Designing for Consensus and the Standards for Mathematical Practice

Johnson, Raymond

Graduate Thesis Or Dissertation

Designing for Consensus and the Standards for Mathematical Practice Public Deposited

Analytics

Citations

Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/tm70mv36f

Abstract

This design research study examined how professional development in the context of a research practice partnership developed Algebra 1 teachers’ collective understanding of the eight Standards for Mathematical Practice (SMPs), part of the Common Core State Standards. Over two years, 15 teachers participated in a task analysis routine that included the alignment of mathematical tasks to the SMPs. Group consensus of these task ratings were analyzed quantitatively using Randolph’s kappa, along with a measure of individual contributions to consensus that was based on calculations of pairwise agreement. Task rating discussions, which targeted disagreement in the task ratings, were analyzed qualitatively using a grounded theory approach. The analyses revealed that consensus for SMP alignment decisions increased over time. Practice 4, model with mathematics, was the only practice for which there was a strong consensus that tasks were aligned to a practice. When alignment to SMPs was correlated with task ratings for cognitive demand, a positive correlation existed between demand and practices one through four, but no correlation existed between demand and practices five through eight. Examination of individual raters’ contributions to SMP alignments showed differences in the use of content knowledge, use of standards definitions, and attention to alignment criteria. Teachers who attended most to the alignment criteria scored highest in their individual contributions to consensus. These findings add to Brown’s theories of design capacity for enactment and pedagogical design capacity (2002, 2009) by arguing that curriculum alignment to academic standards is a process of perceiving affordances in curricular materials, and that the process necessarily relies on consensus interpretations of standards and socially developed criteria for alignment. The implications of this study suggest that task analysis is useful, but not sufficient for developing teachers’ understanding of the SMPs, and that the quantitative methods employed in the analysis of this study could have utility as a formative measure in other professional development and research.

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