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Investigators often rely on the proportion of correct responses in an assessment when describing the impact of early mathematics interventions on child outcomes. Here, we propose a shift in focus to the relative sophistication of problem-solving strategies and offer methodological guidance to researchers interested in working with strategies. We leverage data from a randomized teaching experiment with a kindergarten sample whose details are outlined in Clements et al. (2020). First, we describe our problem-solving strategy data, including how strategies were coded in ways that are amenable to analysis. Second, we explore what kinds of ordinal statistical models best fit the nature of arithmetic strategies, describe what each model implies about problem-solving behavior, and how to interpret model parameters. Third, we discuss the effect of "treatment", operationalized as instruction aligned with an arithmetic Learning Trajectory (LT). We show that arithmetic strategy development is best described as a sequential stepwise process and that children who receive LT instruction use more sophisticated strategies at post-assessment, relative to their peers in a teach-to-target skill condition. We introduce latent strategy sophistication as an analogous metric to traditional Rasch factor scores and demonstrate a moderate correlation them (r = 0.58). Our work suggests strategy sophistication carries information that is unique from, but complimentary to traditional correctness-based Rasch scores, motivating its expanded use in intervention studies.

This study examines the impact of the Primarily Math Elementary Mathematics Specialist program on K-3 teachers' mathematical content knowledge for teaching, attitudes toward learning mathematics, and beliefs about mathematics teaching and learning. Three cohorts of teachers participating in the program were compared to a similar group of non-participating teachers. Teacher outcomes were measured longitudinally across 5 years. Participating teachers showed changes in their knowledge, attitudes, and beliefs in line with program goals immediately after completion of coursework. Moreover, these changes were sustained in subsequent years, following program completion. Relative to the comparison group, participants demonstrated greater gains in knowledge as well as greater improvements in attitudes and beliefs. Implications of these results for professional development design, implementation, and evaluation are discussed.