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Based on the Trends in International Mathematics and Science Study 2007 study and a follow-up national survey, data for 3,901 Taiwanese grade 8 students were analyzed using structural equation modeling to confirm a social-relation-based affection-driven model (SRAM). SRAM hypothesized relationships among students’ perceived social relationships in science class and affective and cognitive learning outcomes to be examined. Furthermore, the path coefficients of SRAM for high- and low-achieving subgroups were compared. Given the 2-stage stratified clustering design for sampling, jackknife replications were conducted to estimate the sampling errors for all coefficients in SRAM. Results suggested that both perceived teacher–student relationships (PTSR) and perceived peer relationships (PPR) exert significant positive effects on students’ self-confidence in learning science (SCS) and on their positive attitude toward science (PATS). These affective learning outcomes (SCS and PATS) were found to play a significant role in mediating the perceived social relationships (PTSR and PPR) and science achievement. Further results regarding the differences in SRAM model fit between high- and low-achieving students are discussed, as are the educational and methodological implications of this study.

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  • Anderson, J. & Gerbing, D. (1988). Structural equation modeling in practice: A review and recommended two-step approach. Psychological Bulletin, 103, 411–423.

    Article  Google Scholar 

  • Armitage, C. J. & Conner, M. (2001). Efficacy of the theory of planned behaviour: A meta-analytic review. British Journal of Social Psychology, 40, 471–499.

    Article  Google Scholar 

  • Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84, 191–215.

    Article  Google Scholar 

  • Bao, X. H. & Lam, S. F. (2008). Who makes the choice? Rethinking the role of autonomy and relatedness in Chinese children’s motivation. Child Development, 79(2), 269–283.

    Article  Google Scholar 

  • Bollen, K. A. (1989). Structural equation modeling with latent variables. New York: Wiley.

    Google Scholar 

  • Chien, C.-L., Jen, T.-H. & Chang, S.-T. (2008). Academic self-concept and achievement within and between math and science: An examination on Marsh and Köller’s unification model. Bulletin of Educational Psychology, 40, 107–126.

    Google Scholar 

  • Cosmovici, E. M., Idsoe, T., Bru, E. & Munthe, E. (2009). Perceptions of learning environment and on-task orientation among students reporting different achievement levels: A study conducted among Norwegian secondary school students. Scandinavian Journal of Educational Research, 53(4), 379–396.

    Article  Google Scholar 

  • Dorman, J. P. (2001). Associations between classroom environment and academic efficacy. Learning Environments Research, 4, 243–257.

    Article  Google Scholar 

  • Erlauer, L. (2003). The brain-compatible classroom: Using what we know about learning to improve teaching. Alexandria, VA: Association for Supervision and Curriculum Development.

    Google Scholar 

  • Fornell, C. & Larcker, D. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18, 39–50.

    Article  Google Scholar 

  • Foy, P., Galia, J. & Li, I. (2008). Scaling the data from the TIMSS 2007 mathematics and science assessments. In J. F. Olson, M. O. Martin & I. V. S. Mullis (Eds.), TIMSS 2007 technical report (pp. 225–279). Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

    Google Scholar 

  • Hardre, P. L., Chen, C.-H., Huang, S.-H., Chiang, C.-T., Jen, F.-L. & Warden, L. (2006). Factors affecting high school students’ academic motivation in Taiwan. Asia Pacific Journal of Education, 26, 189–207.

    Article  Google Scholar 

  • Hoelter, J. W. (1983). The analysis of covariance structures: Goodness-of-fit indices. Sociological Methods Research, 11, 325–344.

    Article  Google Scholar 

  • Jöreskog, K. G. & Sorbom, D. (2004). LISREL 8: User’s reference guide. Lincolnwood, IL: Scientific Software International.

    Google Scholar 

  • Keller, H. (2012). Autonomy and relatedness revisited: Cultural manifestations of universal human needs. Child Development Perspectives, 6(1), 12–18.

    Article  Google Scholar 

  • Kline, R. B. (2010). Principles and practice of structural equation modeling (3rd ed.). New York: Guilford.

    Google Scholar 

  • Langendyk, V. (2006). Not knowing that they do not know: Self-assessment accuracy of third-year medical students. Medical Education, 40, 173–179.

    Article  Google Scholar 

  • Ma, X. & Xu, J. (2004). Determining the causal ordering between attitude toward mathematics and achievement in mathematics. American Journal of Education, 110, 256–280.

    Article  Google Scholar 

  • Markus, H. R. & Kitayama, S. (2003). Culture, self, and the reality of the social. Psychological Inquiry, 14(3), 277–283.

    Article  Google Scholar 

  • Marsh, H. W. (1990). Causal ordering of academic self-concept and academic achievement: A multiwave, longitudinal panel analysis. Journal of Educational Psychology, 82, 646–656.

    Article  Google Scholar 

  • Martin, M. O. & Preuschoff, C. (2008). Creating the TIMSS 2007 background Indices. In J. F. Olson, M. O. Martin & I. V. S. Mullis (Eds.), TIMSS 2007 technical report (pp. 225–279). Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

    Google Scholar 

  • McCoach, D. B., Black, A. C. & O’Connell, A. A. (2007). Errors of inference in structural equation modeling. Psychology in the Schools, 44(5), 461–470.

    Article  Google Scholar 

  • Mislevy, R. J. (1991). Randomization-based inference about latent variables from complex samples. Psychometrika, 56(2), 177–196.

    Article  Google Scholar 

  • Multon, K. D., Brown, S. D. & Lent, R. W. (1991). Relation of self-efficacy beliefs to academic outcomes: A meta-analytic investigation. Journal of Counseling Psychology, 38, 30–38.

    Article  Google Scholar 

  • Nelson, R. M. & DeBacker, T. K. (2008). Achievement motivation in adolescents: The role of peer climate and best friends. The Journal of Experimental Education, 76, 170–189.

    Article  Google Scholar 

  • Ng, F. F. Y., Kenney-Benson, G. A. & Pomerantz, E. M. (2004). Children’s achievement moderates the effects of mothers’ use of control and autonomy support. Child Development, 75(3), 764–780.

    Article  Google Scholar 

  • Ryan, R. M. & Deci, E. L. (2000a). Intrinsic and extrinsic motivations: Classic definitions and new directions. Contemporary Education Psychology, 25, 54–67.

    Article  Google Scholar 

  • Ryan, R. M. & Deci, E. L. (2000b). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55, 68–78.

    Article  Google Scholar 

  • Shrigley, R. L. (1990). Attitude and behavior are correlates. Journal of Research in Science Teaching, 27, 97–113.

    Article  Google Scholar 

  • Tabachnick, B. G. & Fidell, L. S. (2007). Using multivariate statistics (5th ed.). Boston, MA: Allyn & Bacon.

    Google Scholar 

  • Taylor, I. M. & Lonsdale, C. (2010). Cultural differences in the relationships among autonomy support, psychological need satisfaction, subjective vitality, and effort in British and Chinese physical education. Journal of Sport & Exercise Psychology, 32(5), 655–673.

    Google Scholar 

  • Tsai, C.-C. & Kuo, P. C. (2008). Cram school students’ conceptions of learning and learning science in Taiwan. International Journal of Science Education, 30, 353–375.

    Article  Google Scholar 

  • United States National Research Council (2007). Taking science to school: Learning and teaching science in grades K–8. Washington, DC: National Academies Press.

    Google Scholar 

  • Weinburgh, M. (1995). Gender differences in student attitudes toward science: A meta-analysis of the literature from 1970 to 1991. Journal of Research in Science Teaching, 32(4), 387–398.

    Article  Google Scholar 

  • Wolf, S. J. & Fraser, B. J. (2008). Learning environment, attitudes and achievement among middle-school science students using inquiry-based laboratory activities. Research in Science Education, 38, 321–341.

    Article  Google Scholar 

  • Yore, L. D., Anderson, J. O. & Chui, M.-H. (2010). Moving PISA results into the policy arena: Perspectives on knowledge transfer for future considerations and preparations. International Journal of Science and Mathematics Education, 8(3), 593–609.

    Article  Google Scholar 

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Correspondence to Tsung-Hau Jen.


Appendix 1

The path coefficients in SRAM were estimated by averaging the coefficients already estimated through the same modeling process by using different sets of plausible values as the indicator of science achievement (see Eq. 1), and the standard error of each coefficient was the combination of measurement error and sampling error according to the following steps:

$$ \widehat{\mu } = \frac{1}{M}\sum\limits_{{i = 1}}^M {{{\widehat{\mu }}_i}} $$
  1. Step 1:

    Estimation of the measurement error

    Based on the five sets of coefficients estimated through corresponding sets of students’ plausible values, the measurement errors were aggregated according to Eq. 2 (Mislevy, 1991; Foy et al., 2008).

    $$ \widehat{\sigma }_{{\left( {\text{PV}} \right)}}^2 = \frac{1}{{M - 1}}{\sum\limits_{{i = 1}}^M {\left( {{{\widehat{\mu }}_i} - \widehat{\mu }} \right)}^2} $$

    In Eqs. 1 and 2, \( \widehat{\mu } \) can be any statistic (e.g. mean, correlation, or path coefficients), and M is the number of sets of PVs, which is equal to five here.

  2. Step 2:

    Estimation of the sampling error

    In addition to measurement error, the other source of the variability for path coefficients comes from the sampling error. TIMSS 2007 used a two-stage stratified cluster sampling design. In the first stage, 150 schools were selected according to some variables of interest, such as school type or location. In the second stage, one or two classes in the sampled school were selected at random and all the students in the selected classes were surveyed. Because students in the same class will have the same contextual variables at the class and school levels, the effective sample size could be much less than for the same number of students selected by simple random selection. If we treat the sampled students as though they were sampled through simple random selection, we may underestimate the standard errors of all the coefficients. The two-stage jackknife (JK) replication technique can be utilized to estimate the standard errors caused by the sampling design. In order to conduct the JK replications, theoretically an additional 75 replications should be processed for each set of PVs and the results of 375 replications in total should be aggregated through Eqs. 3 and 4 (Foy et al., 2008).

  3. Step 3:

    Standard error estimation

    To estimate the standard errors for all the statistics, the last step is to combine the sampling error and the measurement error portions according to Eq. 5 (Foy et al., 2008).

    $$ {\widehat{\sigma }_{{\left( {\widehat{\mu }{\text{PV}}} \right)}}} = \sqrt {{\widehat{\sigma }_{{\left( {\widehat{\mu }} \right)}}^2 + \left( {1 + \frac{1}{M}} \right) \cdot \widehat{\sigma }_{{\left( {\text{PV}} \right)}}^2}} $$

    Due to the fact that the same distribution constraints hold for the five sets of student PVs, in this study only an additional 75 replications for the first set of PVs were conducted in order to estimate the sampling errors for all the coefficients. In other words, is utilized instead of in Eq. 5.

Appendix 2

TABLE 6 Correlation matrix, means, and standard deviations of the indicators for total sample (n = 3,901)
TABLE 7 Correlation matrix, means, and standard deviations of the indicators for HAG (n HAG = 1,956)
TABLE 8 Correlation matrix, means, and standard deviations of the indicators for LAG (n LAG = 1,945)

Appendix 3

TABLE 9 Path coefficients and their error estimations of SRAM for the three sample groups

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