Competence as a continuum in the COACTIV study: the “cascade model”

• Published in: ZDM Vol. 52; no. 2; pp. 311 - 327
• Main Authors: Krauss, S., Bruckmaier, G., Lindl, A., Hilbert, S., Binder, K., Steib, N., Blum, W.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2020; Springer; Springer Nature B.V
• Subjects: Achievement Gains; Achievement Tests; Causal Models; Cognitive psychology; Education; Elementary School Teachers; Foreign Countries; International Assessment; Knowledge; Knowledge representation; Learning; Mathematical analysis; Mathematics; Mathematics Education; Mathematics Teachers; Measures (Individuals); Original Article; Path Analysis; Pedagogical Content Knowledge; Pedagogy; Physics; Predictive Validity; Preservice Teachers; Quantitative psychology; Secondary School Students; Secondary School Teachers; Student Teachers; Students; Taxonomy; Teacher Characteristics; Teacher competencies; Teacher Competency Testing; Teacher Effectiveness; Teachers; Teaching; Video Technology; Vignettes; Germany; Pedagogical content knowledge; Cascade model; Video vignettes; Paper-and-pencil test; Competence as a continuum; COACTIV
• ISSN: 1863-9690; 1863-9704
• DOI: 10.1007/s11858-020-01151-z

Two different tools for assessing pedagogical content knowledge (PCK) of mathematics teachers used in the framework of the COACTIV study are systematically compared in this paper, namely the paper-and-pencil test consisting of items on the three facets knowledge of explaining and representation , knowledge of student thinking and typical mistakes , and knowledge of the potential of mathematical tasks , and the video vignettes instrument that examines teachers' proposed continuations for presented lesson video clip s specific to their subject-related and methodological competence aspects. Initially, both COACTIV PCK assessment tools are systematically contrasted for the first time with respect to their predictive validity for instructional quality ( N  = 163 German secondary mathematics teachers) as well as student learning gains ( N  = 3806 PISA students from 169 different classes) by means of path models showing that PCK, when assessed by the paper-and-pencil method, can better predict instructional quality than the video vignettes instrument can. Next, we theoretically propose the cascade model as capable of integrating pertinent theories on teacher competence and instructional quality. This model implies five ‘columns’ that are ordered according to a sequential causal chain (teacher disposition → situation-specific skills → observable teaching behavior → student mediation → learning gains). Finally, we specify four out of the five ‘columns’ of this cascade model, based empirically on the COACTIV data.