Teacher attitudes and beliefs influence the acquisition of pedagogical and content knowledge and can enhance or impede the translation of that knowledge into actual teaching practices. Attitudes also have been shown to predict effort and persistence. This has important implications for those charged with designing professional development programs. The ABC-EM (Attitudes, Behaviors, and Confidence in Early Mathematics) survey was designed to assess beliefs and attitudes regarding the teaching and learning of early mathematics among preschool to grade 3 teachers.
The survey consists of 48 statements that fall into three categories. “Attitudes” taps into teachers’ attitudes toward math in general and their enjoyment in teaching math. “Beliefs” explores teachers’ beliefs about the appropriateness of early math for young children, effects of home environment on mathematics learning, English Language Learners and math learning, personal mathematics competence, adequacy of preparation, and current need for support. “Confidence” measures teachers’ confidence in understanding math content for teaching and performing specific math teaching tasks.
The ABC-EM is completed online. Teachers are asked to rate each statement on a 1 (strongly disagree) to 10 (strongly agree) scale. Cronbach’s alpha, a measure of the degree to which the survey items are measuring the same underlying construct, was .94 (excellent) in a sample of 182 pre-kindergarten to third grade teachers.
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.
Pedagogical content knowledge (PCK) for mathematics involves knowledge of the mathematical content, knowledge of appropriate teaching strategies, and knowledge of students’ individual characteristics (e.g., learning styles, prior knowledge, and likely misconceptions about a particular concept). The High-Impact Strategies for Early Mathematics (HIS-EM) observation tool uses this understanding of pedagogical content knowledge as a basis for assessing an individual math lesson and determining the degree of evidence in teaching practice for each of these kinds of knowledge. It is used in preschool through third-grade classrooms in order to measure the quality of mathematics teaching.
Based on our learning from the HIS-EM tool, we are currently working on a new preschool-specific observation tool, called Evaluating Quality Interactions in Preschool Mathematics (EQUIP-M), which is in active development.
The Big Ideas that convey the core concepts of mathematics are at the heart of this book that gives early childhood educators the skills they need to organize for mathematics teaching and learning during the early years.
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Our latest book Growing Mathematical Minds bridges research and practice. We translate research on early mathematics from developmental psychology into terms that are meaningful to teachers and readily applicable in early childhood classrooms.