Disciplinary Content Knowledge

Teachers’ knowledge of proportional reasoning is important, particularly in the middle grades in the USA. This exploratory study investigated 32 teachers’ use of knowledge resources in two mathematically similar tasks (one a paper and pencil task, the other a dynamic task) around proportional reasoning. The two tasks invoked different knowledge resources by the same teachers. Results suggest questions to the field around how we access or invoke teacher knowledge and the need to more purposefully explore the potential benefits of using a dynamic task to invoke knowledge resources.

The purpose of this study was to investigate how teachers understand one specific aspect of proportional reasoning. We were interested in understanding the extent to which practicing teachers were able to make sense of reasoning that involved the fixed number of variable-sized parts perspective. We used two items, drawn from a larger dataset, that encouraged teachers to reason about proportional situations using a variable parts perspective.

This chapter explores a way of describing the teacher education curricular materials being developed by mathematics teacher educators through their interaction with the LessonSketch online platform (www.lessonsketch.org). We briefly describe the platform and the larger project and then using the experiences created by two fellows illustrate the kinds of materials being created by the teacher educators.

In this paper, using written responses of 37 PSTs preparing to teach grades 1-8 mathematics, we examined explanations they constructed to support their problem solutions and explanations they provided in support of their critiques of student-generated explanations. We also examined features of explanations on which PSTs drew in their critiques of mathematical explanations of students. Our results draw attention to the importance of helping PSTs develop competencies in constructing and critiquing mathematical explanations concurrently.

Hapgood, S., Paprzycki, P., Czerniak, C.M. (2019). Scientific Inquiry for Young Children: Linking Teacher Professional Development and Family Engagement to Improve Student Achievement. Paper presented at the Society for Research on Child Development conference [SRCD], Balitmore, MD. March 2019.

Czerniak, C. M., Paprzycki, P., Hapgood, S., & Kaderavek, J. (2019). Longitudinal Impact of Early Childhood Science Instruction on Middle Grades Literacy and Mathematics. Paper presented at the Global Conference on Education and Research [GLOCER], Sarasota, FL. May 2019.

Czerniak, C. M., Kaderavek, J., Paprzycki, P., Hapgood, S., Mentzer, G., Molitor, S., & Mendenhall, R. (2019). Longitudinal Impact of Early Childhood Science Instruction on 5th Grade Science Achievement. Paper presented at the European Science Education Research Association [ESERA], Bologna, Italy. August 2019.

Hapgood, S., Heuring, J. & Wilson, G., Czerniak, C. (Accepted for January 2020). Early Childhood Educators’ Declarative Knowledge of the Next Generation Science Standards. A poster to be presented at the Association of Science Teacher Educators [ASTE] International Conference, San Antonio, Texas.