### Pedagogical Content Knowledge in Early Mathematics (PCK-EM)

The complexity of foundational math requires teachers to acquire a sophisticated understanding of underlying mathematical ideas and present them precisely to young children. The PCK-EM (Pedagogical Content Knowledge in Early Mathematics) survey was designed to capture preschool to grade 3 teachers’ content understanding of foundational math.

Drawing from Shulman’s pedagogical content knowledge theory, we developed a framework for measuring subject matter knowledge as it relates to teaching foundational math. The framework consists of three domains: 1) What? – understanding of foundational math concepts; 2) Who? – knowledge of young children’s mathematical learning trajectories; and 3) How? – math-specific teaching strategies and representations. According to our conceptualization of PCK (see figure below), to teach early math effectively, teachers must coherently integrate these three aspects of understanding.

The PCK-EM survey is a video-elicited, open-ended online survey. Teachers watch two authentic teaching videos each featuring a single lesson. After watching each video, the teacher answers nine open-ended questions that tap into his or her knowledge and understanding of the Big Ideas (central concepts of early mathematics) presented in the video and related concepts, prior knowledge young children need to have to participate in the activity, and effective teaching strategies that can be used to facilitate, reinforce, and extend the learners’ understanding of the mathematical concept.

Teacher responses to the questions are then scored by coders familiar with early childhood education and trained to analyze responses to each video. A 7-point Likert scale (1 = low; 7 = high) is used to quantify teachers’ mathematical understanding for teaching through three lenses: 1) recognition – level of math recognition present in a teacher response; 2) accuracy – accuracy of teacher responses with respect to the mathematical content of the video; and 3) depth – level of analysis, critical reflection, and inference in responses in regards to the mathematical content, student understanding/development, and instruction presented in the video stimulus. Inter-rater reliability has ranged from 82% to 91% for the nine questions among coders.