Early Childhood Teachers' Pedagogical Content Knowledge in Mathematics: A Research Report From the United States

• In Event: 65.048 - Pedagogical Content Knowledge in Early Mathematics: Investigations in Three Cultures

Abstract

Objectives: This presentation describes a study of early childhood teachers’ pedagogical content knowledge (PCK) necessary for effective mathematical teaching. It contributes to our understanding of early math teaching by portraying a math knowledge profile of American early childhood teachers and by suggesting approaches to improve the mathematical competence of early childhood teachers.

Perspectives: American early childhood teachers are frequently described as lacking mathematical content understanding (Ginsburg & Golbeck, 2006). Such statements are largely based on individual classroom observations and few existing empirical investigations. Based on the conceptual framework of PCK proposed by Shulman (1986), this study systematically investigates the math teaching knowledge of early childhood teachers.

According to Shulman (1986), PCK consists of three components: 1) what—a deep and coherent understanding of mathematics content necessary for teaching young children; 2) who—knowledge of learners’ conceptions about specific mathematics content; and 3) how—math specific pedagogical knowledge to effectively represent ideas and accommodate students’ diverse needs. Because it combines content understanding with pedagogy that is needed to promote learning, PCK provides a unique perspective for investigating content knowledge in teaching.
Modes of Inquiry: Guided by Shulman’s conceptual framework, a PCK survey in early mathematics (PCK-EM) was developed. Teachers were asked to watch authentic classroom teaching videos of math-focused lessons, and then respond to nine open-ended questions about the content (what), students (who) and pedagogy (how) seen in the video. The narrative responses were coded using 6 sub-components (see Table 1) according to a rubric of 1-5 scales. The PCK-EM has achieved inter-rater reliability, repeated intra-rater reliability, and concurrent validity with observed mathematical teaching quality (Author, 2014).

Data Sources: 182 Pre-K through 3rd grade teachers from 16 elementary schools in the Chicago Public School System participated in the study. All teachers completed the online PCK-EM survey by watching an early math teaching video and responding to open-ended questions. There was no time constraint for teachers to complete the survey.

Results: First, the relatively low mean scores in Table 2 indicated limited understanding of the content, students, and pedagogy in mathematics teaching among the participating teachers. Latent profile analysis revealed three clusters of teachers regarding their PCK profiles. Only 7 teachers (4%) earned scores that demonstrated their deep, coherent conceptual understanding about mathematics (what), students’ learning (who) and effective strategies (how) in math learning (See Table 3). Secondly, repeated ANOVA suggested that compared to mathematics content knowledge (what), the teachers showed even poorer understanding of students’ learning (who) and pedagogy (how) in mathematics (F (2, 362) = 7.74, p < .01).

Significance: The single most important determinant of what students learn is what their teachers know (Darling-Hammond & Bransford, 2005). The PCK-EM provides a useful way to study the professional knowledge necessary to teach early mathematics. The results suggest a need to improve early childhood teachers' PCK in mathematics. More specifically, efforts should be made to improve conceptual understanding of math content as well as integrate pedagogy and understanding of students’ learning in the context of mathematics teaching.

Authors

• Yinna Zhang, Erikson Institute

• Jie-Qi Chen, Erikson Institute