An understanding of whole number place value is a critical component of second-grade mathematics. This understanding of place value provides the foundational concept for operations with whole numbers. The ability to understand the concept of place value and transfer that understanding to teaching addition and subtraction are often problems associated with teachers’ limited pedagogical content knowledge. Teachers must understand teaching place value does not consist of merely teaching students to name the digit in a particular location. A possible solution to the problem is to provide professional development trainings and implementation support through instructional coaching focused on the teaching of place value in a conceptual manner consistent with best pedagogical practices. Therefore, the purpose of this mixed method study is to describe the pedagogical content knowledge of second-grade teachers in order to answer the research question: What can you expect to see in the classroom teaching of place value from second-grade teachers who have attended 12 hours of professional development and have received instructional coaching? Quantitative data includes the use of the Learning Mathematics for Teaching assessment paired with participant observations, discussions, and interviews in order to gain a deeper understanding of the participants’ thinking. The participants of this study are four second-grade teachers from a rural school district outside of Houston, Texas. Each of the four participants attended 12 hours of professional development and received instructional coaching support through classroom observation with post-observation discussions, a model lesson, and instructional planning. The results of the study show that every participant implemented activities from the professional development, used questioning modeled by the presenter during the sessions, and discussed critical concepts in their classrooms. Additionally, teacher pedagogical content knowledge did improve after 12 hours of professional development and instructional coaching. However, the participants believe that further support should be given through a more detailed scope and sequence, which provides information as to when and how the new concepts and activities need to be incorporated in the classroom.

The main purpose of this study is to assess pedagogical content knowledge (PCK) of in-service physics teachers about electricity topic in high school level by developing a paper-and-pencil instrument consisting of open-ended items. The instrument was developed with four different implementations by administration to the 278 in-service physics teachers. An exploratory and confirmatory factor analysis including only PCK items was conducted in validation processes. The relations among teachers&rsquo / job satisfaction levels, perceived self-efficacy levels, years of teaching experience and specific experiences, attendance to in-service training seminars related to physics teaching programs and teachers&rsquo / PCK were also analyzed by a confirmatory structural equation modeling study in validation of test scores. SPSS and AMOS programs were used in the analyses. Results of the study showed that teachers&rsquo / perceived self-efficacy level, attendance to in-service training seminars and specific experiences were significant predictors of their PCK. Teachers&rsquo / years of teaching experience and job satisfaction level were not significant predictors of their PCK. Inter-rater reliability scores were calculated as 0.86 and 78% for scoring and coding of the participant teachers&rsquo / responses respectively. Results also showed that there are many Turkish physics teachers whose PCK scores regarding students&rsquo / learning difficulties and misconceptions are below the average and participants mostly prefer to implement direct instruction in their classrooms as the instructional strategy.