An investigation of how preservice teachers' ability to professionally notice children's mathematical thinking relates to their own mathematical knowledge for teaching

The National Council of Teachers of Mathematics and the standards movement promoted reform-based instructional practices as the most effective way to teach mathematics. Thus, teachers are encouraged to teach students mathematics to build conceptual understanding through providing students with opportunities to problem solve, draw conclusions, justify answers, communicate with peers, and make connections to the real world and other content areas. Due to the robust nature of mathematics, it is critical for preservice teachers to develop a strong content and pedagogical-content knowledge of mathematics. This combination of knowledge is referred to as Mathematical Knowledge for Teaching (Ball & Hill, 2009). The ability to professionally notice a child's mathematical thinking is also needed to effectively teach mathematics using reform-based methods. Research has shown that both Mathematical Knowledge for Teaching and professional noticing of mathematical thinking is developed over time. The intent of this study was to determine if preservice teachers' Mathematical Knowledge for Teaching and their ability to professionally notice a child's mathematical thinking developed over the course of a semester, in which they were involved in a mathematics methods course and a field experience in an elementary classroom. The study also examined if there was a relationship between preservice teachers' Mathematical Knowledge for Teaching and their ability to professionally notice mathematics thinking. Data were gathered through child response videos with preservice teachers noticing different components of a child's mathematical thinking and preservice teacher completion of the Learning Mathematics for Teaching instrument, which evaluates Mathematical Knowledge for Teaching. Analysis of Variance and Pearson-Product Moment Correlation were used to analyze the data from those instruments.;The results of the study showed a positive statistical change in the preservice teachers' abilities to make appropriate instructional decisions for a child who was answering mathematics questions, which is one component of professional noticing. There was however no statistical change in the other components of professional noticing or in their Mathematical Knowledge for Teaching scores. These results emphasize the necessity for teacher education to provide more opportunities for preservice teachers to grow in both their content and pedagogical-content knowledge. Expanded opportunities during their teacher education program will help preservice teachers develop Mathematical Knowledge for Teaching and the ability to professionally notice a child's mathematical thinking, which will better prepare them for their time in the classroom.