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Assessing Knowledge for Teaching Early Mathematics

Sat, April 18, 2:45 to 4:15pm, Hyatt, Floor: East Tower - Purple Level, Riverside West


This study investigated an innovative measurement to assess early childhood professionals’ knowledge of teaching foundational mathematics.
Pedagogical content knowledge (PCK) represents the blending of content knowledge and pedagogy that is needed to effectively promote learning (Shulman, 1986). Despite the popularity of PCK conceptualization, few studies have reported the psychometric properties of assessment measuring PCK, due to the lack of agreement on the operational definition of PCK and effective way to capture this specialized knowledge. Little evidence existed regarding the validity of the assessing PCK (Authors, 2012).
The current study proposed a three dimension model of PCK for early mathematics and developed an assessment tool according to this framework: what—a deep understanding of mathematics topics necessary for teaching young children; who—knowledge of learners’ conceptions about specific mathematics content; and how—math specific pedagogical knowledge.
Modes of Inquiry
The PCK-EM survey is an online survey utilizing video stimuli to assess teachers’ knowledge of the content, pedagogy, and students’ development in early mathematics education. Responses to the open-ended questions were coded by 6 aspects (i.e., the sub-components of PCK dimensions) at a 1-5 scale. Teaching quality was revealed by an on-site observation at a 1-7 scale.
Three coders were involved in coding responses to the PCK-EM survey. The coding was completed within 6 weeks. Inter-coder reliability was examined by assigning the same set of responses to two coders; repeated within-coder reliability was checked through giving each coder a portion of their previously coded responses (4 weeks apart). The whole process was blind to the coders (see table 1 and table 2).
Data Sources: 182 Pre-K through 3rd grade teachers working at a large urban school district in the Midwest of the United States took the PCK-EM survey and were observed by trained researchers for mathematics teaching quality.
Inter-rater reliability was calculated using percent-within-one (PWO) analysis, percentage of exact agreement and intra class correlations (ICCs) (See table 3 and table 4). The PWO ranged between 90% to 97% between coders, and 40% to 65% if using exact match criteria. Individual ICCs were between .48 and .84; and average ICCs were between .65 and .91. Intra-rater repeated reliability was calculated using PWO analysis as well as percentage of exact agreement (See table 5). PWO ranged from 87.5% to 100%, with exact match percentage ranged from 50% to 62.5%. Regression analysis indicated that the overall PCK significantly predicted teaching quality (r = .496, p < .05, N = 162).
There is a need to reliably and effectively assess teachers’ knowledge of mathematics that matters for teaching young children, which serves as a starting point for further effort. The present study indicated promising reliability and validity of the PCK-EM survey. Using PWO and ICC, the most commonly applied criteria of objective ratings, the tool demonstrated robust reliability between coders and for the same coders within one month apart. The significant relationship between teachers’ knowledge and teaching quality also suggested external concurrent validity of the assessment.