How teachers perceive their expertise: The role of dimensional and social comparisons

Accepted Manuscript How teachers perceive their expertise: The role of Dimensional and Social Comparisons Isabell Paulick, Jörg Großschedl, Ute Harms, Jens Möller PII: DOI: Reference:

S0361-476X(17)30279-5 http://dx.doi.org/10.1016/j.cedpsych.2017.06.007 YCEPS 1629

To appear in:

Contemporary Educational Psychology

Please cite this article as: Paulick, I., Großschedl, J., Harms, U., Möller, J., How teachers perceive their expertise: The role of Dimensional and Social Comparisons, Contemporary Educational Psychology (2017), doi: http:// dx.doi.org/10.1016/j.cedpsych.2017.06.007

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Roles of dimensional and social comparisons Running head: ROLES OF DIMENSIONAL AND SOCIAL COMPARISONS

Title: How teachers perceive their expertise: The role of Dimensional and Social Comparisons

Isabell Paulicka, Jörg Großschedlb, Ute Harmsc, & Jens Möllera

a

Institute for Psychology of Learning and Instruction at Kiel University, Olshausenstraße 75, D-24118 Kiel, Germany

b

Institute of Biology Education at the University of Cologne, Herbert-Lewin-Straße 10, D-50931 Cologne, Germany

c

Leibniz Institute for Science and Mathematics Education (IPN) at Kiel University, Olshausenstraße 62, D-24118 Kiel, Germany

Isabell Paulick (corresponding author): E-mail: [email protected], telephone number: +49-431-880-1254, fax number: +49-431-880-5467 Jörg Großschedl: E-mail: [email protected], telephone number: +49-221-4707375 Ute Harms: E-mail: [email protected], telephone number: +49-431-880-3129 Jens Möller: E-mail: [email protected], telephone number: +49-431-880-1241

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Roles of dimensional and social comparisons

How teachers perceive their expertise: The role of Dimensional and Social Comparisons

Abstract

Teachers´ self-concepts have shown correlations with the effectiveness of their teaching, but we know little about the development of their self-concepts. According to the generalized internal/external frames of reference (GI/E) model, social and dimensional achievement comparisons may affect not only students’ but also pre-service teachers’ self-concepts. Thus, we extended and applied this model to examine relations between estimates and self-concepts of 430 pre-service biology teachers’ professional knowledge in three domains: content knowledge (CK), pedagogical content knowledge (PCK), and pedagogical and psychological knowledge (PPK). Structural equation modelling provided strong support for the GI/E model’s capacity to explain teachers’ self-concepts: with positive paths from CK, PCK, and PPK to the corresponding self-concepts, indicating social comparison effects, and negative paths from CK and PPK test scores to the PPK and CK self-concepts, respectively, indicating dimensional comparison effects. In addition, CK was negatively related with the teachers’ PCK self-concept. The results are discussed in terms of their implications for both teacher education and the proposed GI/E model. Key words: I/E model, teacher education, professional knowledge, social comparisons, dimensional comparisons

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Roles of dimensional and social comparisons How teachers perceive their expertise: The role of Dimensional and Social Comparisons

1 Introduction Enhancement of self-concepts is a central goal of education, as thinking and feeling positively about oneself has numerous benefits. For example, a meta-analysis by Judge and Bono (2001) showed that self-concept is among the best predictors of job performance and job satisfaction, and abundant empirical evidence indicates that teachers benefit from high professional self-concept. Notably, it reduces burnout symptoms (Friedman & Farber, 1992; Villa & Calvete, 2001), and enhances both teachers’ resistance to stress and their sense of personal accomplishment (Hughes, 1987). However, although we have substantial knowledge of the formation of students’ domainspecific self-concepts, empirical information on the formation of teachers’ self-concepts is very scarce. To address this knowledge gap, this study examines the formation of preservice teachers’ self-concepts in terms of two well-established (dimensional and social comparison) processes. Thus, by extending these approaches to teacher self-concepts, it contributes to self-concept research based on the traditional Internal/External frame of reference model (I/E model: Marsh, 1986) and its extension to the generalized I/E model (GI/E model: Arens & Möller, 2016; Möller, Helm, Müller-Kalthoff, Nagy, & Marsh, in press; Möller & Marsh, 2013). In addition, teachers’ professional self-concepts have received little attention in previous research, and this study provides the first information (to our knowledge) on the formation of pre-service teachers’ self-concepts. In the following text we introduce the theoretical models seeking to explain the development of students’ domain-specific self-concepts, particularly the GI/E model (and

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Roles of dimensional and social comparisons its extension to teachers’ self-concepts), and describe the focal dimensions of teachers’ professional knowledge. We then present our hypotheses, participants and applied methodology. Finally, we present the results and discuss their implications.

1.1 The GI/E model The I/E model (Marsh, 1986) is a well-established model explaining the development of academic self-concept. It has been applied to describe the relations between students’ verbal and math achievements, and self-concepts, as illustrated in Figure 1A. According to this model, students compare their level of academic ability using two frames of reference (external and internal) to construct their academic selfconcepts. The external frame of reference is constructed by students comparing their achievements with those of their classmates in given subjects. Through this form of social comparison (Festinger, 1954), students with, for example, higher mathematics achievement than their classmates develop a correspondingly high mathematics selfconcept. However, students with equal mathematics achievement may develop different levels of mathematics self-concepts (Marsh & Yeung, 1998), due to variations in their internal frames of reference. These are constructed by students comparing their achievements in one subject with their achievement in other subjects; a form of dimensional comparison (Möller & Köller, 2001). Through dimensional comparisons, relatively high mathematics achievement will lead (for instance) to relatively low verbal self-concept. Thus, a student with average mathematics achievement but higher than average verbal achievement may develop a lower mathematics self-concept than a student with the same mathematics achievement but lower verbal achievement.

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Roles of dimensional and social comparisons

********************** Insert Figure 1 about here ********************** In a meta-analysis of 69 data sets, Möller, Pohlmann, Köller, and Marsh (2009) found support for the I/E model across age groups, genders, and countries. Mathematics and verbal achievement were strongly positively correlated overall, but correlations between mathematics and verbal self-concepts were close to zero. Furthermore, there were positive paths from achievements to the corresponding self-concepts, indicating social comparison effects, and negative paths from achievement in one subject to selfconcept in the other subject, indicating dimensional comparison effects. In addition to such cross-sectional evidence, several longitudinal (Möller, Retelsdorf, Köller, & Marsh, 2011; Niepel, Brunner, & Preckel, 2014), experimental (Möller & Savyon, 2003; Pohlmann & Möller, 2009; Strickhouser & Zell, 2015), and diary studies (Möller & Husemann, 2006) support the tenets of the dimensional comparison theory (DCT; Möller & Marsh, 2013). According to DCT, dimensional comparisons occur when a person compares his/her perceptions of aspects of a particular domain with his/her perceptions of aspects of another particular domain, thereby affecting motivation and learning in these domains. Almost all studies that have tested and/or applied the I/E model have been conducted with school students, focusing on their mathematics and verbal achievements and self-concepts. Recently, the I/E model was extended to other variables, thereby forming the GI/E model (Möller et al., 2015; Figure 1B). Several studies support this extension for diverse variables including: self-regulated learning (Miller, 2000), emotions

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Roles of dimensional and social comparisons (Goetz, Frenzel, Hall, & Pekrun, 2008), intrinsic motivation (Marsh et al. 2015), interest (Schurtz, Pfost, Nagengast, & Artelt, 2014), student-teacher relationships and perceived instruction quality (Arens & Möller, 2016). In all these cases the cited authors found positive effects of social comparisons within domains and negative effects of dimensional comparisons across domains. Other studies retained students’ self-concepts as criteria but expanded the original model to other domains, such as students’ self-concepts in science and different languages (e.g., Jansen, Schroeders, Lüdtke, & Marsh, 2015; Marsh et al., 2014; Marsh et al., 2015). More importantly for teachers and their professional selfconcept, Dietrich, Dicke, Kracke, and Noack (2015) found dimensional comparison effects when analyzing cross-domain relations of teacher support and motivation (levels of perceived teacher support in one subject were negatively related to students’ intrinsic value and effort in another subject).

However, as yet studies that have tested and/or applied the GI/E model have only addressed students’ outcome variables, none (to our knowledge) have examined the potential operation of dimensional and social comparison processes in the formation of pre-service teachers’ self-concepts. This is despite known positive links between teachers’ self-concepts, their well-being and both the effectiveness and innovativeness of their teaching. Notably, Yeung, Craven, and Kaur (2014) recently showed that teachers’ self-concepts are good predictors of teaching behaviors. They found teachers with a positive self-concept to be more likely to engage their students in learning activities and deep learning processes than teachers with a negative self-concept. Therefore, aims of the study presented here were to extend knowledge of the formation of pre-service teachers’

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Roles of dimensional and social comparisons self-concepts, and extend the GI/E model to three core aspects of teachers’ knowledge, as described by Shulman (1986) and presented below.

1.2 Pre-service Teachers’ Professional Self-Concept According to Shulman (1986), teachers’ professional knowledge can be divided into content knowledge (CK), pedagogical content knowledge (PCK), and pedagogical knowledge (PK). CK is defined as knowledge of the subject to be taught (Grossman, Schoenfeld, & Lee, 2005). Clearly, strong conceptual understanding of the subject matter is crucial for teacher competence (Baumert et al., 2010), and (accordingly) CK is essential for effective teaching (Ball, Lubienski, & Mewborn, 2001; Baumert et al., 2010; Grossman et al., 2005). Recent studies found a positive correlation between teachers’ CK and student achievement (Hill, Rowan, & Ball, 2005; Krauss, Brunner et al., 2008). However, several studies have shown that CK alone is not sufficient for either effective teaching or strongly promoting students’ learning progress (Abell, 2007; Baumert et al., 2010). PCK is another domain of content-related knowledge that is important for effective teaching (Mahler, Großschedl, & Harms, 2017). It is an “amalgam of content and pedagogy” according to the original definition by Shulman (1987, p. 8); the type of knowledge that makes the subject matter comprehensible for students (Shulman, 1986). Today, it is widely accepted that PCK comprises at least two facets of knowledge: knowledge of instructional strategies that integrate the representation of subject matter and responses to specific learning difficulties, and knowledge of students’ conceptions and preconceptions (Großschedl, Harms, Kleickmann, & Glowinski, 2015; Hill, Ball, & Schilling, 2008; Lee & Luft, 2008; Schmelzing, van Driel, Jüttner, Brandenbusch,

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Roles of dimensional and social comparisons Sandmann, & Neuhaus, 2013). Recent studies showed that CK and PCK impact instructional quality and student progress (Baumert et al., 2010; Hill et al., 2005; Mahler et al., 2017). In contrast to CK and PCK, PK transcends the subject matter (e.g., Shulman, 1986, 1987), and can be defined as knowledge of the “broad principles and strategies of classroom management and organization” (Shulman, 1987, p. 8). Voss, Kunter, Seiz, Hoehne, and Baumert (2014) found a positive relation between a sample of mathematics teachers’ PK and the quality of their classroom instruction. Members of this group (Voss, Kunter, and Baumert, 2011) also extended Shulman’s original definition of PK by including psychological aspects relating to the classroom and heterogeneity of students, thereby forming a construct called pedagogical and psychological knowledge (PPK). Thus, the three different domains of teachers’ professional knowledge have repeatedly been shown to positively impact different aspects of learning: CK and even more PCK are important determinants of the quality of instruction and, consequently, of students' progress (Baumert et al., 2010; Senk, Tatto, Reckase, Rowley, Peck, & Banko 2012; Mahler et al., 2017). Recently, we investigated the structure of pre-service teachers’ self-concepts with regard to the three domains of professional knowledge (Authors, 2016). We explored the CK, PCK, PPK and corresponding self-concepts of sets of German pre-service mathematics and science teachers, and found that their self-concepts were empirically separable into CK, PCK, and PPK, even during their teacher preparation programs. In efforts to extend these findings, we have applied the GI/E model to analyze the impact of dimensional and social comparisons on pre-service teachers’ self-concepts of their professional knowledge.

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Roles of dimensional and social comparisons

1.3 Hypotheses To apply the GI/E model to pre-service teachers’ professional knowledge and their domain-specific self-concepts we first addressed the relation between the two professional knowledge domains CK and PPK, because they are distinctly different domains. As already stated, CK is knowledge of the subject to be taught (here biology), whereas PPK is knowledge of the generic principles and strategies of classroom management and organization. Thus, both DCT and the GI/E model would predict positive paths from achievements to self-concepts within the domains, as indicators of social comparison, and negative paths from achievements to self-concepts across the domains (i.e. from CK achievement to PPK self-concept, and vice versa) as indicators of dimensional comparisons. Thus, our first hypothesis was: 1. There are positive paths from achievements to self-concepts within domains and negative paths from achievements to self-concepts across domains (from CK achievement to PPK self-concept, and vice versa).

We subsequently added PCK to the model. Because PCK forms an “amalgam of content and pedagogy” (p. 8, Shulman, 1986), we expected the paths from PCK testscores to CK and PPK self-concepts to be close to zero. Thus, our second hypothesis was: 2. There are positive paths from achievements to self-concepts within domains when PCK is integrated. The paths from achievements to self-concepts across the domains are close to zero for PCK. We also predicted small paths from both CK test scores and PPK test scores to PCK self-concept.

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Roles of dimensional and social comparisons Because the two different tracks of the German teacher program differ considerably in many respects, we expected that the results of the GI/E model could be different for academic and the non-academic track.

2 Methods 2.2 Sample In Germany, teacher education training involves two stages (Cortina & Thames, 2013). The development of CK, PCK, and PPK prioritizes the first stage (3.5–5 years of higher education). It consist of instructional practice in schools (about 2–5 months in total). Pre-service secondary teachers can choose either of two teacher education programs: academic or non-academic track, which provide qualifications to teach in schools that get students ready for an academic career (grades 5–12 [or 13]) or a vocational career (grades 5-10), respectively. Although both teacher education programs accomplish with a teaching certificate for at least two subjects (e.g., biology and mathematics; KMK, 2013), academic-track pre-service teachers have to master higher CK demands (approximately one third more) than their non-academic track colleagues. Accordingly, the national standards for teacher education (KMK, 2008) contain some biological contents (e.g., immunobiology) for academic track teachers only. With regard to the contents common to both pre-service teacher populations (e.g., human biology), they state that these contents have to be studied in more detail by academic track preservice teachers than non-academic track pre-service teachers. With reference to PCK and PK, in contrast, the national standards for teacher education (KMK, 2004, 2008) contain comparable demands to both populations of pre-service teachers. Therefore, the

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Roles of dimensional and social comparisons German sample allows drawing conclusions as to the effect of CK on PCK and PK development. The COACTIV study (Cognitive Activation in the Classroom) investigated mathematics teachers' CK and PCK (Baumert et al., 2010; Brunner et al., 2006; Kleickmann et al., 2013). They compared in-service teachers' CK and PCK dependent on the track. The study shows that German academic track mathematics teachers actually outperformed their non-academic track colleagues with regard to CK and PCK. Whereas this result is consistent with the higher CK requirements stated in the national standards for teacher education (KMK, 2008) for academic track teachers (in comparison to nonacademic track teachers), it is astonishing with regard to PCK. As CK is viewed as a prerequisite for PCK development by many researchers (e.g., Ball, Hill, & Bass, 2005; Ma, 1999), the result of COACTIV could reflect a transfer effect of CK on PCK (Baumert et al., 2010). This is confirmed by the result that mere mathematicians come up to mathematics teachers in regard of their PCK performance (Krauss, Baumert, & Blum, 2008). The participants were 430 pre-service secondary biology teachers (80.2 % female) attending 11 German universities located in eight federal states: 78.4 and 21.6 % assigned to academic and non-academic tracks, respectively. Their mean age was 23.4 years (SD = 2.81 years) and they had completed 2.9 years of training in higher education on average (SD = 1.4 years) at the time of the study. Data obtained from tests with these participants have also been used to construct an instrument to measure content knowledge and pedagogical content knowledge in biology (Authors, 2016), as part of the project Measuring the Professional Knowledge of Pre-service Mathematics and Science Teachers (German acronym: KIL; Kleickmann et al., 2014) funded by the Leibniz

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Roles of dimensional and social comparisons Foundation. Further details of the project and participants’ recruitment are provided in the cited papers.

2.1 Procedure Pre-service teachers who participated in the KIL project (Kleickmann et al., 2014) had four hours to complete a questionnaire, including two 15-minute breaks after the first and third hours. Before the first break they responded to a questionnaire that included items about their self-concept. After the first break, they completed standardized achievement tests to measure their CK, PCK, and PPK. They each received compensation of 40 Euros (approximately US$ 54 at the time of the survey) for their participation. As mentioned above, some of the gathered data have already been presented, and the analysis here focuses on the relationships between their CK, PCK and PPK estimates and self-concepts.

2.3 Measures 2.3.1 Self-concepts To measure the participants’ pre-service biology self-concepts, we used the knowledge processing subscale of the Berlin Evaluation instrument for self-evaluated student competencies (BEvaKomp; Braun, Gusy, Leidner, & Hannover, 2008). This instrument operationalizes knowledge processing as subjects’ self-reported competencies for CK, PCK, and PPK, which closely correspond to academic self-concepts in the respective domains of professional knowledge (cf. Braun et al., 2008). Although the BEvaKomp instrument relates to “self-evaluated competences”, Braun et al. (2008) stated

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Roles of dimensional and social comparisons that the subscale which was used in our study, is equivalent to academic self-concept (p. 38). Participants were invited to provide Likert-type responses — from “does not apply at all” (1) to “fully applies” (4) — to the same five items regarding each of the three domains of professional knowledge (CK, PCK, and PPK; see Appendix A). Cronbachs α obtained for the three self-concept factors (α = .85, M = 3.21, SD = 0.51 for CK; α = .89, M = 2.69, SD = 0.66 for PCK, and α = .88, M = 2.49, SD = 0.63 for PPK) indicate that reliabilities of the constructs were adequate (Authors, 2016).

2.3.2 Pre-service teachers’ achievement To capture the three domains of professional knowledge of pre-service biology teachers we used a battery of items developed from an in-depth analysis of the curricula of 16 representative universities (one located in each German federal state) and the national teacher education standards of Germany (Secretariat of the Standing Conference of the Ministers of Education & Cultural Affairs of the Länder in the Federal Republic of Germany [KMK], 2004, 2008). The procedure is described in more detail in Kleickmann et al. (2014).

2.3.3.1 Content knowledge (CK) Pre-service teachers’ CK in biology was assessed using 37 items (seven short answer items, 30 closed-ended items) designed to measure their knowledge of ecology, evolution, genetics & microbiology, morphology, and physiology. These items, for example “Mark which cell structures can be found in all living cells of prokaryotes and

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Roles of dimensional and social comparisons eukaryotes (one answer is correct)”, were developed by biology educators and experienced biologists based at various German universities. A coding scheme was provided for each item. Pre-service teachers had to choose from one of four answer alternatives. For more details on the construction of the achievement test, see Großschedl et al. (2015). The CK test included a mixture of dichotomously (0 = wrong answer vs. 1 = correct answer) and polytomously scored items (0 = wrong answer; 1 = answer half correct [partial credit]; 2 = correct answer). The Cronbach’s α value for the scale was .83 (M = 27.82; SD = 8.13) indicating good reliability.

2.3.3.2 Pedagogical content knowledge (PCK) Pre-service teachers’ PCK in biology was assessed using 34 items (12 openended, 10 short answer and 12 closed-ended items) designed to probe their knowledge of students’ conceptions and preconceptions, as well as instructional strategies (cf. Großschedl et al., 2015). An example item is: “Identification keys are means to obtain an overview of the diversity and systematics of living things. A particular scientific method, which is a requirement to use identification keys has to be communicated and practiced with students. Specify the scientific method.” (Großschedl et al., 2015). The PCK test also included a mixture of dichotomously and polytomously scored items. The Cronbach’s α value for PCK was .77 (M = 27.51, SD = 7.52), indicating good reliability. 2.3.3.3 Pedagogical and psychological knowledge (PPK) The pre-service teachers’ PPK was assessed using 67 items (12 open-ended, four short answer and 51 closed-ended), based on the national teacher education standards in Germany and developed by experienced educational researchers in an analogous manner

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Roles of dimensional and social comparisons to the content-related items (Hohenstein, Zimmermann, Kleickmann, Köller, & Möller, 2014; Kleickmann et al., 2014). The items also addressed the pre-service teachers’ knowledge of instructional strategies and students’ conceptions and preconceptions (cf. Großschedl et al., 2015). An example item is: “What is inert knowledge? Please check the correct answer.” Pre-service teachers had to choose one of four answer alternatives. All items were dichotomously scored. The test provided sufficiently reliable scores (Cronbach’s α = .92, M = 82.60, SD = 29.38).

2.4 Statistical analyses Two structural equation models were used to analyze the data and assess the GI/E model’s validity in the focal context. Both Models 1 and 2 addressed the relations between the pre-service teachers’ CK and PPK self-concepts and test scores, but Model 2 also addressed their PCK self-concept and test scores. Because the two tracks of the German teacher education program differ considerably in the education and the level of knowledge, we analyzed whether the results of Model 2 are similar for the academic and the non-academic track. The self-concept constructs were modelled as latent variables. Since the items probing participants’ CK, PCK, and PPK self-concepts had the same wordings, both models provided indications of correlated uniqueness between these constructs, assuming shared method variance. The models were estimated using the maximum likelihood procedure, with robust standard errors, as implemented in Mplus version 7.11 (Muthén & Muthén, 1998-2013). To account for the nested structure of the data (students within universities), we used the option Type = complex. Missing data (all self-concept items were missing, 2.3%; achievement, 5.3%) were estimated using the full

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Roles of dimensional and social comparisons information maximum likelihood method. To evaluate the models’ fit to the data, we used several indexes, including the comparative fit index (CFI), Tucker Lewis index (TLI), and root-mean-square error of approximation (RMSEA). Fit is regarded as very good if CFI and TLI values exceed 0.95 and the RMSEA is less than 0.06 (Hu & Bentler, 1999; Yu, 2002).

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Roles of dimensional and social comparisons 3 Results Correlations between the considered variables are presented in Table 1. The correlations between the three self-concept factors were positive (r = .16 to .47, p < .001), and somewhat weaker than or similar to the correlations between the test scores (r =.34 to .57, p < .001). Correlations between CK, PCK, and PPK self-concept scores and test scores for the respective domains were all positive (r = .16 to .31, p < .001).

********************** Insert Table 1 about here ********************** Model 1, including pre-service biology teachers’ CK and PPK (Figure 2) fits the data particularly well (CFI = .98, TLI = .97, RMSEA = .05). The correlation between the test scores across the domains was positive (r = .34, p < .001) and stronger than the correlation between the self-concepts (r = .19, p < .001). Moreover, the paths from test score to self-concept within the same domain (social comparisons) were also positive and significant (β = .31 and .21, p < .001). Most importantly, the cross paths from test score in one domain to self-concept in the other domain (dimensional comparisons) were negative and significant (β = -.15 and -.18, p < .01). Thus, the results provide strong support for our hypotheses. ********************** Insert Figure 2 about here **********************

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Roles of dimensional and social comparisons As shown in Figure 3, Model 2 (including pre-service biology teachers’ CK, PCK, and PPK) also has excellent fit to the data (CFI = .99, TLI = .98, RMSEA = .03). The additional correlations between the test scores across the domains were also positive (r = .45 and .57, p < .001) and somewhat stronger than the correlations between the selfconcepts (r = .32 and .48, p < .001). Moreover, the additional within-domain path, from PCK test score to PCK self-concept, was also positive and significant (β = .39, p < .001). The cross paths from PCK test score to CK and PPK self-concepts, and PPK test scores to PCK self-concept, were not significant. However, the cross path from CK test scores to PCK self-concept was negative and significant (β = -.20, p < .001). The other two cross paths, from CK and PPK test scores to PPK and CK self-concepts, respectively, remained negative and significant (β = -.19 and -.20, p < .01 and p < .001). When comparing the results of Model 2 for the academic and the non-academic track, two cross paths were somewhat smaller and not significant for non-academic track pre-service teachers: the path from CK test score to PCK self-concept (β = -.09, n.s.) and PPK self-concept (β = .02, n.s.). However, the cross path from PCK test score to PPK self-concept became negative and significant for non-academic track pre-service teachers (β = -.35, p < .05). The correlations between the three different self-concept domains were close to zero or rather smaller for non-academic track pre-service teachers (correlation between CK and PCK self-concept: r = .01, n.s.; between PCK and PPK self-concept: r = .18, p < .001). ********************** Insert Figure 3 about here **********************

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Roles of dimensional and social comparisons 4 Discussion The results of our investigation of relations between pre-service biology teachers’ achievement and self-concepts in the three considered domains of professional knowledge (CK, PCK, and PPK) confirmed our hypotheses. The first question we addressed was whether the GI/E model is applicable to the two professional knowledge domains CK and PPK. As predicted, CK and PPK achievements were positively correlated, while the correlation between CK self-concept and PPK self-concept was weaker (but still positive). The path analysis revealed positive paths from CK and PPK test scores to the corresponding self-concepts, and negative paths from CK and PPK test scores to PPK and CK self-concepts, respectively. The positive cross paths from achievements to self-concepts indicate effects of social comparison: pre-service teachers with higher than average test scores seem to develop correspondingly high domainspecific self-concepts. This applied to both CK and PPK, although the participants received no feedback about their individual test performance. Thus, our set of pre-service teachers appear to have self-evaluations in terms of Shulman’s basic categories of professional knowledge appear to have empirically detectable reliability. The negative cross paths between knowledge and self-concept in both models suggest that pre-service biology teachers also carry out dimensional comparisons. They seem to compare their personal achievements across CK and PPK domains, as their CK test scores were negatively correlated with their PPK self-concept, and vice versa. In accordance with the DCT, the results show the juxtaposition of the two knowledge domains in the minds of pre-service teachers: CK and PPK seem as antagonistic as mathematics and language achievements reportedly are in the minds of students (Marsh,

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Roles of dimensional and social comparisons 1986). The findings have important implications for both DCT and teacher education. They extend DCT to teachers and their knowledge and self-concepts, and show that the GI/E model is applicable to achievement predictors beyond school subjects and people other than students in school. Regarding teacher education, the results show that social and dimensional comparisons are important psychological processes in the formation of teachers’ self-concepts. A major goal of teacher training is to optimize teachers’ professional knowledge, which has positive effects on corresponding self-concepts and subsequently on corresponding motivation and engagement within the domains. However, teacher educators should also be aware of the negative paths from CK to PPK self-concept, and vice versa. The second question addressed concerned effects on the paths of adding PCK to the model. The paths in Model 1 remained significant and changed only marginally after adding PCK. There was a positive path from PCK test scores to PCK self-concept, so positive associations were detected between all three dimensions of professional knowledge and corresponding self-concepts. There was also a significant negative path from CK test scores to PCK self-concept, but paths from PPK test scores to PCK selfconcept and from PCK test scores to both CK and PPK self-concepts were nonsignificant. These results underline the key role of CK in the formation of pre-service teachers’ self-concepts. CK is positively correlated with CK self-concept, but negatively correlated with PCK and PPK self-concepts. Thus, high achievement in CK tests seems to be detrimental to pre-service teachers’ self-concepts in the other knowledge domains, despite positive achievement correlations. When comparing the results of the academic and the non-academic track pre-service teachers, the detrimental characteristics of CK

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Roles of dimensional and social comparisons disappears at least for the non-academic track. This domain of knowledge seems to have no impact on the self-concept of the other two domains. Thus, pre-service teachers that were trained for the non-academic track, make less dimensional comparisons. Only one additional cross path became significant for the non-academic track pre-service teachers: from PCK to PPK self-concept. The higher the PCK, the lower the PPK self-concept. PCK and PPK seem as antagonistic for non-academic track pre-service teachers, but not for academic track pre-service teachers. Our correlations between the self-concept domains were higher than the correlations between math and verbal self-concepts in school. In studies that investigated social and dimensional comparison processes, small or near-zero correlations (.10) between the self-concept in different domains (mostly math and verbal) were found. These patterns have been found for different age groups in a variety of countries using different methodologies (Möller, Pohlmann, Köller, & Marsh 2009). Compared to these studies on the effects of (math and verbal) achievements on (math and verbal) self-concepts (Möller et al., 2009), there were relatively strong correlations between PCK and both CK and PPK self-concepts in our study, indicating that the three self-concept scales may not be clearly distinguishable. This is interesting as we found that pre-service biology and physics teachers’ CK, PCK, and PPK self-concepts are empirically separable in previous confirmatory factor analyses (Authors, 2016). Thus, relations between PCK and self-concepts in the three professional knowledge domains clearly require more attention. Thus, when looking at the results for the academic and the non-academic track pre-service teachers separately, we found that correlations between the CK self-concept and the other two domains (PCK and PPK) were smaller and no longer significant for non-academic track pre-service teachers. Thus, self-concept

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Roles of dimensional and social comparisons regarding CK of the pre-service teacher seems to be largely independent of the other two self-concept domains (PCK and PPK). Our measure of self-concept differs somewhat compared to the commonly used measures like the SDQ II (Marsh, 1999) since it refers to a more specific knowledge domain compared to the more general math and verbal domain in other studies on the I/E model. Therefore, it could be seen as measuring self-efficacy instead of self-concept. However, there is a close relationship between self-concept and self-efficacy (Bandura, 1986; Schunk, 1987, 1989). Self-efficacy can be defined as a person’s subjective appraisal of his or her ability to succeed in a particular task. Both, self-concept and selfefficacy are based on inferences drawn from prior performances. To measure selfefficacy, people were asked to judge their capability to succeed at specific target tasks. For example, students were asked to gauge their ability to solve a mathematical problem resembling those in an upcoming exam. Self-efficacy is hypothesized to promote appropriate task choice, persistence in the face of difficulty, and, ultimately, achievement. However, there are some differences between self-concept and self-efficacy, as Bong and Clark (1999) and Bong and Skaalvik (2003) pointed out: Self-efficacy is more future oriented and malleable, whereas self-concept is more past oriented and stable. Compared to self-concept, social and dimensional comparison processes are almost irrelevant for self-efficacy. However, as Valentine et al. (2004) demonstrated in their meta-analysis, the impact of both self-concept and self-efficacy on subsequent achievement seems to be similar. Although self-efficacy measures typically refer to a more narrowly defined domain than self-concept measures, Marsh (1993; also see Bong & Skaalvik, 2003) noted that this is not an inherent difference— self-concept can be defined in relation to very

22

Roles of dimensional and social comparisons specific domains, and self-efficacy can be defined more globally. However, research on the I/E model has revealed additional differences between the two constructs. In contrast to the typical I/E results, Skaalvik and Rankin (1990) found math and verbal self-efficacy measures to be substantially positively correlated (Bong, 1998). In direct comparisons, Marsh, Walker, and Debus (1991) and Skaalvik and Rankin (1995) showed that the I/E model predictions are valid for self-concept measures but not for self-efficacy measures. Results of the meta-analysis of Möller et al. (2009) indicate that the I/E model is valid for self-concept but not for self-efficacy beliefs. Our study makes contributions to the GI/E model, DCT, knowledge of teachers’ self-concepts and processes that form them. Previous studies that have tested and/or applied the GI/E model have exclusively addressed the frames of references of students in schools, while we focused on pre-service teachers. Our results confirm its applicability for participants in teacher preparation programs, showing that they develop separable self-concepts regarding each of Shulman’s knowledge domains. The findings also show that their CK self-concept is weakly related to their PCK and PPK self-concepts, while their PCK and PPK self-concepts are more strongly correlated. Such differences in relationships among subject-specific self-concepts can be regarded as reflecting positions of domains along a continuum, in which the mathematical and verbal domains may represent extremes (Möller & Marsh, 2013), or perhaps more accurately positions in a multi-dimensional space. One reason for these variations may be that students think of subjects as having varying degrees of similarity, and hence that correlations among the corresponding abilities vary accordingly (Helm, Müller-Kalthoff, Nagy, & Möller, 2016; Möller, Streblow, Pohlmann, & Köller, 2006). Whether or not pre-service teachers and

23

Roles of dimensional and social comparisons other teachers perceive such variations in similarity among CK, PCK, and PPK is an open question. However, a particularly interesting observation is that we detected the predicted relations between achievement and self-concept within and across the CK and PPK domains, but relations between PCK achievement and self-concepts were more nuanced, in accordance with the idea that PCK is an amalgam of CK and PPK. Further research is needed to overcome limitations of this study due to our cross-sectional design. Furthermore, an extension of our results to other knowledge domains would be of great interest. Recently, Shulman’s construct of Pedagogical Content Knowledge (PCK) was extended to the framework of Technological Pedagogical Content Knowledge (TPACK; Koehler & Mishra, 2008; Mishra & Koehler, 2006), which describes the type of teacher knowledge required to teach effectively with technology. TPACK is an understanding that emerges from interactions among content, pedagogy, and technology knowledge. Up until now there are no studies known, that investigate the GI/E model regarding TPACK or even the relation between TPACK and achievement. This could be of interest for future research. Perhaps our results can be transferred to these knowledge domains. To obtain more empirical information about relationships between pre-service teachers’ achievements and formation of their self-concepts our study should be complemented by studies with different designs, including longitudinal studies to examine possible reciprocal relations between knowledge and self-concept in this context.

24

Roles of dimensional and social comparisons Appendix A Self-concept Items (Adapted from Braun, Gusy, Leidner, & Hannover, 2008) 1. I can see the connections and inconsistencies in… 2. I can give an overview of the topic of… 3. I can clearly present complicated issues of… 4. Now I see myself in the position to process a typical question of… 5. I can work out the contradictions between different models or methods of…the subject area of content knowledge (vs. pedagogical content knowledge vs. pedagogical and psychological knowledge)

25

Roles of dimensional and social comparisons References Abell, S. K. (2007). Research on science teacher knowledge. In S. K. Abell & N. G. Lederman (Eds.), Handbook of research on science education (pp. 1105–1149). Mahwah, NJ: Lawrence Erlbaum. Arens, K., & Möller, J. (2016). Dimensional comparisons in students’ perceptions of the learning environment. Learning & Instruction, 42, 22-30. Authors (2016). Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 59(1), 14-17, 20-22, 43-46. Ball, D. L., Lubienski, S., & Mewborn, D. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 433–456). New York: Macmillan. Bandura, A. (1986). Social Foundations of Thought and Action. A social cognitive theory. Englewood Cliffs, NJ: Prentice Hall. Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., & Tsai, Y. M. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133-180. Bong, M., & Clark, R. E. (1999) Comparison between self-concept and self-efficacy in academic motivation research, Educational Psychologist, 34(3), 139-153, DOI: 10.1207/s15326985ep3403_1

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Roles of dimensional and social comparisons Bong, M., & Skaalvik E. M. (2003). Academic Self-Concept and Self-Efficacy: How Different Are They Really? Educational Psychology Review, 15, 1-40. Braun, E., Gusy, B., Leidner, B., & Hannover, B. (2008). Das Berliner Evaluationsinstrument für selbsteingeschätzte, studentische Kompetenzen (BEvaKomp) [The Berlin Evaluation instrument for self-evaluated student competences]. Diagnostica, 54(1), 30-42. Brunner, M., Kunter, M., Krauss, S., Baumert, J., Blum, W., Dubberke, T., et al. (2006). Welche Zusammenhänge bestehen zwischen dem fachspezifischen Professionswissen von Mathematiklehrkräften und ihrer Ausbildung sowie beruflichen Fortbildung? [How is the content-specific professional knowledge of mathematics teachers related to their teacher education and inservice training?] Zeitschrift für Erziehungswissenschaft, 9(4), 521-544. Cortina, K. S., & Thames, M. H. (2013). Teacher education in Germany. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers: Results from the COACTIV project (pp. 49-62). New York, NY: Springer. Dietrich, J., Dicke, A. L., Kracke, B., & Noack, P. (2015). Teacher support and its influence on students’ intrinsic value and effort: Dimensional comparison effects across subjects. Learning and Instruction, 39, 45-54. doi: http://dx.doi.org/10.1016/j.learninstruc.2015.05.007 Festinger, L. (1954). A Theory of Social Comparison Processes. Human Relations, 7(2), 117–140. doi: http://doi.org/10.1177/001872675400700202

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Roles of dimensional and social comparisons Figure Caption Figure 1. (A) The traditional I/E model according to Marsh (1986). (B) The generalized I/E model according to Möller et al. (2015). Figure 2. Results of GI/E Model 1. CK test score = content knowledge test score; PPK test score = pedagogical/ psychological knowledge test score; CK SC = content knowledge self-concept; PPK SC = pedagogical/ psychological knowledge self-concept. **p < .01; ***p < .001.

Figure 3. Results of GI/E Model 2. CK test score = content knowledge test score; PCK test score = pedagogical content knowledge test score; PPK test score = pedagogical/ psychological knowledge test score; CK SC = content knowledge self-concept; PCK SC = pedagogical content knowledge self-concept; PPK SC = pedagogical/ psychological knowledge self-concept. **p < .01; ***p < .001.

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Roles of dimensional and social comparisons

38

Table 1 Descriptive statistics and correlations between the considered variables CK SC

PCK SC

PPK SC

CK test score PCK test score

M

SD

CK SC

3.21

0.51

PCK SC

2.69

0.66

.30***

PPK SC

2.49

0.63

.16***

.47***

CK test score

27.82 8.13

.23***

.06

-.08

PCK test score

27.51 7.52

.12*

.31***

.03

.57***

PPK test score

82.60 29.38 -.06

.18***

.16***

.34***

.45***

Note. CK SC = content knowledge self-concept, PCK SC = pedagogical content knowledge self-concept, PPK SC = pedagogical/ psychological knowledge self-concept, CK test score = content knowledge test score, PCK test score = pedagogical content knowledge test score, PPK test score = pedagogical/ psychological knowledge test score. *p < .05; ***p < .001.

Roles of dimensional and social comparisons Figure 1

B

A ++

Percep!on Domain A

Math self-concept

Math achievement

Mo!va!on & Learning Domain A

++

++ Verbal achievement

Verbal self-concept

++

Percep!on Domain B

Effects of social comparisons Effects of dimensional comparisons

Figure 2

CK test score

.31***

CK SC

-.15** .34***

.19*** -.18**

PPK test score

PPK SC

.21***

Mo!va!on & Learning Domain B

39

Roles of dimensional and social comparisons

Figure 3

CK test score

.29***(.26***/.39**)

CK SC

-.20***(-.15**/-.09) .32***(.42***/.01)

-.19**(-.15*/-.02) .57***(.52***/.65***) .05 (.05/-.02) .34***(.32***/.49***)

PCK test score

.39***(.40***/.23)

PCK SC

.05(.09/-.35*)

.45***(.45***/.51***) .48***(.46***/.18***)

-.20***(-.15**/-.36**) .09(.08/.04)

PPK test score

.22***(.21***/.19)

PPK SC

.19***(.21*/.12)

40