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DOI: 10.1039/C2RP20031G (Paper) Chem. Educ. Res. Pract., 2012, 13, 357-368

Structural equation modeling in assessing students' understanding of the state changes of matter

Dimitrios Stamovlasis *a, Georgios Tsitsipis b and George Papageorgiou b
aAristotle University of Thessaloniki, Greece
bDemocritus University of Thrace, Greece

Received 11th March 2012 , Accepted 25th April 2012

First published on 6th June 2012

Abstract

In this study, structural equation modeling (SEM) is applied to an instrument assessing students' understanding of the particulate nature of matter, the collective properties and physical changes, such as melting, evaporation, boiling and condensation. The structural relationships among particular groups of items were investigated. In addition, three cognitive variables, such as logical thinking, field-dependence/field-independence and convergence/divergence dimension were included in the SEM analysis and their effects on students' performance were estimated. Specifically, three models were tested: a confirmatory factor model (CFM), a multiple-indicator multiple-cause (MIMIC) model and a path analysis. The results showed that the three cognitive variables, along with achievements in the dimensions of structure understanding, sufficiently explain students' understanding of physical changes, providing additionally their direct and the indirect effects. Moreover, a theoretical analysis and interpretation of the results are provided that adds to our understanding about the role of cognitive variables in the mental processes involved in learning the specific-domain material. Implications for science education are discussed.

Introduction

Students' understanding of the particulate nature of matter and its importance for the interpretation of the phenomena (physical and chemical ones) has been studied in a variety of contexts over the last three decades. Research has focused either on students' misconceptions and the inherent difficulties or on the exogenous-independent variables, e.g., individual differences that can explain the variability in students' performance on this matter. The latter, the effect of individual differences on this subject matter, has been very little explored so far. The present paper is seeking to shed light on this effect with the help of advanced contemporary statistical methods such as structural equation modeling (SEM).

Students' understanding of the nature of matter and the changes of state

Starting from the significance of the particulate nature of matter for the understanding of the real world, it is certainly worth being reminded of Feynman's statement that, if all of scientific knowledge was to be destroyed and only one sentence has to be passed to the next generation, this would be the statement of the atomic hypothesis (Feynman, 1963). What's more, this notion has influenced the basic directions of science education, especially when relevant research brought to light evidence showing that students often have difficulties understanding the nature of matter, considering it as continuous. As Krnel et al. (1998) reported in their survey of research related to the concept of matter, even from 1982 relevant students' misconceptions have been recorded and their ideas have been explicitly studied in the following years. During that period, the difficulties in understanding of both the particulate model of matter and the collective behaviour of the particles were becoming more and more evident. These difficulties, apart from the existence of the particles themselves, focus mostly on the space between particles, the intrinsic motion of the particles, the relative spacing between the particles in the three states, the attractions between particles and the nature of the particles themselves (Johnson, 1998a). Thus, many students think that the space among particles is also material (e.g., Lee et al., 1993; Johnson, 1998a). Also, the intrinsic motion of particles is not an easy notion for pupils to acknowledge or it is acceptable only for particular cases or states. For instance, Dow et al. (1978) reported that although the majority of students accepted the idea of particle motion in the liquid and gas state, about a third of them indicated that there was no particle movement in the solid state. Furthermore, students have shown difficulties in understanding the collective behavior of particles. They often consider a particle as a little quantity of a substance having the macroscopic properties of the substance. Thus, for instance, ice molecules are regarded as ‘solid molecules’, or water molecules as ‘liquid molecules’, whereas, molecules are often described to undergo the same changes as the visible changes in the substances, i.e., they can expand, contract, melt, evaporate or condense (e.g.,Lee et al., 1993; Johnson, 1998a).

Expectedly, when students cannot understand the nature of matter, they also have difficulties in explaining its transformations. Regarding the physical ones, difficulties have been reported for all changes of states, including melting, evaporation, boiling and condensation. From the early 80's Osborne and Cosgrove (1983) pointed out that students not only cannot understand the process in a change of state, but very often they cannot even recognize the substances involved. In the case of boiling water for instance, students often believe that, the bubbles were made of heat, air or a mixture of oxygen and hydrogen. As a result students cannot explain the formation of steam above the surface of boiling water or their condensation when a cold plate is placed above them. Evaporation also appeared to be a problematic phenomenon for the students. When the question of explaining the evaporation of an amount of water onto a plate was posed, common students' responses were: water has gone into the plate; it has just gone…it has dried up; it goes into the air and comes back as rain; it changes into air. Even less complicated changes, like that of melting, seemed to remain unexplained by the students. Studies that took place in the following years just confirmed and extended these findings (e.g., Bar and Travis, 1991; Bar and Galili, 1994; Lee et al., 1993; Johnson 1998b, 1998c; Papageorgiou and Johnson, 2005). According to Johnson (1998b, 1998c), all these findings are related to the lack of understanding of the concept of ‘substance’ in the context of particle theory. When a student cannot understand what a substance is, its states are in fact unexplored and the changes of states cannot be explained. Among the three states, Johnson, along with other researchers (e.g., Stavy, 1990a, 1990b; Lee et al., 1993), give an emphasis to the gas state and exemplify that there is a high consistency between pupils' responses to phenomena such as evaporation, condensation and boiling, and the understanding of the nature of the gas state. Problems that have been recorded for the conservation of matter during changes of states (e.g., Lee et al., 1993; Hatzinikita and Koulaidis, 1997) are mostly related to that state.

Individual differences

Although students' ideas on the particulate nature of matter and the understanding of its transformations appear to be related to each other, the question of whether the prerequisite knowledge of the first is sufficient by its own for attaining a satisfactory achievement in the second, still remains. That is, even when all students have reached an adequate level of understanding the particulate nature of matter (and especially that of the gas state, which has proven to be particularly challenging), could it be expected that conceptual understanding of boiling or evaporation would be attained to the same degree for all of them? Nevertheless, practice did not confirm that conceptual change can be realized by the appropriate instructions and theoretical explanations cannot be given merely by our knowledge on student models and misconception.

Studies on students' ideas have been driven by the dominated psychological theories of conceptual change, which mainly belong to two competing theoretical perspectives: One which considers students' knowledge as coherent or theory like (Chi, 1992; Vosniadou and Brewer, 1992, 1994), and the other which considers it fragmented (diSessa, 1988; diSessa et al., 2004; Harrison et al., 1999). However, both theories have primarily focused on difficulties arising from the nature of concepts itself, without providing explanations about their origin or correlating them with independent variables.

On the other hand, psychological theories such as, information processing models or neo-Piagetian theories can explain variation in performance on cognitive tasks by implementing individual-difference constructs corresponding to mental resources. They provide a valuable theoretical framework and in addition the variables that can operationalize the theoretical constructs. These theories were quite established also in science education research. As a result, the role of individual differences such as, logical thinking (formal reasoning ability), field-dependence/independence, convergence/divergence, prior knowledge, M-capacity and working memory capacity becomes present in the relevant literature (Lawson, 1983; Chandran et al., 1987; Zeitoun, 1989; Johnstone and Al-Naeme, 1995; Niaz, 1996; Tsaparlis and Angelopoulos, 2000; Kang et al., 2005; Tsitsipis et al., 2010). Specifically, logical thinking, field-dependence/independence and convergence/divergence, were shown to play a significant role in a wide range of tasks related to learning science and particularly on conceptual understanding of physical changes.

A brief presentation of these three cognitive variables follows:

a. Logical thinking (LTh) refers to the ability of a subject to use concrete- and formal-operational reasoning, which are needed for understanding of concrete- and formal-operational concepts, respectively, and they are related to the Piagetian's developmental level. Research studies have reported that logical thinking plays a major role in students' performance in science and mathematics and in social studies as well (e.g., Lawson, 1982; Niaz, 1996; BouJaoude et al., 2004; Stamovlasis and Tsaparlis, 2005; Tsitsipis et al., 2010, 2012). It was assessed by the Lawson test, a pencil-paper test of formal reasoning (Lawson, 1978).

b. Field dependence/independence (FDI) is associated with one's ability to dissemble relevant information from complex and potentially confusing contexts. One who can sufficiently separate the ‘signal’ (e.g., an item) from the ‘noise’ (i.e., its context) is characterized as field-independent, while the one who cannot is described as field-dependent (Witkin and Goodenough, 1981). Field dependence/independence has been related to the information processing models as a moderator variable. Field-dependent subjects appear to possess lower information processing ability, since part of their capacity is being used to process irrelevant information (Johnstone and Al-Naeme, 1991; Tsaparlis and Angelopoulos, 2000; Stamovlasis, 2006, 2011).

c. Convergence/divergence (CD) refers to another way of measuring aspects of intelligence. Convergent characterizes someone who focuses down-converges-on the right answer in order to find the one conventionally accepted solution of a problem when this solution is clearly obtainable from the information available. On the contrary, divergent is the one who can respond successively to problems requiring the generation of several equally acceptable solutions. Convergers use close reasoning, while divergers show fluency and flexibility (Child and Smithers, 1973).

Purpose and research hypotheses

From a methodological point of view, research findings on the effects of the three cognitive variables described above, i.e., logical thinking, field-dependence/independence and convergence/divergence, have been established by implementing correlation analysis, multiple linear regression and logistic regression (Danili and Reid, 2004, 2006; Tsitsipis et al., 2010, 2012). However, the particularity of the understanding of physical changes, requiring the prerequisite knowledge on the structure of matter along with the operation of mental resources related to cognitive variables, appears to be a quite complex matter that demands further investigation. Latent variables are involved when assessing students' achievement and combined effects are expected to play a significant role. A more detailed portrait of these effects, if known, would be a valuable asset for the theory and practice in science education. Focusing on advanced statistical procedures, structure equation modeling appears to be one suitable modeling approach to analyze the effect of the contributing components on students' performance.

The purpose of the present study is to reveal the structural relation among variables, observable or latent, constituting students' knowledge on the structure of matter and changes of state on the one hand, and the above cognitive variables affecting their performance on the other.

Three models were tested: First, a confirmatory factor model was applied in order to verify the two dimensions of structure understanding, the particulate and the collective dimension, proposed in the literature. Second a multi-indicator multi-cause (MIMIC) model was applied, to explain students' performance by latent and observed variables simultaneously (Jöreskog and Sörbom, 1998). Finally, a path analysis, where the contributed components were used as observed variables, was implemented to demonstrate direct and indirect predictor effects on selected students' achievement scores.

The research hypotheses tested by the implementation of the above statistical approaches are:

(1) The dimensions of structure understanding, the particulate and the collective dimension respectively, comprise two latent variables measured by the corresponding observables used in the instrument.

(2) The dimensions of structure understanding, the particulate and the collective dimension, both effect students' understanding of the state changes of matter.

(3) The three cognitive variables: (a) logical thinking, (b) field-dependence/independence and (c) convergence/divergence affect the dimensions of structure understanding, the particulate and the collective dimension.

(4) The three cognitive variables: (a) logical thinking, (b) field-dependence/independence and (c) convergence/divergence have all direct and indirect effects and effect students' understanding of the changes of state of matter.

(5) The three cognitive variables: (a) logical thinking, (b) field-dependence/independence and (c) convergence/divergence affect students understanding of physical changes and their competence in their interpretations.

Methodology

Participants

A number of 329 ninth-grade junior high school Greek students, who were distributed in 18 classrooms from different schools located in the area of central Greece, took place in the present study. The age of the participants was 14–15, 52% of which were female and 48% male. Students were of different socioeconomic status and living conditions.

Measurements

Data were collected during one school year through paper-and-pencil tests. The instruments used were the following:
Field dependence/independence (FDI). FDI ability of the subjects was assessed by a version of the Witkin et al. (1971) Group Embedded Figures Test (GEFT). This is a timed test (20 min) in which the subject's task was to locate and outline simple figures concealed in complex ones. In this study a Cronbach's alpha reliability coefficient of 0.84 was obtained.
Convergence/divergence (CD). A six-item test was used to measure the extent of divergency of the subjects. Each item substantially constituted a mini test from itself. Briefly, the six mini-tests asked students to do the following kind of tasks: test-1: to generate words of the same or similar meaning to those given, test-2: to construct as many sentences as possible using four given specific words in each sentence, the words to be used in the form as given, test-3: to draw up to five different pictures to relate to the idea of a given word, test-4: to write as many things as possible that have a common trait, e.g., things that are round or that are round more often than any other shape, test-5: to think and write as many words as they could that begin with one given letter and end with another given letter, test-6: to list all of the ideas they could about a given topic whether or not it seemed important to them. The whole test had been widely used by Bahar (1999). It had also been used by Danili and Reid (2006) for measuring divergency of a Greek student sample. For the measures in this study, the Cronbach's alpha reliability coefficient of the instrument is 0.76.
Logical thinking (LTH). Pupils' logical thinking abilities were measured with the Lawson paper-and-pencil test of formal reasoning (Lawson, 1978). The test consists of 15 items involving the following: conservation of weight (1 item), displaced volume (1 item), control of variables (4 items), proportional reasoning (4 items), combinational reasoning (2 items) and probabilistic reasoning (3 items). The students had to justify their answers. A Cronbach's alpha reliability coefficient of 0.79 was obtained for the present sample.
Pupils' achievement, concerning their understanding of the particulate nature and the changes of state of matter. The test consists of 3 parts covering the following topics: the particulate nature of matter (first part), the properties of state as a result of the collective behavior of particles (second part) and the changes of state that is: melting, boiling, evaporation and condensation (third part). A detailed description of all the parts is given in the Appendix. In short, the first part includes three items that refer separately to the solid state (which characterized by the number 1 in the Appendix), the liquid state (number 2 in the Appendix) and the gas state (number 3 in the Appendix). The second part includes two items that refer to a particular substance in three different temperatures (number 4) and three different substances in normal (same) conditions (number 5). The third part includes four items that refer separately to the phenomena of melting (number 6), boiling (number 7) evaporation (number 8) and condensation (number 9). In each one of those tasks, there were sub-items characterized by the letters A, B, or C. Cronbach's alpha reliability coefficient of 0.86 was obtained for the above instrument and the present sample.

The instrument was synthesized by selected items utilized in a number of related research studies (Johnson, 1998a,1998b,1998c; Papageorgiou et al., 2010). A pilot study followed by interviews was carried out in order to correct possible communication deficiencies of the test and thus enhanced validity is expected. Note that pupils' assessment in the present research was carried out without any notification, almost one year after they had finished the relevant courses. Thus, the instrument is considered to measure the residual knowledge on this matter. The data collection and analysis was undertaken in Greek. A description of the instrument and the data collection procedure is presented in the Appendix.

Statistical analysis and results

A predetermined marking scheme was applied to the pupils' responses. Based on this scheme, we awarded one to three points depending on the difficulty of each item. For example, questions, which require a simple response or choice (e.g., item 1A) received one point, while questions which required threefold responses (e.g., item 7A), received three points. In particular:

a. one point for each one of the items 1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C, 6A, 8B, 9A

b. two points for each one of the items 4A, 4B, 4C, 5A, 5B, 6B, 6C, 8A, 9B

c. three points for each one of the items 7A, 7B, 8C.

The variables used as the observed variables in the LISREL procedures were the sum scores of the items in each one of the nine parts: S1, S2, S3, S4, S5 S6 S7, S8 and S9 respectively, and the three cognitive variables LTH, FDI and CD. Table 1 presents the correlation matrix of the twelve observed variables.

Table 1 Correlation matrix of the observed variables (LISREL input)
Variable 1 2 3 4 5 6 7 8 9 10 11 12
p < 0.001 for all.
S1 1.00                      
S2 0.51 1.00                    
S3 0.51 0.58 1.00                  
S4 0.36 0.39 0.47 1.00                
S5 0.21 0.20 0.27 0.41 1.00              
S6 0.43 0.55 0.55 0.53 0.38 1.00            
S7 0.25 0.34 0.43 0.44 0.31 0.51 1.00          
S8 0.40 0.42 0.53 0.46 0.38 0.57 0.48 1.00        
S9 0.19 0.24 0.33 0.28 0.22 0.34 0.22 0.37 1.00      
FDI 0.20 0.16 0.33 0.37 0.19 0.36 0.31 0.32 0.21 1.00    
LTH 0.38 0.43 0.50 0.50 0.33 0.60 0.47 0.48 0.37 0.46 1.00  
CD 0.05 0.23 0.28 0.30 0.21 0.40 0.29 0.33 0.22 0.35 0.42 1.00

Three analyses were carried out:

a. A confirmatory factor analysis

b. A multi-indicator multi-cause (MIMIC) model

c. A path analysis.

The Analyses were conducted via LISREL8.8 structural equation modeling computer program (Jöreskog and Sörbom, 1996, 1998). The following indexes were used as measures of goodness-of-fit: First the comparative fit index (CFI) was used as a focal index, since it has advantageous statistical properties: it has standardized range, small sample variability, and stability with various sample sizes (Jöreskog and Sörbom, 1981; Bentler 1990). A value of CFI greater than 0.95 indicates an adequate model fit (Hu and Bentler, 1999). In addition, the goodness-of-fit χ2, the Standardized Root Mean-square Residual (SRMR), the Root Mean-Square Error of Approximation (RMSEA), the Non-Normed Fit Index (NNFI) and the Adjusted Goodness of Fit Index (AGFI), were also used. Note that the goodness-of-fit χ2 indicates the difference between the observed and implied by the proposed theoretical model variance-covariance matrices. Thus, the non-significant values of χ2 are desired indicating that the proposed theoretical model significantly reproduced the sample variance-covariance relationships in the matrix (Schumacker and Lomax, 2010).

A confirmatory factor analysis. The confirmatory factor model was used to demonstrate the existence of two latent variables, the Particulate and the Collective, which have been proposed as the dimensions of structure understanding (Johnson, 1998a; Tsitsipis et al., 2010).

Fig. 1 shows the confirmatory factor model of structure understanding. The observable variables load the two latent variables, the Particulate and Collective. Three of the questions (S1, S2, and S3) load the Particulate and the other two (S4 and S5) load the Collective.


Confirmatory factor model for Particulate Collective dimensions. Three of the questions (S1, S2, and S3) load the Particulate (PARTICUL) and the other two (S4 and S5) load the Collective (COLLECTI). Circles denote latent variables and squares denote observable variables. The model is statistically significant (goodness-of-fit χ2 = 3.62, p = 0.46; Root Mean-Square Error of Approximation RMSEA = 0.0).
Fig. 1 Confirmatory factor model for Particulate Collective dimensions. Three of the questions (S1, S2, and S3) load the Particulate (PARTICUL) and the other two (S4 and S5) load the Collective (COLLECTI). Circles denote latent variables and squares denote observable variables. The model is statistically significant (goodness-of-fit χ2 = 3.62, p = 0.46; Root Mean-Square Error of Approximation RMSEA = 0.0).

The value of CFI is 0.999; the goodness-of-fit χ2 = 3.65, df = 4, p = 0.46; the Standardized Root Mean-square Residual SRMR is 0.016; the Root Mean-Square Error of Approximation RMSEA is 0.0; the Non-Normed Fit Index NNFI is 1.0 and the Adjusted Goodness of Fit Index AGFI is 0.983. They indicate an adequate model fit.

A multiple-indicator multiple-cause (MIMIC) model. The Structural equation modeling involved the twelve observed variables (Table 1) and three latent variables. Particulate and Collective were measured as indicated by the above factor model and the latent variable understanding changes of state (UnChSt) measured by S6, S7, S8 and S9 item. The model is a multiple-indicator multiple-cause model (MIMIC), where latent variables are predicted by latent and observed variables. Latent variables, such as Particulate (PARTICUL), Collective (COLLECTI) and Understanding changes of state (UnChSt) are predicted by the three cognitive variables, LTH, FDI and CD. The effects of understanding the structure of matter on UnChSt are also shown.

Fig. 1 shows the MIMIC factor model. The value of CFI is 0.995; the goodness-of-fit χ2 = 51.89, df = 39, p = 0.08; the Standardized Root Mean-square Residual SRMR is 0.029; the Root Mean-Square Error of Approximation RMSEA is 0.032; the Non-Normed Fit Index NNFI is 0.992 and the Adjusted Goodness of Fit Index AGFI is 0.95. They indicate an adequate model fit.

Path analysis. The observed indicators which synthesize Understanding changes of state (UnChSt) could be distinguished into two groups: one group includes items which emphasize understanding changes of state of matter and the other includes items which emphasize interpretations. Thus, two additional observed variables were calculated from the corresponding questions: CHANGE and INTERPRE respectively. Then, path analysis of students' understanding changes of state (CHANGE) and their competence in interpretation of these changes (INTERPRE) was conducted to show the effects of Particulate (PARTICUL), Collective (COLLECTI), LTH, FDI and CD. Fig. 3 shows the Path model. The value of CFI is 1.00; the goodness-of-fit χ2 = 2.23, df = 39, p = 0.33; the Standardized Root Mean-square Residual SRMR is 0.011; the Root Mean-Square Error of Approximation RMSEA is 0.018; the Non-Normed Fit Index NNFI is 0.998 and the Adjusted Goodness of Fit Index AGFI is 0.97. The above indicate an adequate model fit.

Interpretation of results and discussion

Structural equation modeling, a robust statistical analysis, provided a more analytical portrait of the relations among the observed and latent variables involved in learning sciences and contributed to our understanding about students' knowledge on the matter under investigation. Moreover, it facilitates the theoretical interpretation and the establishment of relations between aspects of the cognitive skills that are behind the psychometric measurements and the nature of mental tasks involved when learning this specific domain material. The result supported most of the research hypotheses and specifically:

The confirmatory factor model supported the proposed dimensions of structure understanding (Johnson, 1998a; Tsitsipis et al., 2010), particulate and collective, and reveals the two latent variables that are behind students' responses.

The MIMIC model, which involves latent variables that are predicted by observed and latent variables, provided answers to the hypotheses 2, 3 and 4. It shows how the variables involved in predicting students' understanding of these changes are related to the dependent variables and to each other. First it confirms that the dimensions of structure understanding, i.e., the particulate and the collective dimensions, both have an effect on students' understanding of the changes of states. This prior knowledge seems to be a determining factor of students' performance. Moreover, this knowledge is being affected by individual differences, however, not as it had initially been hypothesized. Logical thinking affects both the particulate and the collective dimension, while field-dependence/independence affects only the collective dimension. Convergence/divergence does not have an immediate impact on any of the two dimensions. The standardized effects are shown in Fig. 2 and Table 2. Fig. 2 shows overall the relations that were sought by application of structural equation modeling. The role of the three cognitive variables is adequately supported by revealing their direct and indirect effects on Understanding changes of state (UnChSt). LTH demonstrates direct effects on UnChSt and indirect ones via the particulate and the collective dimensions. FDI has an indirect effect via the collective dimension and CD demonstrates only direct effects on the latent variable UnChSt.


Structural equation modeling for students' understanding physical phenomena. Latent variables, such as Particulate (PARTICUL), Collective (COLLECTI) and Understanding changes of state (UnChSt) are predicted by the three cognitive variables, LTH, FDI and CD. Circles denote latent variables and squares denote observable variables. The model is statistically significant (goodness-of-fit χ2 = 51.89, p = 0.08; Root Mean-Square Error of Approximation RMSEA = 0.032).
Fig. 2 Structural equation modeling for students' understanding physical phenomena. Latent variables, such as Particulate (PARTICUL), Collective (COLLECTI) and Understanding changes of state (UnChSt) are predicted by the three cognitive variables, LTH, FDI and CD. Circles denote latent variables and squares denote observable variables. The model is statistically significant (goodness-of-fit χ2 = 51.89, p = 0.08; Root Mean-Square Error of Approximation RMSEA = 0.032).
Table 2 Structural equation coefficients, standard errors, t-values, error variances and R2, for SEM equation in the MIMIC model
Model b esd t R 2
a p < 0.05. b p < 0.01. c p < 001.
Particulate dimension       0.367
Predictor LTh 0.488 0.046 10.69c
  Error variance 0.411 0.057 7.22c
Collective dimension
(Dependent variable)       0.419
Predictors LTh 0.289 0.046 6.17c
FDI 0.080 0.037 2.10a
Error variance 0.1587 0.038 4.15b
Understanding changes of state     0.855  
Predictor Particulate 0.240 0.055 4.33b
Collective 0.337 0.099 3.41b
LTh 0.071 0.031 2.26a
CD 0.054 0.023 2.37a
Error variance 0.029 0.011 2.65a

The path analysis, which aims to reveal the effect of the independent variables (LTH, FDI, CD, particulate and collective dimensions) on understanding changes of state (CHANGES) and interpretations (INTERPRET), is depicted in Fig. 3. LTH operations appear, along with the prerequisite knowledge, to be necessary for understanding changes of state and providing interpretations of these changes, which is by all accounts a deeper understanding. These results are consistent with other findings in previous studies that reported the supremacy of logical thinking as a predictor variable on science achievement (Chandran et al., 1987; Lawson and Thompson, 1988; Johnson and Lawson 1998; Kang et al., 2005). SEM analysis supports what is more the hypothesis that a sufficient level of logical thinking is necessary for students to understand the particulate nature of matter and its state changes.


Path analysis of students' understanding changes of state of matter (CHANGE) and their competence in interpretation of physical changes (INTERPRE) and the effects of Particulate (PARTICUL), Collective (COLLECTI), LTH, FDI and CD. The model is statistically significant (goodness-of-fit χ2 = 2.23, p = 0.33; Root Mean-Square Error of Approximation RMSEA = 0.018).
Fig. 3 Path analysis of students' understanding changes of state of matter (CHANGE) and their competence in interpretation of physical changes (INTERPRE) and the effects of Particulate (PARTICUL), Collective (COLLECTI), LTH, FDI and CD. The model is statistically significant (goodness-of-fit χ2 = 2.23, p = 0.33; Root Mean-Square Error of Approximation RMSEA = 0.018).

CD cognitive style was also a significant predictor of the students' understanding changes of state (UnChSt), which represent a total score of their achievement. CD effect is relatively small on students' achievement variance and this might explain why it appears merely on the total achievement. However, it is statistical significant. CD affects also the sub-score CHANGES (Fig. 3). It appears that divergent pupils were favored in understanding physical changes. The content of scientific material that the assessing instrument covered in this study involves a diversity of concepts, properties and models, which mostly require detailed descriptions in order to be understood when studied or taught. Therefore, it is reasonable to assume that linguistic skills may have played a major role in students' understanding of the relevant scientific topics. Linguistic skills such as comprehension and interpreting of a scientific text are considered to be of paramount importance for reasoning in science (Byrne et al. 1994). Students, though, who show superiority in language, are thought to be divergent thinkers (Hudson, 1966; Runco, 1986; Danili and Reid, 2006). Links between divergency and science has also been reported in the literature. As it was mentioned in a previous section of this study, Hudson (1966) noted that the convergers tended to choose the sciences, but the divergers who did choose the sciences performed very well. Following, other research findings were consistent with Hudson's claim (Al-Naeme, 1991; Field and Poole, 1970).

Based on the degree of linguistic skills required in a mental task, one could explain why CD cognitive style had an effect on some variables, such as ‘total achievement’ and ‘understanding the changes of state’, while it had no effect on some others. CD had no effect on ‘Particulate dimension’, ‘collective dimension’, and ‘structure understanding’ because teaching and studying of the corresponding themes can be assisted by simple illustrations and no extended additional descriptions are required so that the role of language here does not seem to be determinative. While the effect of CD is favored when the content requires linguistic ability, a limit should exist determined by the complexity of the task. When the task becomes more complex and requires logical operations leading to a conclusion or a unique final answer, then other abilities, such as, formal reasoning and even convergent thinking might prevail and the effect of divergency becomes less significant. Such appear to be the ‘interpretations’ variable case.

Field dependent/independent (FDI) cognitive style was the third significant predictor of students' achievement. Field independent students were those who performed better. This result is consistent with other findings in previous studies, which showed that field independence is an intellectual asset concerning general achievement in science (Lawson, 1983; Johnstone and Al-Naeme, 1995; Niaz, 1996; Tinajero and Paramo, 1998; Bahar and Hansell, 2000; Danili and Reid, 2004; Kang et al., 2005; Tsaparlis, 2005; Stamovlasis and Tsaparlis, 2005; Danili and Reid, 2006). Fig. 2 shows that FDI has an indirect effect on students' understanding changes of state (UnChSt) via collective dimension, while it affects the sub-score CHANGES (Fig. 3). It can be inferred that field independent pupils' ability to separate readily the significant information from its context (Witkin and Goodenough, 1981) or the signal from the noise offered them a serious advantage either in their study or during teaching.

Field dependence/independence (FDI) had direct and indirect effects on some of the latent variables underpinning students' knowledge, the ‘collective dimension’ and ‘understanding of the changes of state’. The above involve a complex context, that might be misleading for students' thought, and thus the field independent style has an advantage. On the contrary, FDI had no effect on ‘particulate dimension’ and ‘interpretations’. The former referred to three specific models, one for each physical state, that are well described by the corresponding figures, so that no room for misleading information is left and thus, no effect of FDI is observed. Nevertheless, when the same models are asked to be recognized by the students, within a more complex and possibly misleading context, e.g., in ‘understanding of the changes of state’ (Fig. 3), FDI appears again as a predictor.

For the ‘interpretations’ case, however, the explanation is different and analogous to the one for CD. Interpretation of phenomena requires a deeper understanding and reasoning skills, so that logical thinking (LTh) prevails among all possible predictors, as the MIMIC model confirms (Fig. 2).

The dimensions ‘collective’ and ‘particulate’ are affected by cognitive variables and in addition are shown to have an effect on students' performance in understanding changes of state and interpretations of these physical phenomena. These effects, direct and indirect, which are shown in MIMIC model and in the path model (Fig. 2 and 3), provide support for the second hypothesis of this study. They indicate that ‘collective’ and ‘particulate’ dimensions of students' understanding on this matter constitute fundamental and substantial presuppositions for interpreting the phenomena of state changes. Similar findings have also been reported in related qualitative (Johnson, 1998c) and quantitative studies (Papageorgiou et al., 2010). As it was mentioned in the introduction section, Johnson (1998c) concluded that understanding of the nature of the gas state was “the underlying issue” for the understanding of the state changes “with the particle theory playing a key role”. Interestingly, ‘interpretations’ variable was also affected directly by LTh, which underlines the importance of formal reasoning in the related cognitive processes. On top, when a deeper knowledge on changes of physical states is pursued, being familiar merely with the particulate models of two physical states, pre and post the change, is not adequate. There is also a dire need for understanding the transition from one model to the other, where reasoning abilities are thought to be of great importance. This is consistent with the effect of logical thinking on interpretations. In the main, logical thinking appears to be the bottom line for competence in ‘interpretations’, since the former, as the path analysis shows, has a direct effect on the latter.

In conclusion, it is important to state that the hypotheses are well supported by the data. In the MIMIC model R2 is 0.855, while the corresponding R2 in the reduced form equations is 0.558, that is, the 54.8% of the students' achievement variance was explained by the latent and observed variables, while all the related model-parameters were statistically significant (Schumacker and Lomax, 2010). Thus, we maintain that the findings of the present research are of paramount importance, because they shed light on the factors hindering students' understanding of the particulate nature of matter and the changes of states. On the other hand, the present study opens a new area of investigations for the conceptual change in this particular domain, where, the individual differences, such as logical thinking and cognitive styles, have been ignored from research hypotheses.

Implications for teaching

Since the understanding of the structure of matter in both its dimensions, i.e., the particulate and the collective, have an effect on the students' understanding of the changes of state, it is indubitable that an explicit and in depth instruction of the former should precede. Moreover, when designing new science curricula or writing text books, experts should take into account this precondition and develop the material accordingly, emphasizing both the particulate and the collective dimension.

Further to the implications for the content, findings related to the three cognitive variables have also implications for teaching methods.

In particular, since logical thinking appears to play a dominant role in understanding of these abstract topics, teachers should foster methods that make abstract concepts more accessible through concrete-operational thought. Such methods include the use of illustrations, diagrams, software and models that constitute perceptible entities or concrete materials to focus attention on critical and variable attributes of abstract concepts. There is evidence that these methods can enhance the attainment of abstract concepts (Cantu and Herron, 1978; Howe and Durr, 1982; Zeitoun, 1984). Another alternative for dealing with this issue is to design training programmes that promote the development of formal operational reasoning (Lawson, 1985) or foster the application of teaching methods that contribute to the acceleration of the development and the improvement of pupils' general cognitive abilities (Adey and Shayer, 1994).

The same methods facilitate learning as far as the convergent/divergent thinking is concerned. Since lack of divergent thinking and restricted linguistic skills appear to affect understanding of the particulate nature of matter and the changes of state, assistance to students could be given by methods that eliminate the dominating role of language as much as possible. Research evidence supports the effectiveness of such methods that can enhance the attainment of abstract concepts (e.g., Zeitoun, 1989; Snir et al., 2003; Papageorgiou et al., 2008).

Moreover, teachers should be aware of the obstacles originating from field-dependent cognitive style. An organized presentation of teaching material should emphasize less the peripheral information that could act as ‘noise’ for those who are field-dependent, which are often focused on less important features of the phenomena (e.g., bright colors). Effort should be made in order to help students make sense of the material taught, when attending lessons in the classroom or reading their school textbooks, by focusing on central ideas and disembedding only the relevant information (Danili and Reid, 2004). Specifically, when attempting the connection between micro and macro level, the plethora of dimensions involved, such as motion, vacuum, bonding, particulate and collective properties, makes the context complex enough so it is more likely to prevent the field-dependent pupils from processing information effectively. Again, a helpful technique for conveying explicit messages might involve the use of illustration or animation, which controls the misleading information and the effect of field-dependence.

Finally, besides the particular findings elucidating the research questions, the present study demonstrates that methodological advancements, such as SEM modeling are appropriate in assessing and explaining students' achievements in science teaching research.

Appendix

A description of all the parts and the items of the instrument implemented in this study:

Part 1: (The particulate nature of matter)

The first 3 items (1A, 1B, and 1C) concern the solid state.

1.A. Pupils are asked to choose among five alternatives (see Fig. 4 in the Appendix), the figure that best represents what they think they would “see” if they observed a sugar grain with a hypothetical magnifying glass enabling the view of the grain structure.


The five alternatives given to the pupils. In each of them a note was helping to clarify the corresponding representation. A description of these notes follows: (1) continuous material, (2) molecules (be it of nearly spherical shape) in array, not touching each other, (3) nothing, (4) molecules (be it of nearly spherical shape) in random position relatively close to each other, not touching each other, (5) molecules (be it of nearly spherical shape) in random position, mostly far away from each other.
Fig. 4 The five alternatives given to the pupils. In each of them a note was helping to clarify the corresponding representation. A description of these notes follows: (1) continuous material, (2) molecules (be it of nearly spherical shape) in array, not touching each other, (3) nothing, (4) molecules (be it of nearly spherical shape) in random position relatively close to each other, not touching each other, (5) molecules (be it of nearly spherical shape) in random position, mostly far away from each other.

1.B. Pupils are asked to explain what they think exists between molecules, in case they chose a figure depicting molecules. Otherwise, they do not have to answer this question.

1.C. Pupils are asked to answer whether or not they think that the view of the sugar structure through the hypothetical magnifying glass would remain “frozen” as the time is passing. They are also asked to explain or justify their answers.

The following 3 items (2A, 2B, and 2C) concern the liquid state.

2.A. Pupils are asked to choose among five alternatives (see Appendix), the figure that best represents what they think they would “see” if they observed a drop of pure water with a hypothetical magnifying glass enabling the view of the structure of the drop.

2.B. Pupils are asked to explain what they think exists between molecules, in case they chose a figure depicting molecules. Otherwise, they do not have to answer this question.

2.C. Pupils are asked to answer whether or not they think that the view of the water structure through the hypothetical magnifying glass would remain “frozen” as the time is passing. They are also asked to explain or justify their answers.

The following 3 items (3A, 3B, and 3C) concern the gas state.

3.A. Pupils are asked to choose among five alternatives (see Appendix), the figure that best represents what they think they would “see” if they observed a very small quantity of oxygen, found within a vase containing pure oxygen, with a hypothetical magnifying glass enabling the view of the structure of the oxygen.

3.B. Pupils are asked to explain what they think exists between molecules, in case they chose a figure depicting molecules. Otherwise, they do not have to answer this question.

3.C. Pupils are asked to answer whether or not they think that the view of the oxygen structure through the hypothetical magnifying glass would remain “frozen” as the time is passing. They are also asked to explain or justify their answers.

Here, pupils are prompted to circumvent the following items 4 and 5 in case they have not adopted a molecular structure of the substances in the previous items.

Part 2: (The properties of state as a result of the collective behavior of particles)

The following 3 items (4A, 4B, and 4C) concern the same substance in three different temperatures.

4.A. Pupils are prompted to make the assumption that they have separated one single molecule from one of the following: a block of ice, some pure water (liquid), or some pure water at a gas state. They are asked whether or not they could understand if the separated molecule has come from ice, water (liquid) or water at gas state respectively. Then, they are also asked to explain or justify their answers.

4.B. Pupils are prompted to make the assumption that they have separated one single molecule from a block of ice, another single molecule from a quantity of pure water (liquid) and a third single molecule from a quantity of water at gas state. They are asked whether or not they could determine a physical state for each of the three molecules and if yes, what this state is. Then, they are also asked to justify their answers.

4.C. Pupils are prompted to make the assumption that they have separated one single molecule from a block of ice, another single molecule from a quantity of pure water (liquid) and a third single molecule from a quantity of water at gas state. They are asked to compare the shape and the magnitude of the three molecules. Then, they are also asked to justify their answers.

The following 2 items (5A and 5B) concern three different substances under normal (same) conditions.

Pupils are prompted to make the assumption that they have separated one single molecule from each of the following three substances: sugar (solid), water (liquid) and oxygen (gas).

5.A. They are asked whether or not they could determine a physical state for each of the three molecules and if yes, what this state is. Then, they are also asked to justify their answers.

5.B. They are asked whether they think that the three molecules are different or not. They are also asked to explain or justify their answers.

Part 3: (The changes of state)

The following 3 items (6A, 6B and 6C) concern melting.

Pupils are prompted to imagine a lump of wax melting on a heating radiator.

6.A. They are asked to identify the substance after melting.

6.B. They are asked to choose among five alternatives (see Appendix), the figure that best represents what they think they would “see” if they observed wax (a) before melting and (b) after melting, with the hypothetical magnifying glass enabling the view of the structure of the substances.

6.C. They are asked to explain the way in which the wax melts by taking into account the structure of the matter and describing the procedure in detail.

The following 2 items (7A and 7B) concern boiling.

Pupils are given a figure depicting a beaker of boiling water, containing many bubbles. They are asked:

7.A. To identify the substance that exists at a point: (a) within a bubble, (b) between the bubbles and (c) above the free level of the boiling water, close to that level.

7.B. To choose among five alternatives (see Appendix), the figure that best represents what they think they would “see” if they looked at each of the three points of the previous question through the hypothetical magnifying glass enabling the view of the structure of the substances.

The following 3 items (8A, 8B and 8C) concern evaporation.

8.A. Pupils are asked to explain the differences, if any, between boiling and evaporation.

8.B. Pupils are asked to choose among five alternatives (see Appendix), the figure that best represents what they think they would “see” if they observed evaporated water with the hypothetical magnifying glass enabling the view of the structure of the substances.

8.C. Pupils are asked to explain the way in which the water evaporates by taking into account the structure of the matter and describing the procedure in detail.

The following 2 items (9A and 9B) concern condensation.

Pupils are given the following description: The water in an open saucepan is boiling intensively. We place a cool Pyrex lid above the saucepan and we immediately notice the formation of drops on the down surface of the lid.

9.A. Pupils are asked to identify the substance of the drops.

9.B. Pupils are asked to explain the way in which the drops were formed by taking into account the structure of the matter and describing the procedure in detail.

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