@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} }
 @inbook{confrey_bao_watson_barbosa_linneweber-lammerskitten_2017, title={Topic Study Group No. 36: Task Design, Analysis and Learning Environments Programme Summary}, ISBN={9783319625966 9783319625973}, ISSN={2520-8322 2520-8330}, url={http://dx.doi.org/10.1007/978-3-319-62597-3_63}, DOI={10.1007/978-3-319-62597-3_63}, booktitle={Proceedings of the 13th International Congress on Mathematical Education}, publisher={Springer International Publishing}, author={Confrey, Jere and Bao, Jiansheng and Watson, Anne and Barbosa, Jonei and Linneweber-Lammerskitten, Helmut}, year={2017}, pages={549–553} }
 @article{confrey_maloney_gianopulos_2017, title={Untangling the "Messy Middle" in Learning Trajectories}, volume={15}, ISSN={["1536-6359"]}, DOI={10.1080/15366367.2017.1404370}, abstractNote={In “Tracing the Assessment TriangleWith Learning Progression-Aligned Assessments in Mathematics,” Lai, Kobrin, and DiCerbo present a learning trajectory on the measurement of area, a topic typically introduced in third and fourth grades. Proposing a five-level progression, they investigated student behavior and thinking in two studies: (1) cognitive think-aloud interviews using paper and pencil tasks and response-pattern coding and (2) computer-based tasks, digital data collection, and latent class analysis. Overall, the researchers find a reasonable degree of confirmation for the first and fifth levels of their LP, and support for the relevance, but nonrigid sequencing, of the middle levels. We commend the authors on the clear conceptualization of their ambitious scope of work. The well-organized and systematic report balances confirmatory and contrary evidence. Based on their conceptualization of the LP, they cleverly used digital-environment affordances to design data gathering on the underlying processes. We comment on two fundamental themes from LP research: (1) the structure of an LP relative to the “messy middle” and (2) the interaction of grain size and cognitive goals.}, number={3-4}, journal={MEASUREMENT-INTERDISCIPLINARY RESEARCH AND PERSPECTIVES}, author={Confrey, Jere and Maloney, Alan and Gianopulos, Garron}, year={2017}, pages={168–171} }
 @article{confrey_maloney_2015, title={A design research study of a curriculum and diagnostic assessment system for a learning trajectory on equipartitioning}, volume={47}, ISSN={1863-9690 1863-9704}, url={http://dx.doi.org/10.1007/S11858-015-0699-Y}, DOI={10.1007/S11858-015-0699-Y}, number={6}, journal={ZDM}, publisher={Springer Science and Business Media LLC}, author={Confrey, Jere and Maloney, Alan}, year={2015}, month={Sep}, pages={919–932} }
 @article{confrey_jones_gianopulos_2015, title={Challenges in Modeling and Measuring Learning Trajectories}, volume={13}, ISSN={1536-6367 1536-6359}, url={http://dx.doi.org/10.1080/15366367.2015.1055131}, DOI={10.1080/15366367.2015.1055131}, abstractNote={Briggs and Peck make a compelling case for creating new, more intuitive measures of learning, based on creating vertical scales using learning trajectories (LT) in place of “domain sampling.” We believe that the importance of creating measurement scales that coordinate recognizable landmarks in learning trajectories with interval scales cannot be understated. As we have learned from the previous decades of high-stakes assessment, when tests are required to serve multiple purposes, such as improving systemic accountability and providing instructional guidance, one purpose often suffers. These high-stakes tests have provided weak instructional guidance, producing unintentional outcomes such as excessive focus on “bubble kids” without sufficient information on how to promote deep learning (e.g., Horn, Kane, & Wilson, 2015). And in spite of the field’s best efforts, we are still without a set of measurement scales that communicate how different areas of the scales are related to qualitatively different states of children’s coming to know big ideas. Our own current research program is devoted to a similar goal. Instead of end-of-year, large-scale testing, however, we target periodic intrayear diagnostic uses of such scales without high-stakes consequences for teachers or students. We are designing our measures to inform teachers and students about student thinking and learning. In this response to the Briggs and Peck paper, we wish to comment on 2 broad issues related to the paper: (1) the modeling theories that underlie the relationships between measures and the phenomena they are designed to index and (2) the details and challenges we have experienced in building such vertical scales and their implications for developing high-stakes assessments based on learning trajectories.}, number={2}, journal={Measurement: Interdisciplinary Research and Perspectives}, publisher={Informa UK Limited}, author={Confrey, Jere and Jones, R. Seth and Gianopulos, Garron}, year={2015}, month={Apr}, pages={100–105} }
 @article{prediger_gravemeijer_confrey_2015, title={Design research with a focus on learning processes: an overview on achievements and challenges}, volume={47}, ISSN={1863-9690 1863-9704}, url={http://dx.doi.org/10.1007/S11858-015-0722-3}, DOI={10.1007/S11858-015-0722-3}, abstractNote={Design research continues to gain prominence as a significant methodology in the mathematics education research community. This overview summarizes the origins and the current state of design research practices focusing on methodological requirements and processes of theorizing. While recognizing the rich variations in the foci and scale of design research, it also emphasizes the fundamental core of understanding and investigating learning processes. That is why the article distinguishes two archetypes of design research, one being focused on curriculum innovations, one being focused on developing theories on the learning processes, which is the main focus of the thematic issue. For deepening the methodological discussion on design research, it is worth to distinguish aims and quality criteria along the archetypes and elaborate achievement and challenges for the future.}, number={6}, journal={ZDM}, publisher={Springer Science and Business Media LLC}, author={Prediger, Susanne and Gravemeijer, Koeno and Confrey, Jere}, year={2015}, month={Sep}, pages={877–891} }
 @article{krupa_confrey_2015, title={Effects of a reform high school mathematics curriculum on student achievement: whom does it benefit?}, volume={49}, ISSN={0022-0272 1366-5839}, url={http://dx.doi.org/10.1080/00220272.2015.1065911}, DOI={10.1080/00220272.2015.1065911}, abstractNote={This study compared the effects of an integrated reform-based curriculum to a subject-specific curriculum on student learning of 19,526 high school algebra students. Using hierarchical linear modelling to account for variation in student achievement, the impact of the reform-based Core-Plus Mathematics curricular materials on student test scores is compared to the subject-specific curriculum. Findings from this study indicate that students enrolled in integrated mathematics outperformed subject-specific students on an Algebra I exam (highly aligned with content), and performed equally on an Algebra II exam (poorly aligned). High minority students in high-need schools demonstrated higher performance when they were enrolled in integrated mathematics.}, number={2}, journal={Journal of Curriculum Studies}, publisher={Informa UK Limited}, author={Krupa, Erin E. and Confrey, Jere}, year={2015}, month={Aug}, pages={191–215} }
 @article{confrey_maloney_2015, title={Engineering [for] Effectiveness in Mathematics Education: Intervention at the Instructional Core in an Era of Common Core Standards}, ISBN={["978-3-319-07715-4"]}, DOI={10.1007/978-3-319-07716-1_17}, journal={LARGE-SCALE STUDIES IN MATHEMATICS EDUCATION}, author={Confrey, Jere and Maloney, Alan}, year={2015}, pages={373–403} }
 @article{penuel_confrey_maloney_rupp_2014, title={Design Decisions in Developing Learning Trajectories-Based Assessments in Mathematics: A Case Study}, volume={23}, ISSN={["1532-7809"]}, DOI={10.1080/10508406.2013.866118}, abstractNote={This article analyzes the design decisions of a team developing diagnostic assessments for a learning trajectory focused on rational number reasoning. The analysis focuses on the design rationale for key decisions about how to develop the cognitive assessments and related validity arguments within a fluid state and national policy context. The study draws on ethnographic methods adapted from science, technology, and society studies to document key rationales for decisions. For this team, concerns about the validity of both the assessments and the hypothetical trajectory, anticipated uses of the assessments, and the available distribution of resources and expertise to different project activities were all considerations for significant design decisions throughout the project. The study findings suggest that success in the design of trajectories-based assessments depends on teams’ attention to balancing core design activities with engagement in the external policy environment, balancing precision with utility for diagnosis in defining the levels of a trajectory, and balancing the goals of supporting and assessing student learning.}, number={1}, journal={JOURNAL OF THE LEARNING SCIENCES}, author={Penuel, William R. and Confrey, Jere and Maloney, Alan and Rupp, Andre A.}, year={2014}, month={Jan}, pages={47–95} }
 @article{confrey_maloney_nguyen_rupp_2014, title={Equipartitioning, a foundation for rational number reasoning elucidation of a learning trajectory}, journal={Learning Over Time: Learning Trajectories in Marhematics Education}, author={Confrey, J. and Maloney, A. P. and Nguyen, K. H. and Rupp, A. A.}, year={2014}, pages={61–96} }
 @article{nguyen_confrey_2014, title={Exploring the relationship between learning trajectories and curriculum a content analysis of rational number reasoning in connected mathematics and UCSMP transition mathematics}, journal={Learning Over Time: Learning Trajectories in Marhematics Education}, author={Nguyen, K. H. and Confrey, J.}, year={2014}, pages={161–185} }
 @book{maloney_confrey_nguyen_school_2014, title={Learning over time: Learning trajectories in mathematics education}, publisher={Charlotte, NC: Information Age Publishing, Inc.}, year={2014} }
 @book{alan p. maloney_nguyen_2014, title={Learning over time: learning trajectories in mathematics education}, ISBN={9781623965693}, publisher={Charlotte, NC:Information Age Publishing, Inc.}, year={2014} }
 @article{confrey_maloney_nguyen_2014, title={Learning trajectories going forward a foundation for coherence in the instructional core conclusion}, journal={Learning Over Time: Learning Trajectories in Marhematics Education}, author={Confrey, J. and Maloney, A. P. and Nguyen, K. H.}, year={2014}, pages={243–255} }
 @article{confrey_maloney_nguyen_2014, title={Learning trajectories in mathematics introduction}, journal={Learning Over Time: Learning Trajectories in Marhematics Education}, author={Confrey, J. and Maloney, A. P. and Nguyen, K. H.}, year={2014}, pages={XI-} }
 @article{confrey_maloney_corley_2014, title={Learning trajectories: a framework for connecting standards with curriculum}, volume={46}, ISSN={1863-9690 1863-9704}, url={http://dx.doi.org/10.1007/S11858-014-0598-7}, DOI={10.1007/S11858-014-0598-7}, number={5}, journal={ZDM}, publisher={Springer Science and Business Media LLC}, author={Confrey, Jere and Maloney, Alan P. and Corley, Andrew K.}, year={2014}, month={Jun}, pages={719–733} }
 @article{confrey_maloney_2014, title={Linking standards and learning trajectories boundary objects and representations}, journal={Learning Over Time: Learning Trajectories in Marhematics Education}, author={Confrey, J. and Maloney, A.}, year={2014}, pages={125–160} }
 @article{wilson_sztajn_edgington_confrey_2014, title={Teachers’ use of their mathematical knowledge for teaching in learning a mathematics learning trajectory}, volume={17}, ISSN={1386-4416 1573-1820}, url={http://dx.doi.org/10.1007/S10857-013-9256-1}, DOI={10.1007/S10857-013-9256-1}, number={2}, journal={Journal of Mathematics Teacher Education}, publisher={Springer Science and Business Media LLC}, author={Wilson, P. Holt and Sztajn, Paola and Edgington, Cyndi and Confrey, Jere}, year={2014}, month={Apr}, pages={149–175} }
 @article{wilson_mojica_confrey_2013, title={Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking}, volume={32}, ISSN={0732-3123}, url={http://dx.doi.org/10.1016/j.jmathb.2012.12.003}, DOI={10.1016/j.jmathb.2012.12.003}, abstractNote={Recent work by researchers has focused on synthesizing and elaborating knowledge of students’ thinking on particular concepts as core progressions called learning trajectories. Although useful at the level of curriculum development, assessment design, and the articulation of standards, evidence is only beginning to emerge to suggest how learning trajectories can be utilized in teacher education. Our paper reports on two studies investigating practicing and prospective elementary teachers’ uses of a learning trajectory to make sense of students’ thinking about a foundational idea of rational number reasoning. Findings suggest that a mathematics learning trajectory supports teachers in creating models of students’ thinking and in restructuring teachers’ own understandings of mathematics and students’ reasoning.}, number={2}, journal={The Journal of Mathematical Behavior}, publisher={Elsevier BV}, author={Wilson, P. Holt and Mojica, Gemma F. and Confrey, Jere}, year={2013}, month={Jun}, pages={103–121} }
 @article{sztajn_confrey_wilson_edgington_2012, title={Learning Trajectory Based Instruction: Toward a Theory of Teaching}, volume={41}, ISSN={["1935-102X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84862614483&partnerID=MN8TOARS}, DOI={10.3102/0013189x12442801}, abstractNote={ In this article, we propose a theoretical connection between research on learning and research on teaching through recent research on students’ learning trajectories (LTs). We define learning trajectory based instruction (LTBI) as teaching that uses students’ LTs as the basis for instructional decisions. We use mathematics as the context for our argument, first examining current research on LTs and then examining emerging research on how mathematics teachers use LTs to support their teaching. We consider how LTs provide specificity to four highly used frameworks for examining mathematics teaching, namely mathematical knowledge for teaching, task analysis, discourse facilitation practices, and formative assessment. We contend that by unifying various teaching frameworks around the science of LTs, LTBI begins to define a theory of teaching organized around and grounded in research on student learning. Thus, moving from the accumulation of various frameworks into a reorganization of the frameworks, LTBI provides an integrated explanatory framework for teaching. }, number={5}, journal={EDUCATIONAL RESEARCHER}, author={Sztajn, Paola and Confrey, Jere and Wilson, P. Holt and Edgington, Cynthia}, year={2012}, pages={147–156} }
 @article{shen_confrey_2010, title={Justifying Alternative Models in Learning Astronomy: A study of K–8 science teachers’ understanding of frames of reference}, volume={32}, ISSN={0950-0693 1464-5289}, url={http://dx.doi.org/10.1080/09500690802412449}, DOI={10.1080/09500690802412449}, abstractNote={Understanding frames of reference is critical in describing planetary motion and learning astronomy. Historically, the geocentric and heliocentric models were defended and advocated against each other. Today, there are still many people who do not understand the relationship between the two models. This topic is not adequately treated in astronomy instruction and is unstudied in science education research. The present small‐scale study suggests that many science teachers of K–8 hold alternative conceptions about the models of the solar system. Most of the 14 teachers in the study believed that the geocentric model should not be used in classroom instruction because they thought that it was wrong. It was found that they justified their knowledge claims by following common sense, authority, pragmatism, or relativism. Their long‐held beliefs, lack of observational experience, and resistance in switching between two models made it difficult for them to have a deep understanding of the relationship of the two models. Specific teaching strategies addressing these learning difficulties on this topic are proposed.}, number={1}, journal={International Journal of Science Education}, publisher={Informa UK Limited}, author={Shen, Ji and Confrey, Jere}, year={2010}, pages={1–29} }
 @article{boerst_lambdin_confrey_white_heck_baltzley_knuth_quander_2010, title={Strengthening research by designing for coherence and connections to practice}, volume={41}, number={3}, journal={Journal for Research in Mathematics Education}, author={Boerst, T. and Lambdin, D. V. and Confrey, J. and White, D. and Heck, D. and Baltzley, P. C. and Knuth, E. and Quander, J. R.}, year={2010}, pages={216–235} }
 @inproceedings{confrey_maloney_nguyen_mojica_myers_2009, title={Equipartitioning/splitting as a foundation of rational number reasoning using learning trajectories}, volume={2}, booktitle={Pme 33: proceedings of the 33rd conference of the international group for the psychology of mathematics education, vol 2}, author={Confrey, J. and Maloney, A. and Nguyen, K. and Mojica, G. and Myers, M.}, year={2009}, pages={345–352} }
 @inproceedings{mojica_confrey_2009, title={Pre-service elementary teachers' utilization of an equipartitioning learning trajectory to build models of student thinking}, volume={4}, booktitle={Pme 33: proceedings of the 33rd conference of the international group for the psychology of mathematics education, vol 4}, author={Mojica, G. and Confrey, J.}, year={2009}, pages={129–136} }
 @article{battista_smith_boerst_sutton_confrey_white_knuth_quander_2009, title={Research in mathematics education: Multiple methods for multiple uses}, volume={40}, number={3}, journal={Journal for Research in Mathematics Education}, author={Battista, M. and Smith, M. S. and Boerst, T. and Sutton, J. and Confrey, J. and White, D. and Knuth, E. and Quander, J.}, year={2009}, pages={216–240} }
 @article{confrey_strutchens_battista_smith_king_sutton_boerst_reed_2008, title={Situating research on curricular change}, volume={39}, ISSN={["1945-2306"]}, DOI={10.2307/30034893}, number={2}, journal={JOURNAL FOR RESEARCH IN MATHEMATICS EDUCATION}, author={Confrey, Jere and Strutchens, Marilyn E. and Battista, Michael T. and Smith, Margaret Schwan and King, Karen D. and Sutton, John T. and Boerst, Timothy A. and Reed, Judith}, year={2008}, month={Mar}, pages={102–112} }
 @article{shen_confrey_2007, title={From conceptual change to transformative modeling: A case study of an elementary teacher in learning astronomy}, volume={91}, ISSN={0036-8326 1098-237X}, url={http://dx.doi.org/10.1002/sce.20224}, DOI={10.1002/sce.20224}, abstractNote={This case study describes a teacher's development of and creativity in ma- nipulating physical models in an astronomy course for in-service science teachers of K-8. Specifically, she organized a data table from several charts of numbers, constructed a moon-ball model in addition to a 2-D model, and created a hula hoop model as a con- crete realization of her mental model. Examination of the transformation and construction processes revealed how she revised existing models and added new elements. These recon- struction experiences afforded her with a higher level of comprehension and self-awareness of her mental models. Three of the teacher's actions contributed to her increased under- standing and deployment of the models: she enhanced her autonomy by changing the given models and solving problems she was interested in; she communicated with her partners and shared her knowledge by materializing her models; and she constructed new models}, number={6}, journal={Science Education}, publisher={Wiley}, author={Shen, Ji and Confrey, Jere}, year={2007}, pages={948–966} }
 @article{confrey_makar_kazak_2004, title={Undertaking data analysis of student outcomes as professional development for teachers}, volume={36}, ISSN={1615-679X}, url={http://dx.doi.org/10.1007/BF02655755}, DOI={10.1007/BF02655755}, abstractNote={The study reports on collaborations with practitioners to examine the results of students’ performances on high stakes tests as a means to strengthen practitioners’ knowledge of probability and statistics and to empower their conduct of investigations on student performance. Four issues are summarized: the development of their statistical reasoning, their understanding of the meaning of and relationships among the concepts of validity, reliability and fairness as applied to testing, their introduction to the history of testing and its relationship to science, society and cultural inequality, and their reports of independent inquiries. Data on performance on pre- and post-tests demonstrate growth in teacher reasoning and in their professionalism in raising important issues about testing}, number={1}, journal={Zentralblatt für Didaktik der Mathematik}, publisher={Springer Science and Business Media LLC}, author={Confrey, Jere and Makar, Katie and Kazak, Sibel}, year={2004}, month={Feb}, pages={32–40} }