The interactions between problem solving and conceptual change: System dynamic modelling as a platform for learning

Computers & Education 55 (2010) 1145–1158

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The interactions between problem solving and conceptual change: System dynamic modelling as a platform for learning Chwee Beng Lee* Nanyang Technological University, Learning Sciences & Technologies Academic Group, National Institute of Education, 1 Nanyang Walk, Singapore 637616, Singapore

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 November 2009 Received in revised form 12 May 2010 Accepted 13 May 2010

This study examines the interactions between problem solving and conceptual change in an elementary science class where students build system dynamic models as a form of problem representations. Through mostly qualitative findings, we illustrate the interplay of three emerging intervening conditions (epistemological belief, structural knowledge and domain knowledge), the choice of learning strategy and the learning outcomes through a theoretical model. Ó 2010 Elsevier Ltd. All rights reserved.

Keywords: Elementary education Interactive learning environments Simulations Learning strategies

1. Introduction Over the last three decades, research in conceptual change has been among the most important aspects in education. Noteworthy attempts were made by Caravita and Hallden (1994), Hatano (1994), and Vosniadou and Verschaffel (2004) to re-frame the conceptual change approach. In recent years, Vosniadou (2007a, 2007b) has conceptualized a constructivist and domain-specific approach to address previous limitations raised by conceptual change researchers. In her work, Vosniadou (2007b) proposed using instruction-induced conceptual change to achieve more significant changes in learning rather than bottom-up implicit additive mechanisms which may produce synthetic models. While bottom-up addictive approach assumes that new information is added to the existing explanatory framework through participation in socio-cultural activities, an instruction-induced approach entails systematic instruction so that learners can understand the complex counterintuitive scientific theory which has a different explanatory framework as compared to their naïve theories. In this study, we argue that problem solving as an instruction-induced strategy may foster conceptual change which requires high cognitive engagement (Jonassen, 2008). Specifically, problem solving intervention can: (a) help students to become aware of the inconsistencies between their naive theories and the scientific ones and (b) create intentional learning and avoid the formation of synthetic models. Although many studies on problem solving have documented the effects of problem solving on learning and performance, few have addressed the interactions between problem solving and conceptual change. Since problem solving involves conceptual change processes (Nersessian, 2008), there is a need to examine this dynamic interaction. In this paper, we discuss a theoretical model that has been developed to explain the dynamics between problem solving and conceptual change. In our study, we gave our subjects a real-world problem pertaining to the water cycle and requested that they identify and determine the parameters of the problem by building computational problem representations. The following perspectives on problem solving in relation to the re-framed (Vosniadou, 2007a, 2007b) approach in conceptual change guided the formation of our research framework. These perspectives are: 1. Problem solving (in this context) entails complex cognitive processes (such as justification, evaluation, and hypothesis-testing) which may encourage cognitive conflicts. 2. While externalizing their understanding of the given problem, and resolving the anomalies that arise, children may need to restructure their modes of learning. 3. For problem solving to be meaningful, the problem given must be authentic and appeal to the children. * Tel.: þ65 67903285; fax: þ65 68968038. E-mail address: [email protected] 0360-1315/$ – see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.compedu.2010.05.012

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2. Problem solving in the context of the re-framed conceptual change approach Problem solving is the cognitive process that is directed at achieving a goal when the solution method is unclear to the problem solver (Mayer, 1992; Schoenfeld, 1985). A problem must have two distinct attributes (a) it is an unknown entity in some context, and (b) finding or solving the unknown must be accompanied with some form of social, cultural or intellectual value (Jonassen, 2004). Because of the nature of the ill-structured problem we have used in this study, the process of solving it requires the acquisition or the activation of metaconceptual awareness. For problem solving to effectively induce conceptual change, referred to as a process of revising one’s conceptual framework when information is inconsistent with one’ beliefs and assumptions (Vosniadou, 1994), problem situations should be based upon phenomena of which each individual has some general awareness and common understanding (Biemans & Simons, 1999). Supporting this claim, Gerrit, van der Veer, Kok, and Bajo (1999) conducted a study to investigate individual differences in mental representations of physics in a problem solving context. The results showed that, if a problem is presented in an “everyday life” context, novices (in this study, the learners) would put more effort and creativity in solving them compared to when the problem is presented in a physics context. Similarly, in one of the experiments, Hallden (1999) noticed that students tended to perceive problem solving tasks in the context of everyday life and applied the kind of problem solving strategies that they had use in everyday life rather than using probability theory because they had found it more meaningful to do so. The realness and the relatedness of the problem to the children’s everyday experiences create a learning intention (Ferrari & Elik, 2003; Pintrich, 2000). Conceptual change was encouraged in this sense because as perturbations to one’s conception occur (during the process of conceptual change), one must be able to recognize these perturbations in order to question current understanding, and this necessarily needs a deliberate goal orientation (Pintrich, 2000). To resolve these perturbations, one must engage in a series of experimentation, questioning, discussion or other types of high engagement for one to compare rival naïve theories (Dole & Sinatra, 1998). While problem solving may induce conceptual change by perturbing learners’ cognitive structure and creating awareness in the learners to construct a coherent and scientifically supported conceptual framework, it is also an extremely engaging process that requires a high level of cognitive understanding as it stimulates students to discover inconsistencies in their thinking (Biemans & Simons,1999). This is true especially when learners encounter complex and ill-structured problems which entail multiple solutions, solution paths, or no solution at all (Kitchner, 1983). Solving such problems challenges problem solvers to question their own hypothesis, and externalize the problem, by going through a series of iterative sequences of testing and revising cycles (Lesh & Harel, 2003). Moreover, building problem representations enables problem solvers to externalize their mental representation, making abstract understanding explicit, and helping problem solvers to reflect upon their knowledge structure and to efficiently identify their own learning or problem gap, and involving conceptual change in order for the problem solver to reconcile his or her problem representation. The process of problem solving requires the elements of the problem situation to be reorganized and restructured in a new way in order to solve the problem (Mayer, 1992). In other words, problem solver must be able to actively search for new ways to externalize their problem in order to generate a coherent problem representation. In this sense, restructuring or reorganizing the elements of problems can be regarded as a state of conceptual change. De Grave, Boshuizen, and Schmidt (1996) showed that, during the process of analyzing a set of medical problems, students demonstrated traces of conceptual change. The above mentioned study suggests that students necessarily go through a series of hypothesis questioning, checking, and revising their initial conceptual understandings during problem solving. Similarly, Vosniadou and Brewer (1994) implicitly referred to such interaction when they discovered that when elementary school children had constructed synthetic models out of their initial model of the earth, they were actually attempting to synthesize two inconsistent pieces of information, and searching for a solution or explanation to construct a coherent understanding. 3. System modelling tool for the construction of problem representations The most important step in problem solving is identifying a problem space that not only enables the restructuring of children’s naïve theories but also their modes of learning. When problem solvers build problem representations, they externalize their mental model and making abstract understanding explicit so that they may reflect upon their knowledge and effectively identify their own learning or problem gap. This process is similar to the problem solving processes of scientists as they create models as systems of inquiry and use these models as means which one reasons to the new conceptual representation (Nersessian, 2008). In this study, we asked students to build system dynamic models which served as a form of problem representation. System dynamic modelling is a highly challenging and engaging activity (Bravo, Joolingen, & de Jong, 2009) that requires learners to analyze, synthesize, and evaluate their domain-specific knowledge in order to create a model that supports their conceptual understanding of the system they are working on (Stratford, Krajcik, & Soloway, 1998). Numerous studies have documented the successes of using models in problem solving activities in science learning (Lesh & Harel, 2003; Stratford et al., 1998; White, 1993). The students in this study used a system modelling tool named “Model-It”. This tool uses accumulations and flows to enable learner to describe rules related to populations of entities and was designed for middle school students who have not yet learned higher-order mathematics used in more sophisticated modelling tools such as Stella and PowerSim. To build a model in Model-It, students are required to identify the measurable, quantifiable factors that are used to predict the outcome they are simulating (Fig. 1). Each factor is described in terms of its measurement units, initial values, minimum, average, and maximum values in the Factor Editor. From factor maps, students define the relationships between the factors using the Relationship Editor (Fig. 2). When the model is complete, students can test their models with the results shown in a graph. The aim of this study was to explore the interactions between conceptual change and problem solving when elementary students solve an ill-structured problem that is situated in an everyday context through the use of system dynamics modelling tool to facilitate the problem-solving process and create productive conceptual change. Our research question is as follows: To what extend does the theoretical model explain the interaction of problem solving and conceptual change in the process of learning science in an elementary science classroom? Specifically,  What are the individual differences that may impede or impact students’ conceptual change process in problem solving? (E.g. students’ domain knowledge)?

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Fig. 1. An example of a system model created using Model-It.

Fig. 2. Creating relationships in Model-It.

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 How does the dynamic interaction process of conceptual change and problem solving influences students’ learning outcomes (Did they construct advanced or simple problem representations? What kind of changes did they make to their conceptual framework?)?

4. Methods 4.1. Grounded theory approach The results reported in this paper is a part of the findings resulted from a larger study which employed both qualitative and quantitative methods to study problem solving in conceptual change. However, due to the extensiveness of its results, only analyses that articulate a theoretical model explaining the interaction of problem solving and conceptual change in the process of learning science will be reported and discussed. Our analysis largely relied on interview transcripts which were obtained from 20 face-to-face interviews with primary 5 students (n ¼ 35, average age ¼ 10) in a science classroom. Such data were number coded and analyzed independently using the qualitative analysis software Qualrus. They are then compared and matched with other sources of data such as classroom observation field notes and reflection logs, for convergent validity. Quantitative data such as students’ problem representations and knowledge test results also provided sources of supporting evidences during theory generation. During interviews, students were given a paper and pencil to draw the water cycle; this was followed by their explanation on their drawing with further probing from the interviewer. This method has been shown to be effective when children can use their drawings to represent their ideas of concepts such as evaporation (McGuigan, Qualter, & Schilling, 1993; Rennie & Jarvis, 1995). These drawings were coded and analyzed together with the interview transcripts that followed the principles of grounded approach. Some of the grounded theory principles guided the qualitative analysis. The data analysis followed the guidelines suggested by Strauss and Corbin (1990) for open, axial, and selective coding. It must be noted that these three processes do not need to take place in a linear and distinct fashion. Open coding involves the breaking down, comparing and categorizing data. In such a coding process, specifying the characteristics of categories is crucial. Initially, general terms were used to describe segments of data. For instance, when asked on how they learned science, one student mentioned: “I try to understand the concepts rather than memorizing them.” This phrase was coded as “learning strategies”. It would then be subcategorized as “memorization.” During open coding, 45 concepts were identified and verified by two researchers. These concepts were later aggregated into four categories and 13 sub-categories. In axial coding, the researcher re-gathered the data and put them back together in new ways by making connections between a category and its sub-categories. That necessarily enabled the researcher to build a “skeleton” of the findings. Using the software, Qualrus, the researcher was able to make links between different categories or sub-categories by using different types of arrow keys and relationships. For example, the researcher was able to link “memorization” to “learning strategies” using the relationship “is a type of.” In selective coding, the aim is to allow a core category to emerge, which captured the essence of the findings. To do so, the researcher re-examined the previously analyzed data and the research purpose and questions in order to narrow down the focus and select a core category. The quantitative results obtained from our previous study were also used to provide supporting evidences as we compare and make sense of our qualitative findings. As a result of this, a theoretical model emerged to represent the relationship among intervening conditions, strategies, problem representations, and conceptual change. The purpose of adopting some of the grounded theory principles was to generate a theory when existing theories do not address the research problem that the researcher plans to study (Creswell, 1998, 2005). Such an approach was salient to this study as it helped to generate a theory to explain the interaction process of conceptual change and problem solving. 4.2. Others sources of data for triangulation During our theory generation process, quantitative data that were generated for the previous larger study were used as supporting evidences. Such quantitative data included the pre- and post-Knowledge Test (KTI) and two versions of students’ computational problem representations constructed using the Model-It software. Internal consistency of KTI was computed during the pilot study and found to be acceptable (r (40) ¼ .672). Inter-rater reliability between independent raters was varied by classification: Misconception conceptual model (r ¼ .918, p < .01), Initial conceptual model (r ¼ .831, p < .01), Textbook conceptual model (r ¼ .831, p < .01), Synthetic conceptual model (r ¼ .581, p < .01), and Scientific conceptual model (r ¼ .887, p < .01). After scoring the justifications independently, the two researchers engaged in a series of discussions and negotiation before reaching a consensus on cases that were difficult to be placed in a specific category. The KTI was designed to assess students’ understanding of evaporation and condensation and it was assessed in two ways. Firstly, one point was awarded for a correct response on the multiple-choice items (total of 14 points for 14 items). Secondly, students provided a short justification for their answer, explaining why they had chosen an answer from the multiple choice. Statistical analyses were performed on KTI and the justifications were coded into 3 categories (initial, synthetic, scientific) of conceptual models based on Vosniadou’s (1994) study. Initial models were based only on students’ everyday experience with no scientific justification (naïve models, according to Vosniadou, 1994). Synthetic models were those that used a combination of everyday and scientific descriptions and justifications, while Scientific models were justifications that were based solely on scientific conceptions. During the coding process, two new categories of conceptual models (Textbook and Misconception) surfaced. Textbook model were justifications based on textbook descriptions of the water cycle and Misconception conceptual model reflected a lack of comprehensions of the water cycle. After this coding, three movements across these categories emerged and were agreed by researchers: (a) Significant leap, (b) Diminutive move, and (c) Reverse move. To capture and trace students’ movements across these categories in their pre- and post-KTI scores, the researchers used a template for coding (see Table 1). A movement of more than 1 category shift would be identified as a significant leap (e.g. from ‘textbook’ to ‘scientific’ conceptual model). A diminutive move would a move one category above the original position (e.g. from ‘textbook’ to ‘synthetic’ conceptual model). If there was a backward shift such as from ‘synthetic’ to ‘textbook’ conceptual model, this would be considered a reverse move.

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Table 1 A sample template for coding the movements across the 5 categories of conceptual models. Script no.

Processes

Change (from)

Directions

Change (to)

Item no.

Comments

1

Evaporation

1 3 1 2 1 2 2 1 3

/ ) / / / / / / /

3 2 5 3 3 4 4 5 4

6 9 11 13 4 6 8 12 14

9 Moves, 1: reverse, 6 significant leaps

2 1 1 2 1 3

/ / / / / )

3 2 3 3 2 1

7 9 11 13 12 14

6 Moves, 1 reverse, 1 significant leap

Condensation

2

Evaporation

Condensation

Note: Script no: script number of the Knowledge Test; Processes: the two main processes (evaporation and condensation) tested in the Knowledge Test; Change (from): the category which the specific justification belongs to in the pre-test; Change (to): the category which the specific justification belongs to in the post-test; Direction: indication of the movement across category; Comments: indicating the number of moves, and specific comments on the movements.

Student’s problem representations were assessed by a pair of raters using a rubric for assessing semantic associations, including the total number of nodes, total number of nodes associated with the central concepts (evaporation and condensation), and propositions and causal attributions which included two rules (Rule 1 states that a hypothesis coheres with what it explains, which can either be evidence or another hypothesis, and Rule 2 states that all hypotheses that explain some other propositions cohere with each other). This rubric was crafted based on principles espoused by Thagard (2000) and ideas suggested by Novak and Gowin (1984). Two trained raters independently scored the problem representations and an inter-rater reliability coefficient of r ¼ .889, p < .01, n ¼ 20 was computed to establish validity evidence. 4.3. Procedure The data collection lasted approximately 10 weeks. The pre-KTI was administered to the class of 35 primary 5 students before the problem solving activity and 10 face-to-face interviews were carried out, each lasting approximately 40 min. The participating students went through four sessions of system modelling of problems in the computer lab after school hours and each session lasted about one and half hour. During those sessions, students modelled the following problem using the Model-It software.

Water is a scarce resource in our country. Due to an increase in population over the years, the demand for water also increases tremendously. Besides buying water from our neighboring country, we can also look into other options to increase the water supply. Based on the fact that our country is an island surrounded by seawater, and your understanding of the concepts learned in the unit of the water cycle (such as evaporation, boiling, precipitation, and condensation), suggest the best possible way to increase the supply of water.

Prior to the beginning of the study, students were taught how to use Model-It software in which were given a procedural planning guide for building their problem representation. Following the training, they began constructing their own models and were told that they could revise and refine their model throughout the four sessions. To better scaffold students when they were generating hypotheses by relating the variables and defining the relationships of the defined variables, a guiding worksheet was provided. A Reflection Log was provided in session 3 to guide students’ reflections about how their models were working. Students could use the reflection log to state their primary prediction about water level in reservoirs, list down what they have learned from running their models, and elaborate on how they had derived the results. At the end of the second and fourth session, students’ problem representations were collected for data analysis. At the end of the fourth sessions, the KTI was administered and 10 face-to-face post interviews were conducted. 5. Results Synthesizing our data, a theoretical model (Fig. 3) that illustrates the interplay of intervening conditions influencing the strategies students used during the problem solving activity, and the learning outcomes emerged. Fig. 3 shows three intervening conditions (structural knowledge, epistemological beliefs and domain knowledge) that influenced students’ choice of strategies. As a result of the interactions between the conditions and strategies, three types of conceptual change were observed and students constructed either sophisticated problem representations or simple problem representations. 5.1. The roles of epistemological belief, structural knowledge and domain knowledge We found that students used a variety of strategies to study science in class. These include: asking (siblings, friends, parents, school teacher/private tutor), constructing mind maps, searching internet for new information or to validate their understanding, memorizing

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Fig. 3. A theoretical model explaining the interactions between problem solving and conceptual change.

information, writing detail notes, and self-questioning. Our coding analysis suggested that conditions such as epistemological belief, structural knowledge, and domain knowledge seemed to have an effect on the strategies employed by students. Epistemological beliefs are beliefs that people hold about knowledge and knowing (Hofer, 2002), had emerged as an intervening condition. Our students adopted two categories of epistemological beliefs. Of the 31 codes on epistemological beliefs, 14 reflected students’ perception that knowledge is ever changing and acquired through constant revisions of one’s understanding. When confronted with new or conflicting information, students not only activate their pre-existing knowledge about the topic but also their beliefs about knowledge itself (Mason & Gava, 2007). The rest of the codes showed a subscription to the belief that knowledge is determined and validated by the textbook or the authority and they are reliable sources. During the interview, when asked whether they ever questioned the reliability of the information presented by the textbook or the teacher, Jason (Pseudo names are used in this manuscript) said that he had never questioned his teacher and the newspapers because he believed that both sources of information were reliable, and that he would faithfully take down information given by his teacher during lessons. Similarly, Sarah also said that she believed that her teacher was always correct. During the post-study interview, when both were asked whether they had face any difficulties during the problem solving activity, both said that they had only faced technical problems and they knew what variables and the kind of relationships to be included in their problem representations. On the other hand, there were some students who believed that knowledge is ever changing and acquired through constant revision of their understanding. For instance, Mike said that he questioned the knowledge and information he received from other people. He even questioned the presentation of the water cycle on the textbook and said; “I think they (referring to those who wrote the textbook) should include things like temperature by which the water turns into hail or rain..and they should elaborate more on precipitation.” Not only did he question the information he had received, Mike also refined his understanding through observations. During the interview, he highlighted that he came to know that humidity affects the rate of evaporation through his experience and observations. He said; “Humidity comes into play when there is a lot of water vapour in the air. That’s why it is hard for water to evaporate quickly. I was in Vancouver last winter, and I noticed that things dry very quickly. Similarly, David constantly challenged his teacher’s and his peers’ conceptions during classroom learning and problem solving sessions. He also believed that knowledge should be acquired through constant revision of one’s own conceptual framework. It was also observed that when building his problem representation, David was always engaged in self-questioning by whispering to himself. Domain knowledge, which is the knowledge about a particular domain or discipline, emerged as another intervening condition that affected students’ employment of strategies. When students chose the self-questioning strategy, they did so according to their level of domain knowledge. For instance, during her problem solving process, Mary said that she had tried to recall her knowledge on the water cycle and thought about the concept of evaporation and condensation. She then questioned her understanding on these concepts when she got confused by the output of her problem representation. To be able to engage in self-questioning, students needed to possess a strong base of domain knowledge. This was especially so for Mike. Based on the evidences gathered from the KTI, interview transcripts, and reflection logs, it was evident that Mike had possessed sufficient scientific knowledge which he used to constantly questioning his understanding in order to build a better understanding on what he already knew. The same went for David as well. He was constantly questioning his understanding and relating his problem solving process to his domain knowledge. Below shows the conversation between him and the interviewer: Interviewer: What were some of the problems you faced when you first built your model (problem representation)? David: Not enough variables, like I can only think of reservoirs, evaporation and condensation..I didn’t think about the effects in the reservoirs and then later when I think about it, I though of the animals in the reservoirs, and build them in the model, then I add algae that will compete for sunlight and put it in the model.

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Interviewer: How did you come up with these variables? David: In fourth grade we learned the water cycle.then there is water pollution that brings in algae, so I tried to relate these to the model. Interviewer: How did the problem solving helps in your model building? David: The problem solving activity helps me to understand the concepts and relate them to the model building. A limited domain knowledge base would deter students from using the self-questioning strategy. This was evident in the case of Sarah who preferred using a lot of information to elaborate her points. She also showed traces of misconceptions on the water cycle. During the first interview, when asked whether there would be any evaporation if the sun was taken away from her drawing on the water cycle, Sarah said: “The water cannot evaporate without the sun.” And when asked about the humidity, another student Jason said that the humidity level in Singapore was very low (in actual fact it is always above 80%). Structural knowledge which referred to as “internal connectedness, integrative understanding, or as conceptual knowledge” (Jonassen, Beissner, & Yacci, 1993, p. 5) was another intervening condition. When the students were able to understand the relationships among the variables in the system, it was more likely that they had engaged in self-questioning. For example, Alice, who told the interviewer that she had questioned her own problem representation during the problem solving activity, had obtained a score of 63 (M ¼ 23.7) on the semantic associations for the first version of her problem representation, and a 65 (M ¼ 34) on the same section for the second version of her problem representation. This may imply that she had sufficient structural knowledge to enable her to construct a more coherent problem representation. When asked on the possible factors that could be included in the water cycle during the interview, she mentioned factors such as “evaporation,” “condensation,” “heat,” and “weather,” water droplets.” Not only did she have the knowledge of the water cycle, she was also able to build relationships among these variables to exhibit her understanding. Her second version of problem representation (Fig. 4) shows that she was able to identify and relate the important concepts of the water cycle, in particular, the relationships among the variables. Mike also showed that he was able to link concepts by explaining the interactions of concepts, using examples and analogies. In the following excerpts, he demonstrated the ability to understand how different relevant concepts were associated with each other: Interviewer: Now you have the sun here (referring to the drawing). What is the function of the sun in the water cycle? Mike: The sun acts like the energy generator that evaporates the water. Interviewer: So you say that the sun is very important in the water cycle. Now if I take away the sun. Did evaporation still take place? Mike: It could but it couldn’t happen at such a rate. That means that there will be less and less water over time. Interviewer: If I take away the sun what is causing the evaporation then? Mike: Could be wind. Another possibility is that we have no sun and no heat and water will freeze. I guess with no sun then the atmosphere wouldn’t be able to trap as much heat. From the dialogue with the interviewer, it seemed that Mike was equipped with sufficient structural knowledge to help him understand that the sun produces heat for water to evaporate, but there could still be evaporation without the presence of the sun because heat is still present and that without the sun, the atmosphere is not able to trap much heat. Not only could he explain the relationship between concepts, he was also using an analogy such as: “The sun acts like the energy generator that evaporates the water”, to explain the function of sun with regard to the water cycle. A check on his problem representation showed that he had obtained a score of 47 (M ¼ 34) on the semantic associations for the second version of his problem representation.

Fig. 4. A problem representation (second version) created by Alice.

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5.2. Restructuring conceptual framework 5.2.1. Case one: Peter’s story During the problem solving process, Peter made drastic changes to his knowledge structure. Results from the scores of his two knowledge tests revealed that he had made 13 moves-four significant leaps, three reverse moves and six diminutive moves. Our analysis also showed that he made three significant leaps for his justifications on the concept of condensation. In both pre-test and post-test on the following question: Jane’s mother parked her car along the pavement outside their house. Early in the morning, Jane noticed tiny droplets on the windscreen. These droplets were formed because of water vapour.? Peter chose option B which was: “from the air changes to a liquid state which falls on the windscreen”. In the pre-test, he justified his option by saying that: “the night is very cold and thus met the temperature of condensing.” This justification was classified as category 1 (Misconception) conceptual model. However, on the same question, his justification was categorized as category 4 (Synthetic) conceptual model when he stated: “At night, it is very cold, so water evaporates from the ground did not get enough heat for it to rise. As a result, it will turn into water droplets and form mist, or low clouds.” Peter showed improvement in his understanding on condensation in the post-knowledge test. This could be also seen in the justification provided in question 2 (“Mary took out a can of Coke from the refrigerator and left it on the kitchen table. After a while, what could be observed?”). In both the pre-test and post-test, Peter chose the correct response (“water droplets will form on the outside of the can), but his justification in the pre-test could only be classified as a category 1 (Misconception) conceptual model as he had said: “Water droplets will form on a cold surface.” Peter did not relate the justification he had provided to the context of the question. However, in the post-test, he wrote: “As the Coke can is cold, water droplets will meet the cold surface and condenses on it, thus making water droplets.” This justification was classified as a category 4 (Synthetic) conceptual model. It was apparent that the child was trying to assimilate the new information (i.e., water vapour condenses on cool surface) into his existing understanding. During the interview, Peter said that when he faced difficulties in learning science, he would either ask someone else, or search for more information. More importantly, he showed signs of engaging in the self-questioning when he said; “You know, sometimes I ask what happen? Why is this behaving in that way?” It was probably true that this student believed that knowledge can be constructed and it could be enhanced with new information gathered either from someone else or from his own inquiry. At the first interview, Peter said that he would check with his sister or search for information from the Internet if he was in doubt. This suggested that Peter was engaged in self-questioning during the problem solving activity when he realized the vagueness in his knowledge structure. During the second interview, Peter told the interviewer that he had encountered problems while building his problem representation, and he would “sometimes question himself” and “refine the model.” When his problem representations were examined, it was found that he made a 110% improvement on his second representation compared to his initial one, judging by his score of 61 for the second problem representation compared to a score of 29 for the first representation. Although Peter made three reverse moves, this was perhaps insignificant as compared to his four significant leaps. Moreover, his second problem representation (Fig. 5) was much more elaborated and complex compared to his first representation (Fig. 6), which was linear and simple. Peter seemed to have understood that in a real-world environment, the relationships of variables are intertwined, resulting in an improvement in his score on the semantic associations. In his first version of the problem representation, he had obtained a score of 25 (M ¼ 23.7) and in the second version of the problem representation, 44 (M ¼ 34) on the semantic association. This suggested that he may have built structural knowledge during the second problem representation activity. In this case, it was unclear whether domain knowledge had been the intervening condition. However, it was clear that Peter believed that knowledge was not static, and that he had employed both the self-questioning (implicitly) and information seeking strategy. 5.2.2. Case two: Jenny’s story During the first interview, Jenny said that she believed the information presented by the textbook was reliable and showed signs of possessing misconception when she stated that if there was no sun there would not be any evaporation. In other words, she was not sure whether evaporation did take place at any temperature. However, after the problem solving activity, she made seven moves with one reverse move, one diminutive move and five significant leaps. She was able to shift most of her justifications to categories that were either

Fig. 5. The second version of problem representation created by Peter. (This figure also appears in Lee, Jonassen, & Teo, in press.)

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Fig. 6. The first version of problem representation created by Peter. (This figure also appears in Lee et al., in press.)

scientific or closer to the scientific conceptual models. In fact, the number of her justifications falling into category 1 (Misconception) and 2 (Initial) conceptual models were greatly reduced, from 3 to 0 for category 1 conceptual model and from 4 to 1 for category 2 conceptual model. On question 1 of the KTI: Which of the following best describes evaporation? Jenny chose the correct response: “It occurs at any temperature” during the pre-test and post-test. Although she was not able to make any justifications for her response in pre-test, her justification in the post-test was categorized as category 4 (Synthetic) as she stated: “Water changes to gas at any temperature below 100  C. This gas is called water vapour, it does not need to be hot. This process is called evaporation.” For question 12 which asked for an example of condensation near the ground, she selected the correct response (the forming of mist in the early morning of the Seletar Reservoir) in her pre-test. Similarly, she was not able to provide a logical justification for her choice. Her justification indicated a category 1 (Misconception) model. However, in her post-test, she provided a logical rationale for her choice by stating that: “The water in the reservoir evaporates. The water vapour is cooled due to the fact that the temperature is lower. The vapour condenses into water droplets and forming mist.” This justification was identified as a category 5 (Scientific) conceptual model because she showed an understanding on the cause of the mist. Generally, she had made improvement in her justifications. It was clear that Jenny had experienced significant improvements on her understanding and made great progress in her problem representations. Comparing her first (Fig. 7) and second problem representations (Fig. 8), it was evident that Jenny was able to create a more complex and advanced problem representation and had achieved a 144% improvement in her second problem representation by scoring 61 marks compared to a score of 25 in her first problem representation. It seemed that Jenny had changed her strategy in order to achieve a more coherent understanding during the problem solving activity. When she was first interviewed, she stated that she did not question the information presented by the textbook because she believed that it was reliable. However, during the post interview, when she was asked why she had shuffled the positions of the water vapour and water droplets on her drawing (students were told to draw the water cycle during pre- and post-interviews), she said that she had realized her mistake during the problem solving activity: “I started to question myself. When I went home, I read my textbook and other reference books and then I returned to refine my problem representation (model).” The problem solving activity could have created cognitive conflicts in her and influenced her choice of strategy. In this case, it was self-questioning in order to build a more advanced and coherent problem representation. It was suggested in the previous section that epistemological belief could be an intervening condition. Jenny, although she had changed her strategy, her initial epistemological belief on knowledge was still determined by the textbook in playing a part in her knowledge restructuring process. This was evident when six of her category 3 (Textbook) conceptual models remained unchanged. Cases one and two have shown the dynamic interaction of conceptual change and problem solving. In a problem solving environment, students employed appropriate strategies to help them build a coherent understanding of science concepts. And this action was influenced by intervening conditions such as their epistemological beliefs and structural knowledge. It seemed that when the child was able to engage in self-questioning, perturbations occurred. In order to reconcile such perturbation, the child would have to build a more logical problem representation and restructure his or her conceptual framework.

Fig. 7. The first version of problem representation created by Jenny.

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Fig. 8. The second version of problem representation created by Jenny.

5.2.3. Case three: Sarah’s story At the pre-test interview, Sarah told the interviewer that she often believed that the information provided by her teachers were accurate. In studying Science, she would memorize information by hard, and would ask her private tutor whenever she was in doubt. Sarah was observed to possess misconceptions before and after the problem solving activity. This was evident when asked whether there would be any evaporation without the sun, she replied: “Then the water cannot evaporate.” A close examination after the problem solving activity revealed that she had made five reverse moves, one diminutive move and no significant leaps. In addition, her category 2 (Initial) and category 3 (Textbook) conceptual models were stable. In other words, three of her category 2 and four of her category 3 conceptual models were found to be unchanged in the post-test for the KTI. When her problem representations were examined, it showed a fall in her overall score. She had previously scored 36 (M ¼ 30.8) for her first problem representation, but it dropped to 33 (M ¼ 44.8), below the mean score. Her first and second problem representations (see Fig. 9) were exactly the same but she had deleted some information on the relationships of variables in the second version. Her problem representation resembled a simple and linear model. Not only did she not make many changes to her problem representation, she also produced exactly the same drawing on the water cycle during the pre- and post-problem solving activity interview (Figs. 10 and 11). This could mean that her knowledge structure was fairly stable throughout the study. During the post problem solving activity interview, when asked whether she had encountered any difficulties in building her problem representation, she confidently said: “Not really, I know what to add.” Although she said at a later stage that she might have encountered some difficulties when determining the relationships of the variables, she could not recall what they were and she preferred to “works alone.” Despite the fact that she did not experience any significant leap or improvement on her problem representation, it was inappropriate to conclude in her case that there was no interaction between conceptual change and problem solving. To a certain extent, she did experience perturbations, and this was apparent when she made five reverse moves and one diminutive move. However, a possible reason that could have posed a barrier to her deep learning was the strategies she used to build her understanding. It was not clear whether she had

Fig. 9. A first and second version of problem representation created by Sarah.

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Fig. 10. A drawing produced by Sarah during pre intervention interview.

engaged in self-questioning when learning science, and whether she had questioned her understanding and restructured her conceptual framework in order to reach a more logical and coherent understanding during the problem solving activity. What may have caused an effect on her choice of strategy might be the epistemological belief, domain knowledge, and possibly structural knowledge. During the pre interview, she had shown signs of believing that knowledge was determined by the textbook or authority, and at the post interview, she showed that she was confident enough to build her problem representations with her existing knowledge. Moreover, she also seemed to have misconceptions during the interview. This was evident when she said that evaporation could not take place without the presence of the sun. In addition, she did not score well on the semantic associations for both versions of her problem representations, indicating that her

Fig. 11. A drawing produced by Sarah during post intervention interview.

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Fig. 12. A second version of problem representation created by Jason.

structural knowledge was relatively weak as compared to her peers. In the first version of the problem representation, she had obtained a score of 27 (M ¼ 23.7) and a score of 26 (M ¼ 34) for the second version of the problem representation. 5.2.4. Case four: Jason’s story Like Sarah, Jason also experienced a similar learning process. During the pre problem solving activity interview, he said that whenever he came across a problem he would: “think through what I learned and try to think slowly.” He mentioned that he once came across an inconsistent piece of information presented by the textbook and the newspaper but he chose to believe the newspaper over the textbook because he thought the newspaper would be a more reliable source. This might be an indication of his belief on knowledge determined by the higher authority. During the interview, he showed inconsistency in explaining the concept of evaporation. When asked what would happen to evaporation without the presence of the sun, he said that evaporation could not happen. However, at a later stage, when asked whether evaporation could take place with the presence of the wind but in the absence of the sun, he hesitated and said: “Maybe the evaporation would be smaller. It will not evaporate as much as the sun makes the water.” This showed that although Jason had understood the concept of evaporation, he had difficulty relating it to the other concepts. It was unsure whether he had engaged in self-questioning mode, but it was apparent that he had preferred an elaborated explanation in the process of building a coherent understanding. This was evident when he added more elaborate explanations in his second drawing during the post interview. Similar to Sarah’s experience, Jason made more reverse moves than significant leaps. In his 12 moves, he had seven reverse moves, two significant leaps and three diminutive moves. Also, he scored lower for his second problem representation than the first one. In his first and second version of his problem representation, he obtained an overall score of 34 (M ¼ 30.8), and also 34 (M ¼ 44.8) respectively. Although he had made attempts to shift his conceptual understanding (he made 12 moves), the majority of his conceptual models were in category 2 (Initial) or category 3 (Textbook). His performance on the building of problem representations, both knowledge tests, and his dialogues with the interviewer, suggested that it might not be domain knowledge that influenced his choice of strategy but rather his epistemological belief and structural knowledge. In the process of problem solving, his epistemological belief and structural knowledge could have determined his choice of strategy. When asked whether he had encountered any difficulties in the problem solving activity, he said that he knew what he wanted and therefore he did not face any difficulties. Perhaps he believed that he had already possessed sufficient knowledge to help him build a coherent problem representation. On the other hand, he seemed to have difficulty in connecting the relationships among the variables. He made minimal changes to his second problem representation (Fig. 12) as compared to his first problem representation (Fig. 13). When providing an elaborated explanation to describe the relationship between the amount of rainfall and the rate of condensation in his second representation, he said: “When the rate of condensation increases, the amount of rainfall increases because water condenses to make clouds. When the clouds get too heavy, they will fall down to Earth as rain.” His problem representations suggested that he was not able to see the interactions between the related variables. This was reflected in his score obtained for the semantic associations on the problem representations. He had an overall score of 27 (M ¼ 23.7) and 26 (M ¼ 34) for his first and second version of the problem representations respectively. During the first interview, he stated that the area of exposure, wind and humidity would affect the rate of evaporation but he did not include them in his problem representations. Case three and four have explained why some students did not make much improvement in their problem representations and conceptual models. Students who were influenced by the three intervening conditions while adopting other strategies other than selfquestioning would experience less intense interaction between problem solving and conceptual change in their process of learning. As a result of this, they tended to build simple problem representations and experience less or no significant leaps, or more reverse moves in their conceptual models.

Fig. 13. A first version of problem representation created by Jason.

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6. Discussion & implications By adopting a grounded approach and supporting our analysis with quantitative results obtained from our previous study, we were able to generate a theoretical model explaining the dynamic interactions among the three intervening conditions (structural knowledge, domain knowledge and epistemological beliefs), types of conceptual change (significant leap, diminutive move and reverse move) and problem solving through examining problem representations (sophisticated and simple problem representations). Students used a variety of strategies to help them understand science. It was observed that students’ choice of strategies was very much affected by their domain knowledge, structural knowledge and epistemological beliefs in three identified intervening conditions. The findings in this study were consistent with Windschitl and Andre (1998) who discovered that epistemological beliefs of learners interacted with the type of learning environments in determining achievement. These researchers found that students with greater epistemological sophistication performed better in the exploratory (constructivist) simulation experience. Another intervening condition that might have played a pivotal role in determining students’ choice of strategy could be domain knowledge. When students chose the self-questioning strategy, they do so according to their level of domain knowledge. This finding echoed what Limon and Carretero (1997) found in their research on the origin of life that if learners’ interest in a domain or the task and the domain-specific knowledge were high, a willingness to change was more likely than if their domain-specific knowledge was low. We also identified structural knowledge as another intervening condition. When students were able to understand the organizations and relationships of the variables in the system, they were more likely to engage in selfquestioning. Supporting this finding, Robertson (1990) found that learners’ semantic networks were a strong predictor of how well learners would solve transfer problems in physics. Similarly, Liu (2004) also found that high school students who had undergone concept mapping instruction had promoted relational conceptual change. Due to the extensiveness of our data, we could only use four cases to delineate the dynamic interactions between conceptual change and problem solving. The first two cases showed that when students operate in the reflective period (King & Kitchener, 2002) or hold sophisticated notions that knowledge changes over time and resulting from reasoned, constructive efforts (Elder, 2002), they were more likely to adopt the self-questioning strategy. Such a strategy could have helped them not only to construct logical and coherent problem representations but also recognize the inconsistencies in their initial knowledge structure during problem solving, engaging students in the an interactive process of conceptual change. In these two cases, when the interaction between conceptual change and problem solving was intense, students performed better in terms of their problem representations and their conceptual knowledge, as manifested in the movement of the conceptual models. The next two cases (cases 3 and 4) showed that students who were influenced by the three intervening conditions while adopting other strategies other than self-questioning would experience less intense interaction between problem solving and conceptual change in their process of learning. This led to the construction of simple and perhaps linear problem representations and less or no significant leaps, or experiencing more reverse moves in the development of their conceptual models. From the literature, little research that directly addressed the effects of systems modelling on conceptual change has been conducted (Jonassen, 2008). In this regards, this study has the potential to reveal additional insights on the way systems modelling and problem solving for conceptual change can be integrated in learning. The theoretical model which was generated and illustrated in this paper may provide guidance to curriculum designers as it contains several principles for designing science learning. First, educators must realize that conceptual change is multi-faceted, interactive and theoretically complex (Sinatra & Mason, 2008). With technologies, it is possible that students develop important thinking skills such as evaluating data, developing theories and hypothesis-testing (Gardner, 2000) and achieve desirable conceptual change. However, systems modelling activity (building problem representation in this case) cannot be done as an isolated activity (Trundle & Bell, 2010). There is a need to consider learners’ domain knowledge, structural knowledge, and epistemological beliefs to tailor instruction accordingly. Second, it is crucial to teach the necessary learning strategies to help students build more sophisticated problem representations and achieve “Significant leap” in conceptual change. Throughout our study, we have provided evidence that “self-questioning” strategy plays a pivotal role in students’ learning. Hence, instruction may need to equip students with the ability to ask and answer questions effectively, a task which is central to learning (Korkmaz, 2009). 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