the interlude between the two teaching periods when the two problems were administered to the students of school A, the solution to problem 1 was presented and relevant discussions were carried out by both the EG and the CG. We assume that the model solution and the related discussion must have contributed greatly to the improved results of the students from school A in problem 2.

We repeat that the equivalence of the two groups of students (EG and CG) was established by a proper composition that was based on their achievement in chemistry and physics in-term exams, as well as in the Lawson test of scientific reasoning. In addition, the equivalence was checked by comparing achievement, during the first 15 minutes of the test for each of the two problems of this study, where the performance of the two groups was found to be similar.

A deeper analysis of the students’ solution procedures showed that marks were low irrespective of the use or non-use of the simulations. This suggests that there is a mental ‘jump’ from the solution of the component subproblems to the synthesis and solution of the whole problem. It appears that the effect of the simulations for the relevant experimental set-ups did not really lead to the final solution of the problems. The simulations rather appeared to help with the solution of the subproblems or component steps in a problem. Therefore, the overall performance on the problem improved, because after viewing the simulations more students were successful in using the equations, relationships, and data appropriately. Examples of students attempting to solve exercises or problems by using equations, relationships, and data unsuccessfully or combining them at random (or by using incorrect equations and relationships) are well-known both to experienced teachers and in the problem solving literature. According to our marking schemes (see Appendix 1), a total mark of 30–40% could be achieved by a student who just knew the proper equations and relationships, and applied them correctly. In particular, the handling of volumes (volume of the vessel, volume of water, volume of the gas) proved difficult. It is at this point that the simulations appeared particularly helpful.

Research question 2. Is the ability of students to solve problems related to their scientific reasoning/developmental level?

As mentioned earlier, research has shown that the developmental level of students is the most consistent predictor of success when dealing with significant changes in the logical structure of chemistry problems (Niaz and Robinson, 1992; Tsaparlis et al., 1997). Our results indicate that the two problems of this study (especially problem 2) had a rich logical structure (see comments after the two problems). With one exception, formal students performed better than transitional students, and transitional students better than concrete ones, with the differences between EG and CG being highest in the case of the formal students. In most cases, the EG students performed better than the CG students at all levels of logical thinking, but, due to the small sample sizes, the differences are not statistically significant except in the case of formal students in the sum A (problem 1) + B (problem 2).

Research question 3. Is disembedding ability (degree of field dependence/independence) connected to students’ ability in problem solving?

It is known from the literature that in the solving of realistic/novice problems, disembedding ability plays an important and dominant role (Demerouti et al., 2004; Tsaparlis, 2005; Overton and Potter, 2011). Our results indicate that both problems used in this study have features of novelty/were real problems for our students. With some exceptions, field independent students outperformed field intermediate students, and field intermediate students outperformed field dependent ones. Also, with one exception, the EG students performed better than the CG students at all levels of disembedding ability. However, due to small sample sizes, the differences are not statistically significant.

Final comments

The data undoubtedly demonstrate that the use of computer simulations can be helpful in improving problem solving scores. We recognize that other types of intervention, for example, just talking through the problem with the students, demonstrating the experiment, or by having the students perform the experiment themselves, might have been equally effective, but the issue here was to check whether a particular approach (the computer simulation) would be effective.

Our previous study examined the effect of a laboratory/practical activity involving the ammonia-fountain experiment on the solution of problem 1 (Kampourakis and Tsaparlis, 2003). While both studies were carried out with tenth-grade general education Greek students (around 16 years old), the previous study also involved some eleventh-grade students (around 17 years old), who were following a stream of studies that included advanced chemistry among its main subjects. The tenth-grade students of the experimental group of this previous study had a mean achievement of 18.6% in problem 1, while the corresponding eleventh-grade students achieved a mean score of 37.0%. The second score is about the same as the marks achieved by the EG students in the present study. The difference for tenth grade students between the present and the previous study could be attributed, in part, to the fact that chemistry was taught as a one-period per week course in the previous study, whereas the teaching time had been doubled in the present study. Finally, the students involved in the present study came from an urban region of Piraeus, while those from the previous study came from a semi-urban region in north-western Greece.

It follows from a comparison of the two studies, that we cannot with any certainty assert that the simulations are more effective than, and hence preferable to, real practical activities. However, we would point out that actual experiments often involve extra, background information that is not relevant to a particular problem. This may prevent students from paying attention to key stimuli relevant to the problem, by causing an overload of the working memory [Kempa and Ward, 1988; Johnstone and Letton, 1990 – see the relevant discussion in Kampourakis and Tsaparlis (2003)]. It is also important to appreciate that simulations are, usually, safer, faster, more economical and easier to perform and repeat than real experiments. A good understanding of the relevant theory is of course very important for problem solving. “Students who lack the requisite theoretical framework will not know where to look, or how to look, in order to make observations appropriate to the task in hand, or how to interpret what they see. Consequently, much of the activity will be unproductive” (Johnstone and Al-Shuaili, 2001). “Knowing what to observe, knowing how to observe it, observing it and describing the observations are all theory-dependent and therefore fallible and biased” (Hodson, 1986). Last but not least, let us not forget that an important first step in problem solving in science (after reading the problem) is to make a drawing of the problem situation (Mettes et al., 1980; Reif, 1981, 1983; Genya, 1983). Simulations are capable of providing a better picture of a problem than is possible with a simple drawing.

Appendix 1. Marking schemes for the two problems

Tables 6 and 7

Table 6 Marking scheme for problem 1

Solution step	Solution procedure	Numerical computation
• Moles ns of NH3 dissolved in water	10.0	2.5
• p1V1 = n1RT	11.25
• p2V2 = n2RT	11.25
• Conversion of °C into K.		2.5
• Knowledge or estimation of the value of R		2.5
• Final moles of NH3 in the flask (n2 = n1 − ns)	20.0
• Algebraic calculations	22.5
• Numerical computation		10.0
• Correct result (value and units)		7.5
Total marks	75.0	25.0

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Table 7 Marking scheme for problem 2

Solution step	Solution procedure	Numerical computation
• Moles n1 of SO2 dissolved in water	10.0	2.5
• Knowledge of STP	2.5
• Moles n2 of SO2 that were collected in a reversed tube	10.0	2.5
• Conversion of °C into K.		2.5
• Knowledge or calculation of R		2.5
• Moles n of SO2 produced (n = n1 + n2)	20.0
• Stoichiometric calculation of moles of O2 (from chemical equation)	20.0
• Calculation of pressure of O2 (from the ideal-gas equation)	12.5
• Algebraic calculations		10.0
• Correct result (value and units)		5.0
Total marks	75.0	25.0

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Appendix 2. Further details about the simulations

Simulation of problem 1

Three screens were constructed for this visualization. The main screen provides a visualization of the experimental set up, while the other two play an auxiliary role. On starting the program, picture 1 appears on the main page showing the experimental set up. Initially the student is led to the screen which describes the experiment; here he/she can read basic instructions and a brief description of the software (Fig. 1). One can change screens by using three buttons that are always shown and active for a horizontal navigation within the software. Next, the student can return to the start of the experiment and commence and interact with the simulation.

Fig. 1 Two screens of the simulation for problem 1, showing the ‘Description’ of the system (a), and the instructions provided on opening the ‘Help’ link (b).

As can be seen from Fig. 2, the experimental set up consists of a vessel that contains gaseous ammonia. The vessel is supplied with a pressure gauge that initially shows a reading of 2 atm. The vessel is also supplied with a thermometer that shows a reading of 27 °C. From the vessel, a tube, supplied with a stopcock, joins the vessel to a beaker filled with water. Over the beaker there is a dropper that contains phenolphthalein indicator. This allows the student to check for the presence of base (ammonia) in the beaker by introducing a few drops of the indicator. The students can turn on the stopcock by moving the cursor over it and by left clicking. When the stopcock is turned on, the pressure gauge shows a rapid fall in pressure. The student can turn off the stopcock and stop the flow of ammonia gas. Eventually the pressure falls to 1 atm. Some bubbles appear at the end of the tube inside the water making the flow of gas perceptible. Ammonia molecules in constant motion are shown within the tube (when it is turned on) as well as in the solution. The student is free to choose his/her actions; for instance, if he/she chooses to drop indicator before passing ammonia gas, there will be no color change in the solution. In this case, however, if ammonia is passed after that, the solution will immediately turn red.

Fig. 2 The three screens of the visualization for the ammonia problem (problem 1).

Simulation of problem 2

The same design was used for visualizing problem 2. As can be seen from Fig. 3, the experimental set up consists of a vessel that contains, at the bottom, an amount of sulfur, as well as oxygen gas. Oxygen molecules are shown as small blue balls, while sulfur atoms are represented in yellow. The vessel is closed at the bottom with a piston, which can be pushed by the student. There is no pressure gauge or thermometer in this case.

Fig. 3 Three screens of the visualization for the sulfur combustion problem (problem 2). The piston is gradually pushed.

A tube which starts with a stopcock and ends in a beaker filled with water emerges from the vessel. In the beaker there is also an inverted graduated tube filled with water. This tube is able to collect the sulfur dioxide gas that is not dissolved in the water. The vessel carries a switch that can ignite the mixture.

As in the case of the simulation for problem 1, the ‘Description of the experiment’ button provides a user guide, directing the simulation in an ordered manner: first they ignite the mixture and see the video, then they turn on the stopcock, and finally they push the piston. The ‘Help’ feature is also present.

The student can start and watch a video, showing the combustion of sulfur. Note that the students had previously observed a demonstration of the combustion of sulfur, the production of sulfur dioxide and its dissolution in water. After combustion is complete, the student can transfer all the produced gas into the beaker containing water by pushing the piston. In the beaker, part of the gas is dissolved in the water, and part is collected in the inverted tube. While this occurs, gas bubbles appear within the inverted tube replacing water. Sulfur dioxide molecules appear in constant motion in the solution.

Fig. 3 shows a series of three shots, in which the piston is gradually pushed, so that the produced gas is transferred into the beaker containing water and the inversed test tube.

Acknowledgements

The authors are grateful to Dr Bill Byers for his significant contribution to improving the readability of the paper and to make clear some methodological and presentational issues.

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