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PERCEIVED SOCIAL RELATIONSHIPS AND SCIENCE LEARNING OUTCOMES FOR TAIWANESE EIGHTH GRADERS: STRUCTURAL EQUATION MODELING WITH A COMPLEX SAMPLING CONSIDERATION

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ABSTRACT

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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Correspondence to Tsung-Hau Jen.

Appendices

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)
  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).

    $$ \widehat{\sigma }_{{\left( {\text{PV}} \right)}}^2 = \frac{1}{{M - 1}}{\sum\limits_{{i = 1}}^M {\left( {{{\widehat{\mu }}_i} - \widehat{\mu }} \right)}^2} $$
    (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)
    (4)
  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).

    $$ {\widehat{\sigma }_{{\left( {\widehat{\mu }{\text{PV}}} \right)}}} = \sqrt {{\widehat{\sigma }_{{\left( {\widehat{\mu }} \right)}}^2 + \left( {1 + \frac{1}{M}} \right) \cdot \widehat{\sigma }_{{\left( {\text{PV}} \right)}}^2}} $$
    (5)

    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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Jen, TH., Lee, CD., Chien, CL. et al. PERCEIVED SOCIAL RELATIONSHIPS AND SCIENCE LEARNING OUTCOMES FOR TAIWANESE EIGHTH GRADERS: STRUCTURAL EQUATION MODELING WITH A COMPLEX SAMPLING CONSIDERATION. Int J of Sci and Math Educ 11, 575–600 (2013). https://doi.org/10.1007/s10763-012-9355-y

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