Measures

The Whole Teacher approach attends simultaneously to the social/emotional, cognitive, and behavioral aspects of a teacher’s growth. A significant departure from the traditional approach to PD that speaks primarily to teachers’ acquisition of knowledge and skills, the Whole Teacher framework emphasizes promoting all aspects of a teacher’s development, including her attitudes, knowledge, and practice. A set of measures have been developed based on the Whole Teacher approach to professional development. These tools have been used in past and current early education research projects to examine the impact of the Collaborative’s professional development programs on teachers’ attitudes, knowledge, and practice.

Attitudes, Behaviors, and Confidence in Early Mathematics (ABC-EM)

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.

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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.

Research associated with this measure

High Impact Strategies in Early Mathematics (HIS-EM)


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.

HIS-EM is comprised of nine dimensions organized within three domains. The three domains include: (1) WHAT? – the degree to which observed practice incorporates a deep knowledge of foundational mathematics concepts; (2) WHO? – the degree to which observed practice demonstrates an understanding of young children’s typical developmental growth in mathematics and an understanding of particular, individual students’ learning needs; and (3) HOW? – the degree to which observed practice includes the effective use of mathematics teaching strategies.

Each domain is represented by three dimensions that impact of the quality of mathematics teaching. For example, one dimension used to score the “What?” domain is Learning Objectives. Learning objectives for the observed lesson are assessed for their clarity and centrality as they are presented to the students, along with the degree to which the teacher integrates the objectives with what she knows that the children already understand, and how effectively she is able to reorient students, as needed, toward the purpose of the math lesson.

HIS-EM is completed by a trained observer who sits in on a live mathematics lesson from beginning to end, as determined by the teacher. During the lesson, the observer records general notes about the lesson (e.g., duration, instructional grouping), as well as specific notes related to each dimension. Immediately after the lesson is over, the observer uses the coding manual and observation notes to assign a score of 1 (low quality) to 7 (high quality) for each dimension based on the degree to which highly effective mathematics teaching is observed. The observer also provides justification for each score.

Research associated with this measure