Pre-kindergarten teachers' use and understanding of hypothetical learning trajectories in mathematics education

Teachers' mathematical content knowledge and their understanding of children's learning have been identified as critical elements in current reform movements, (Darling-Hammond & Ball, 1998; Fennema & Franke, 1992; Ma, 1995). Hypothetical learning trajectories (Simon, 1995) have the potential to increase pre-kindergarten teachers' understanding of the mathematical processes young children use and assist them in facilitating their students' growth towards higher levels of mathematical knowledge. Hypothetical learning trajectories are defined by researcher-developers as goals for meaningful learning, a set of tasks to accomplish those goals, and a hypothesis about students' thinking and learning (Clements & Sarama, 2004; Simon, 1995). Increased teacher understanding should result in positive changes in pre-kindergarten mathematics instruction yet there is little research evaluating this potential.; This case study of 14 pre-kindergarten teachers describes the processes these teachers utilized as they implemented a research-based mathematics curriculum; the ways in which they developed understandings and strategies for using hypothetical learning trajectories and changes that occurred in these over the course of a school year. The data sources included semi-structured interviews, classroom and professional development site observations, and classroom and professional development artifacts. Analysis of the teachers' understanding and use of the learning trajectories began immediately and continued throughout the research and writing process using a constant comparative method (Merriam, 1998).; The study found that the teachers' reasons for volunteering influenced their use of HLT components and supports during the year. Teachers who volunteered seeking more math activities concentrated their efforts on moving children through the curriculum while those teachers who sought a better understanding of early childhood mathematics attempted to use various HLT components and supports throughout the year. The teachers' definitions and explanations of the HLT did not consistently correspond to the understandings they demonstrated in their classrooms or their reasons for volunteering. These results have implications for developing teachers' understanding of early childhood mathematics and how reform efforts are implemented.