Reliability, Validity, and Measurement Invariance of Attitudinal and Social Norm Factors in Math

Abstract

The purpose of the present study was to provide a deeper understanding of multidimensional aspects of attitudes and social norms in educational contexts. Specifically, the current investigation aimed to (1) examine reliability and validity of factorial structure of math attitudes (Affective, Behavioral, and Cognitive factors) and perceived math social norms (Parent, Peer, and Teacher factors) and (2) test whether measurement of all factors would be invariant across national groups. Three nationally representative sample data (USA, Hong Kong, and Singapore; N = 15,019) were obtained from the 2012 Programme of International Student Assessment (PISA) database. High values in Cronbach’s Alpha, Composite Reliability scores, and factor loadings indicated strong internal consistency and convergent validity of all factors. Estimated correlations among latent factors were ranged from small to moderate in value (rs = .21 - .51, ps < .001) and each square root of average variance extracted turned out to be greater than all bivariate correlations (.71 - .85), which supported clear discriminant validity. Furthermore, the results of Multigroup Confirmatory Factor Analysis (MGCFA) yielded that measurement of the six factors was equivalent across national groups at the level of strong (scalar) factorial invariance. Implications for math education and future research are discussed.

The ABCs of Math Attitudes: Reliability and Validity of the Three Factor Model

“…Furthermore, inter-item correlation matrices supported clear convergent and discriminant validity. More importantly, the findings further establish the validity and reliability of the theorized model of "Affective-Behavioral-Cognitive math attitudes" by Di Martino (2007, 2014), Eagly and Chaiken (1998;), Walker (2018, and the classical tripartite model of attitudes from social pyschology (Breckler, 1984;Rosenberg & Hovland, 1960).…”

“…Alpha coefficients (.74 -.91), factor loadings (.49 -.90), and inter-item correlation matrices supported strong reliability and clear convergent and discriminant validity of all three subscales of math attitudes. Findings were consistent with the well-documented theoretical model of ABC math attitudes (Eagly & Chaiken, 1998Walker, 2018;Zan & Di Martino, 2007, 2014 as well as the classical tripartite model of attitudes from social psychology (Breckler, 1984;Rosenberg & Hovland, 1960). Implications of the ABC model of math attitudes on math education, limitations of the present study, and future research are discussed.…”

“…Additionally, considering that the four-factor ATMI model includes lengthy survey questionnaires (i.e., 40 items), the present study suggests an alternative (and perhaps, more doable for K-12 students) survey instrument of math attitudes that was utilized from the 2012 PISA SBQs. Certainly, the theoretically grounded ABCs of three-factor model of math attitudes (Eagly & Chaiken, 1998Walker, 2018;Zan & Di Martino, 2007, 2014 does not suggest that the well-established and reputable four-factor model of ATMI should be discredited. The goal of the present study was to establish reliability and validity of the ABCs of math attitudes from the 2012 PISA SBQs with multiple national samples.…”

Perceived Academic Social Influence from Parents, Peers, and Teachers Across Gender Groups: Scale Development

“…To assess model fit, insignificant Chi-Square (χ2) results are desirable. Chi-Square (χ2) testing is known to be sensitive to large samples, which tends to reject the null hypothesis (Marcoulides, Heck, & Papanastasiou, 2005;Raykov & Marcoulides, 2006;Walker, 2018) so that there is no discrepancy between the proposed model (i.e., the PASIS with three subscales) and the sample data from the 2012 PISA. Thus, the following incremental fit indices were used to evaluate model fit: (1) Comparative Fit Index (CFI; Bentler (1990)) (2) Root-Mean-Square Error of Approximation (RMSEA; Browne and Cudeck (1993)), and (3) Standardized-Root-Mean Square Residual (SRMR).…”