Supporting Middle-Grades Mathematics Teachers to Implement a Diagnostic Classroom Assessment System Based on Learning Trajectories

• In Event: Learning Trajectories as Boundary Objects for Psychometricians, Learning Scientists, and Practitioners in Mathematics Education

Abstract

A commissioned review of research on learning trajectories (LTs) in mathematics by the Organization for Economic Cooperation and Development describes a common dilemma faced by teachers globally, i.e. how to comply with local grade-level expectations but also address the learning needs of students who may be functioning outside these expectations (Author C, 2019). To address this dilemma, Author C proposes taking LTs to scale by developing valid models of student thinking and leveraging technology to provide precise data on what students know and need to know to empower teachers to efficiently meet the diverse needs of learners.
LTs are research-based models of how students’ thinking increases in sophistication relative to domain-specific concepts in the context of instruction (Daro, Mosher, & Corcoran, 2011; Lobato & Walters, 2017). LTs articulate and order observable epistemological concepts such as partial conceptions, strategies, and misconceptions, providing educators a lens with which to view a learner’s typical obstacles and landmarks as opposed to deconstructing expert knowledge of a concept into sub-components (Author C, 2009). LTs afford teachers a means to strengthen their own mathematical knowledge for teaching (Ball, Thames, Phelps, & 2008).
In a multi-year project we studied the development, implementation, and validation of a classroom assessment tool, Math Mapper 6-8 (MM), founded on LTs that span the entire middle grades mathematics curriculum. Qualitative data from teacher and student interviews, classroom observations, and Professional Learning Community (PLC) meetings at four middle schools across three districts that have used MM for varying amounts of time were analyzed to answer the following research questions:
How are teachers' assessment practices influenced by their proficiency with assessment tools and teacher knowledge?
What kinds of support (tool-based, professional development(PD), and/or school structures) do teachers need in order to successfully implement a LT-based classroom assessment system?
Preliminary analysis indicate that teacher practices can be classified along two dimensions: strength of tool use and teacher knowledge. Teachers with weak tool use and teacher knowledge tended to dismiss assessment results, drive instruction based on personal preferences, question the alignment of items to their curriculum/standards, and doubt students’ capacity to respond to conceptual, multi-step problems. Teachers with strong tool use and weak teacher knowledge, tended to gradually build up tool use, develop data sharing norms in PLCs, and begin focusing on LT levels underpinning items. Teachers with weak tool use but strong teacher knowledge offered critiques that informed modifications of tool features. Few teachers initially demonstrated both strong tool use and teacher knowledge. These teachers came from a district that had an active supervisor who encouraged teachers to trust LT levels, promote a growth mindset when reviewing data with their class, and modify the curriculum to ensure that all students had the opportunity to reach competency.
These results indicate that supporting teachers to successfully implement classroom assessments based on LTs requires a coordinated approach in which curriculum specialists (coaches and supervisors), assessment directors, and PD providers communicated a shared vision of learner-centered instruction and supported a gradual but steady use of diagnostic tools within PLCs.

Authors

• Jere Confrey, North Carolina State University

• Meetal Shah, LearnPlatform