Abstract
During the last three decades, scholars have proposed several conceptual structures to represent teacher knowledge. A common denominator in this work is the assumption that disciplinary knowledge and the knowledge needed for teaching are distinct. However, empirical findings on the distinguishability of these two knowledge components, and their relationship with student outcomes, are mixed. In this replication and extension study, we explore these issues, drawing on evidence from a multi-year study of over 200 fourth- and fifth-grade US teachers. Exploratory and confirmatory factor analyses of these data suggested a single dimension for teacher knowledge. Value-added models predicting student test outcomes on both state tests and a test with cognitively challenging tasks revealed that teacher knowledge positively predicts student achievement gains. We consider the implications of these findings for teacher selection and education.
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Notes
Our review of the literature yielded no studies examining the dimensionality of constructs other than CK-PCK and MKT.
Advanced Common Content Knowledge is distinctively different from Horizon Content Knowledge (HCK). The latter should not be equated to knowledge of the mathematics content beyond a teacher’s current grade level, given that this conceptualization captures the students’—as opposed to the teachers’—horizon knowledge (see more on that in Zazkis and Mamolo 2011). This claim resonates with an elaborated definition of HCK, developed in collaboration with Ball and Bass, according to which “HCK is not about curricular development of [the] content;” rather it is an “orientation to, and familiarity with the discipline […] that contribute to the teaching of the school subject at hand, providing teachers with a sense for how the content being taught is situated in and connected to the broader disciplinary territory” (Jakobsen et al. 2013, p. 3128).
Content knowledge items at teachers’ grade level could be considered as prerequisites for teachers’ PCK, given conceptualizations of PCK as the transformation of content knowledge into powerful forms of knowledge that are adaptive to student needs (cf. Mewborn 2003; NMAP 2008). By including content at higher grade levels, aCCK items were expected to not necessarily be prerequisites of PCK, and hence be more distinguishable from items reflecting PCK (i.e., SCK and KCT items).
We limit our review to studies that obtained actual measures of teachers’ knowledge, instead of using proxies for this knowledge, such as teachers’ credentials, number of courses taken, or degrees obtained (e.g., Monk 1994).
Although we recognize the possibility of answering an item correctly just by mere guessing or test-taking skills, a validation study (Hill et al. 2007) showed low rates of strategic test-taking and guessing, especially for the content-knowledge items (around 5% of the items taken). To the extent that such low rates were also true for the current study, the effect of guessing and test-taking skills could be thought to be minimal, especially for the aCCK items (which were fewer than the SCK/KCT items).
The present study was part of a larger study aimed at developing a strong Item Response Theory (IRT) measure of teacher knowledge. Therefore, the expert panel content validated the items for the purposes of the current study after they had been administered.
That only half of the items originally designed were eventually used in the study is telling of the limitations of any replication study, which is highly dependent on the items used; it is also telling of the difficulties inherent in designing items that can be unambiguously categorized in certain MKT domains.
Geomin rotation, an oblique rotation method, is the default rotation method in MPLUS. This method was chosen because it considers the resulting factors as non-orthogonal—which resonates with our assumption about a nonzero relationship between the knowledge factors under consideration. Additionally, parameter estimates obtained with Geomin rotation have been found to be comparable with those yielded from confirmatory factor analysis and to be unbiased (cf. Hattori et al. 2017). Moreover, an appraisal of different rotation methods for dichotomous data—the data used in the current study—showed this method to compare equally well with other oblique rotation methods (cf. Finch 2011).
We also considered bifactor models (Chen et al. 2012) to examine whether more specific factors exist above and beyond a general teacher knowledge factor; however, these models failed to converge.
On average, teachers with data in both Y1 and Y2 (n = 160) exhibited a slight decrease (seven percentage points) in knowledge over time, based on changes in the percentage of survey knowledge items they responded to correctly. Furthermore, teacher self-reports of mathematics-specific professional development were uncorrelated to these changes (results available upon request). Nevertheless, we opted to run this model separately across years to account for the potential of knowledge growth, and because we include different teachers in different years based on participation in the study.
State test scores were scaled to have a mean of zero and a SD of one within grade and district (due to different tests across states). Project test scores were scaled to have a mean of zero and a SD of one within grade.
Similar results were obtained when two other non-orthogonal rotation methods (Equamax and Quartimin) were applied. For example, in the Y1 two-factor solution with Quartimin rotation, one item had similar loadings on both factors; the highest factor loading for another item was lower than 0.40, and two items loaded onto a different factor than that theoretically assumed. For Y2, two items had similar loadings on two factors and seven loaded onto a different factor than that expected.
The Chi-square test for the model was violated for both years (given that its p value was lower than 0.05), but this criterion is sensitive to the size of the analytic sample.
We avoided dropping any items to improve the model fit or the factor loadings because any modifications made to the CFA models need to be theoretically justified (Kline 2011). Additionally, dropping items could have led to construct underrepresentation, a key limitation in exploring construct validity (cf. AERA/APA/NCME 2014).
Non-significant or marginally significant but negligible correlations were found between teacher knowledge and either teachers’ effort or teaching experience (effort: rY1 = − 0.13, p = 0.05; rY2 = − 0.11, p = 0.10; experience: rY1 = − 0.04, p = 0.58; rY2 = − 0.10, p = 0.17).
We did not study knowledge components beyond those related to the content to be taught, such as teachers’ general pedagogical knowledge. Including such components might have led to a multidimensional solution, as suggested in a recent study (Blömeke et al. 2016).
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This research was funded by Grants IES R305C090023 and NSF 08314500. The authors would like to thank the teachers who participated in this study.
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Charalambous, C.Y., Hill, H.C., Chin, M.J. et al. Mathematical content knowledge and knowledge for teaching: exploring their distinguishability and contribution to student learning. J Math Teacher Educ 23, 579–613 (2020). https://doi.org/10.1007/s10857-019-09443-2
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DOI: https://doi.org/10.1007/s10857-019-09443-2