@article{confrey_shah_2021, title={Examining instructional change at scale using data from diagnostic assessments built on learning trajectories}, volume={53}, ISSN={["1863-9704"]}, DOI={10.1007/s11858-021-01259-w}, abstractNote={This study investigated the process of instructional change required to translate data on student progress along learning trajectories (LTs) into relevant instructional modifications. Researchers conducted a professional development session on ratio LTs, which included analyzing 3 years of district-level data from Math-Mapper 6–8, a digital LT-based diagnostic assessment application, with fifteen 6th and 7th grade teachers. Teachers subsequently conducted a lesson study to enact what they had learned, allowing researchers to study how teachers used data on student progress along ratio equivalence LTs to design, implement, and evaluate the lesson study. Researchers applied a framework for LT-based data-driven decision making to analyze video data of the lesson study activities. Teachers successfully scanned data reports to pinpoint the LT levels at which to target modified instruction. In one instance, they focused too narrowly on a single item resulting in excessive lesson time on tasks on graph literacy external to the LT. In the other, their data interpretation was overly general and resulted in the design and implementation of a sequence of tasks that reversed the order implied in the LT and relied on the use of more sophisticated strategies from subsequent LTs. Results suggest a need for more data interpretation skills, a deep understanding of the learning theory underpinning LTs, and more precision in teacher discourse around LTs.}, number={6}, journal={ZDM-MATHEMATICS EDUCATION}, author={Confrey, Jere and Shah, Meetal}, year={2021}, month={Nov}, pages={1265–1283} }
 @article{confrey_shah_toutkoushian_2021, title={Validation of a Learning Trajectory-Based Diagnostic Mathematics Assessment System as a Trading Zone}, volume={6}, ISSN={["2504-284X"]}, DOI={10.3389/feduc.2021.654353}, abstractNote={This study reports how a validation argument for a learning trajectory (LT) is constituted from test design, empirical recovery, and data use through a collaborative process, described as a “trading zone” among learning scientists, psychometricians, and practitioners. The validation argument is tied to a learning theory about learning trajectories and a framework (LT-based data-driven decision-making, or LT-DDDM) to guide instructional modifications. A validation study was conducted on a middle school LT on “Relations and Functions” using a Rasch model and stepwise regression. Of five potentially non-conforming items, three were adjusted, one retained to collect more data, and one was flagged as a discussion item. One LT level description was revised. A linear logistic test model (LLTM) revealed that LT level and item type explained substantial variance in item difficulty. Using the LT-DDDM framework, a hypothesized teacher analysis of a class report led to three conjectures for interventions, demonstrating the LT assessment’s potential to inform instructional decision-making.}, journal={FRONTIERS IN EDUCATION}, author={Confrey, Jere and Shah, Meetal and Toutkoushian, Emily}, year={2021}, month={Aug} }
 @article{confrey_toutkoushian_shah_2020, title={Working at scale to initiate ongoing validation of learning trajectory-based classroom assessments for middle grade mathematics}, volume={60}, ISSN={["1873-8028"]}, DOI={10.1016/j.jmathb.2020.100818}, abstractNote={The paper reports on the design and validation argument for classroom assessments within a digital diagnostic assessment system built on learning trajectories (LTs). It consists of a learning map of nine big ideas, 25 relational learning clusters, and 62 LTs for grades 6−8 mathematics. Students take cluster assessments, and teachers use the data to adapt instruction. An ongoing validation process is presented with data for an algebra cluster. Validation among practitioners, learning scientists, and psychometricians is conceptualized as examining and adjusting inter-level, intra-level, and construct-irrelevant variation in measures of item difficulty and deploying item response theory modeling followed by sequential regressions. Using data from 37,000 assessments collected over three years at 3 middle schools, 167 potentially non-conforming items of the 676 calibrated items (24 %) were identified and revised. The paper discusses how the trajectories and map were refined through a combination of data analysis and feedback from practitioners.}, journal={JOURNAL OF MATHEMATICAL BEHAVIOR}, author={Confrey, Jere and Toutkoushian, Emily and Shah, Meetal}, year={2020}, month={Dec} }
 @article{confrey_toutkoushian_shah_2019, title={A Validation Argument From Soup to Nuts: Assessing Progress on Learning Trajectories for Middle-School Mathematics}, volume={32}, DOI={10.1080/08957347.2018.1544135}, abstractNote={ABSTRACT Fully articulating validation arguments in the context of classroom assessment requires connecting evidence from multiple sources and addressing multiple types of validity in a coherent chain of reasoning. This type of validation argument is particularly complex for assessments that function in close proximity to instruction, address the fine granularity of learning trajectories (LTs), have multiple stakeholders, and are delivered digitally with a quick turn-around for formative assessment purposes. This article describes a validation framework for classroom assessment and uses it to illustrate a validation argument addressing one of several purposes for the assessments, the use of class-level data by individual teachers. The argument concerns the use of a middle-grades digital learning system, Math-Mapper 6–8, which contains LT-based diagnostic assessments. The argument is structured as a set of six claims that examine the assessment structure, the identification and treatment of non-conforming items, the analysis of student data, and the analysis of teachers’ interpretations of data. The article stresses the critical role of scrutiny and debate among learning scientists, psychometricians, and practitioners in the validation process.}, number={1}, journal={APPLIED MEASUREMENT IN EDUCATION}, author={Confrey, Jere and Toutkoushian, Emily and Shah, Meetal}, year={2019}, pages={23–42} }
 @article{confrey_maloney_belcher_mcgowan_hennessey_shah_2018, title={The concept of an agile curriculum as applied to a middle school mathematics digital learning system (DLS)}, volume={92}, ISSN={["0883-0355"]}, DOI={10.1016/j.ijer.2018.09.017}, abstractNote={Curricular theory must evolve to keep pace with the implications of the design, use, and effects of deploying and adapting digital curricular resources, especially when placed within digital learning systems (DLS) with rapid feedback and analytic capacity. We introduce an “agile curriculum” framework describing how to use classroom assessment data to regulate teachers’ practices of iteratively adapting curricula. Our DLS, called Math-Mapper 6–8, is introduced as an example with its diagnostic assessments of students’ progress along learning trajectories. An exploratory video study of middle school teachers reviewing, interpreting, and acting on its data, both during instruction (short cycle feedback) and within professional learning communities (long cycle feedback) illustrates how an agile curriculum framework supports data-driven adjustments based on student learning.}, journal={INTERNATIONAL JOURNAL OF EDUCATIONAL RESEARCH}, author={Confrey, Jere and Maloney, Alan P. and Belcher, Michael and McGowan, William and Hennessey, Margaret and Shah, Meetal}, year={2018}, pages={158–172} }
 @article{confrey_gianopulos_mcgowan_shah_belcher_2017, title={Scaffolding learner-centered curricular coherence using learning maps and diagnostic assessments designed around mathematics learning trajectories}, volume={49}, ISSN={["1863-9704"]}, DOI={10.1007/s11858-017-0869-1}, number={5}, journal={ZDM-MATHEMATICS EDUCATION}, author={Confrey, Jere and Gianopulos, Garron and McGowan, William and Shah, Meetal and Belcher, Michael}, year={2017}, month={Oct}, pages={717–734} }