Learning Progression

CAREER: Black Youth Development and Curricular Supports for Robust Identities in Mathematics

This study seeks to describe trajectories that describe the ways in which Black learners develop as particular kinds of mathematical learners. The study takes place in the context of an established, multi-year college bridge program that has as its goals to increase the representation of historically marginalized groups in the university community.

Lead Organization(s): 
Award Number: 
1845841
Funding Period: 
Wed, 05/01/2019 to Tue, 04/30/2024
Full Description: 

Student success in mathematics correlates with positive identities, dispositions, and relationships towards the subject. As mathematics education research strives to understand historic inequities in mathematics for Black learners, small-scale research has described the relationships between identity, subjectivity, and positionality in Black learners as it relates to their achievement and interest in mathematics. This study builds on that descriptive work by seeking to describe trajectories that describe the ways in which Black learners develop as particular kinds of mathematical learners. The study takes place in the context of an established, multi-year college bridge program that has as its goals to increase the representation of historically marginalized groups in the university community. Students in the bridge program from three communities in the greater Detroit area with strong academic achievement in mathematics will be recruited. Their experiences in the bridge program will be traced to identify trajectories that describe the development of Black learners relative to mathematics, and document the design features of classroom activities that support learners in moving through those trajectories.

At the center of the project is the study of cohorts of students in grades 8-11 as they move through the summer bridge program. The bridge project's current curriculum features a series of lessons focused on identity development related to mathematics. These lessons will be implemented, studied, revised, and redeployed across the duration of the project across the summer sessions. Teacher focus groups and surveys will assess the implementation of the activities and aggregate feedback on the design. Three cohorts of students will be recruited to participate in the broader project activities from three metro areas with distinctly different demographic profiles. Student mathematical efficacy will be assessed for all participating students. Within each of the three metro areas, students will be recruited that represent differing levels of mathematics efficacy to ensure that focus students are likely to experience different trajectories through their engagement with the study. The students will be interviewed three times in each academic year to describe their trajectories. Student achievement data will also be collected for all participating students along with narrative descriptions and autobiographies about the messages students receive about mathematics. These messages include their own internal thinking about how they see themselves as mathematics learners, and messages that are sent to them by other students, teachers, and the community. Products of the study will be case studies that describe trajectories of identity development in Black mathematics learners, and a disseminated curriculum for a mathematics identity-focused bridge program supporting Black learners.

Engaging High School Students in Computer Science with Co-Creative Learning Companions (Collaborative Research: Magerko)

This research investigates how state-of-the-art creative and pedagogical agents can improve students' learning, attitudes, and engagement with computer science. The project will be conducted in high school classrooms using EarSketch, an online computer science learning environments that engages learners in making music with JavaScript or Python code.

Award Number: 
1814083
Funding Period: 
Sat, 09/15/2018 to Wed, 08/31/2022
Full Description: 
This research investigates how state-of-the-art creative and pedagogical agents can improve students' learning, attitudes, and engagement with computer science. The project will be conducted in high school classrooms using EarSketch, an online computer science learning environments that engages over 160,000 learners worldwide in making music with JavaScript or Python code. The researchers will build the first co-creative learning companion, Cai, that will scaffold students with pedagogical strategies that include making use of learner code to illustrate abstraction and modularity, suggesting new code to scaffold new concepts, providing help and hints, and explaining its decisions. This work will directly address the national need to develop computing literacy as a core STEM skill.
 
The proposed work brings together an experienced interdisciplinary team to investigate the hypothesis that adding a co-creative learning companion to an expressive computer science learning environment will improve students' computer science learning (as measured by code sophistication and concept knowledge), positive attitudes towards computing (self-efficacy and motivation), and engagement (focused attention and involvement during learning). The iterative design and development of the co-creative learning companion will be based on studies of human collaboration in EarSketch classrooms, the findings in the co-creative literature and virtual agents research, and the researchers' observations of EarSketch use in classrooms. This work will address the following research questions: 1) What are the foundational pedagogical moves that a co-creative learning companion for expressive programming should perform?; 2) What educational strategies for a co-creative learning companion most effectively scaffold learning, favorable attitudes toward computing, and engagement?; and 3) In what ways does a co-creative learning companion in EarSketch increase computer science learning, engagement, and positive attitudes toward computer science when deployed within the sociocultural context of a high school classroom? The proposed research has the potential to transform our understanding of how to support student learning in and broaden participation through expressive computing environments.

Promoting Engineering Problem Framing Skill-Development in High School Science and Engineering Courses

This project will develop curricular activities and assessment guidance for K-12 science and engineering educators who seek to incorporate engineering design content into their biology, chemistry, and physics classes.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1812823
Funding Period: 
Wed, 08/01/2018 to Sat, 07/31/2021
Full Description: 

This collaborative project involving Ohio Northern University, Ohio State University, and Olathe Northwest High School will develop curricular activities and assessment guidance for K-12 science and engineering educators who seek to incorporate engineering design content into their biology, chemistry, and physics classes. This work is important because students' limited exposure to engineering activities can negatively impact their decisions to enroll in STEM courses and to pursue engineering careers. Further, many states are adopting or considering adopting the Next Generation Science Standards (NGSS), a set of classroom standards which integrate engineering content into traditional science disciplines. While high school teachers under these standards are expected to incorporate the cross-cutting engineering content into their courses, they generally receive little high-quality support for doing so. If successful, the project could provide a powerful model of how to support busy and resource-constrained STEM teachers, and create broader student interest in STEM careers.

Drawing from best practices on instructional design, the project's main objectives are to: (1) design, field-test, and evaluate the impact of 12 NGSS-aligned, engineering problem-framing design activities on students enrolled in grades 9-12 science courses and (2) design and conduct high-quality, sustained professional development that fosters participating high school science teachers' ability to deploy the NGSS concepts-linked activities. Data sources include student design artifacts, video of classroom instruction, and surveys assessing student and teacher attitudes toward engineering, student design self-efficacy and teacher self-efficacy for teaching engineering content. These data will be analyzed to determine what teachers learned from the professional development activities, how those activities informed their teaching and in turn, how students' engagement with the engineering activities relates to their engineering design skills and attitudes. In terms of intellectual merit, the project aims to develop a learning progression of students' engineering design problem-framing skills by characterizing any observed change in students' design work and attitudes over time.

CAREER: Mechanisms Underlying the Relation Between Mathematical Language and Mathematical Knowledge

The purpose of this project is to examine the process by which math language instruction improves learning of mathematics skills in order to design and translate the most effective interventions into practical classroom instruction.

Lead Organization(s): 
Award Number: 
1749294
Funding Period: 
Wed, 08/01/2018 to Mon, 07/31/2023
Full Description: 

Successful development of numeracy and geometry skills during preschool provides a strong foundation for later academic and career success. Recent evidence shows that learning math language (e.g., concepts such as more, few, less, near, before) during preschool supports this development. The purpose of this Faculty Early Career Development (CAREER) project is to examine the process by which math language instruction improves learning of mathematics skills in order to design and translate the most effective interventions into practical classroom instruction. The first objective of this project is to examine if quantitative and spatial math language effect the development of different aspects of mathematics performance (e.g., numeracy, geometry). The second objective is to examine how quantitative math language versus numeracy instruction, either alone or in combination, effect numeracy development. The findings from this study will not only be used to improve theoretical understanding of how math language and mathematics skills develop, but the instructional materials developed for this study will also result in practical tools for enhancing young children's math language and mathematics skills.

This project is focused on evaluating the role of early math language skills in the acquisition of early mathematics skills. Two randomized control trials (RCTs) will be conducted. The first RCT will be used to evaluate the effects of different types of math language instruction (quantitative, spatial) on distinct aspects of mathematics (numeracy, geometry). It is expected that quantitative language instruction will improve numeracy skills and spatial language instruction will improve geometry skills. The second RCT will be used to examine the unique and joint effects of quantitative language instruction and numeracy instruction on children's numeracy skills. It is expected that both types of instruction alone will be sufficient to generate improvement on numeracy outcomes compared to an active control group, but that the combination of the two will result in enhanced numeracy performance compared to either alone. Educational goals will be integrated with and supported through engaging diverse groups of undergraduate and graduate students in hands-on research experiences, training pre- and in-service teachers on mathematical language instruction, and building collaborative relationships with early career researchers. Intervention materials including storybooks developed for the project and pre- and in-service teacher training/lesson plan materials will be made available at the completion of the project.

Measuring Early Mathematical Reasoning Skills: Developing Tests of Numeric Relational Reasoning and Spatial Reasoning

The primary aim of this study is to develop mathematics screening assessment tools for Grades K-2 over the course of four years that measure students' abilities in numeric relational reasoning and spatial reasoning. The team of researchers will develop Measures of Mathematical Reasoning Skills system, which will contain Tests of Numeric Relational Reasoning (T-NRR) and Tests of Spatial Reasoning (T-SR).

Award Number: 
1721100
Funding Period: 
Fri, 09/15/2017 to Tue, 08/31/2021
Full Description: 

Numeric relational reasoning and spatial reasoning are critical to success in later mathematics coursework, including Algebra 1, a gatekeeper to success at the post-secondary level, and success in additional STEM domains, such as chemistry, geology, biology, and engineering. Given the importance of these skills for later success, it is imperative that there are high-quality screening tools available to identify students at-risk for difficulty in these areas. The primary aim of this study is to develop mathematics screening assessment tools for Grades K-2 over the course of four years that measure students' abilities in numeric relational reasoning and spatial reasoning. The team of researchers will develop Measures of Mathematical Reasoning Skills system, which will contain Tests of Numeric Relational Reasoning (T-NRR) and Tests of Spatial Reasoning (T-SR). The measures will be intended for use by teachers and school systems to screen students to determine who is at-risk for difficulty in early mathematics, including students with disabilities. The measures will help provide important information about the intensity of support that may be needed for a given student. Three forms per grade level will be developed for both the T-NRR and T-SR with accompanying validity and reliability evidence collected. The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.

The development of the T-NRR and T-SR measures will follow an iterative process across five phases. The phases include (1) refining the construct; (2) developing test specifications and item models; (3) developing items; (4) field testing the items; and (5) conducting validity studies. The evidence collected and evaluated during each phase will contribute to the overall evaluation of the reliability of the measures and the validity of the interpretations made using the measures. Item models, test specifications, and item development will be continuously evaluated and refined based on data from cognitive interviews, field tests, and reviews by mathematics educators, teachers of struggling students, teachers of culturally and linguistically diverse populations, and a Technical Advisory Board. In the final phase of development of the T-NRR and T-SR, reliability of the results will be estimated and multiple sources of validity evidence will be collected to examine the concurrent and predictive relation with other criterion measures, classification accuracy, and sensitivity to growth. Approximately 4,500 students in Grades K-2 will be involved in all phases of the research including field tests and cognitive interviews. Data will be analyzed using a two-parameter IRT model to ensure item and test form comparability.

Identifying Effective Instructional Practices that Foster the Development of Algebraic Thinking in Elementary School

This project seeks to identify teaching practices that can be linked to students' early algebra learning in grades three, four and five. The goal of the project is to use assessment data and videos of classroom teaching in order to create a tool that can be used to document effective instructional practices. This observation tool can then be used to support teacher professional development in early algebra and research about how teachers' actions can be linked to students' learning.

Lead Organization(s): 
Award Number: 
1721192
Funding Period: 
Thu, 06/01/2017 to Mon, 05/31/2021
Full Description: 

There is a critical need to better prepare all students for learning algebra. Part of this preparation involves developing a strong foundation for algebra in the elementary grades by building on students' informal intuitions about patterns, relationships and structure into more formalized ways of mathematical thinking. This project seeks to identify teaching practices that can be linked to students' early algebra learning in grades three, four and five. The goal of the project is to use assessment data and videos of classroom teaching in order to create a tool that can be used to document effective instructional practices. This observation tool can then be used to support teacher professional development in early algebra and research about how teachers' actions can be linked to students' learning. The project is unique in its work to link an early algebra curriculum with understanding of teachers' practices in implementing that curriculum and students' learning of mathematics.

The project aims to address two research questions. First, what profiles of instructional practice are associated with greater student performance in early algebra? Second, to what extent do these profiles of effective instructional practices vary by grade level? The primary product of the work is an early algebra observation protocol that will capture non-domain and non-grade level specific practices of effective teaching in combination with practices specific to early algebra. Videos of early algebra classrooms will be used to design the observation protocol, which in turn, will then be used along with student assessment data to identify profiles of instructional practices associated with students' learning. Multiple phases of testing and revision will be used to create the observation protocol. The observation protocol will also generate profiles of teacher practices that can be used to describe different models for effectively teaching early algebra. The project will also examine implications of their work for teacher preparation and professional development.

Longitudinal Learning of Viable Argument in Mathematics for Adolescents

This project builds on a prior study that demonstrated increases in students' knowledge of argumentation and their performance on mathematics assessments. The project will extend the use of the argumentation intervention into all eighth grade content areas, with a specific focus on students' learning of reasoning and proof, and contribute to understanding how students' learning about mathematical practices that can help them learn mathematics better.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1621438
Funding Period: 
Thu, 09/01/2016 to Mon, 08/31/2020
Full Description: 

The project will examine learning in eighth grade mathematics with a specific focus on students' learning of reasoning and proof. The intervention builds on a prior study in algebra that demonstrated increases in students' knowledge of argumentation and their performance on mathematics assessments. This project will extend the use of the argumentation intervention into all eighth grade content areas. The investigators will also address support for teachers in the form of teacher materials that link the argumentation content with mathematics standards and state-wide assessments, and a learning progression to engage students in proving tasks. The project will use assessments of mathematics learning and additional data from teachers and students to understand the impact of the argumentation intervention on teachers and students. The project contributes to understanding how students can learn about mathematical practices, such as proving, that can help them learn mathematics better. A significant contribution will be the definition of aspects of proving and descriptions of student outcomes that can be used to measure how well students have achieved these components of proving. The Discovery Research PreK-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. This project is also supported by NSF's EHR Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field.

The project suggests twelve conceptual pillars that are combined with classroom processes and assessable outcomes to examine the use of argumentation practices in the teaching of eighth grade mathematics content. The investigation of classroom support for argumentation includes research questions that focus on improvement on state-level assessments, students' ability to construct mathematical arguments, and the conceptual progression that supports students' understanding of argumentation and proof. In addition, the study will examine teachers' role in argumentation in the classroom and their perception of potential challenges for classroom implementation. The study will use an experimental design to examine an intervention for mathematical reasoning and proof in eighth grade. The project includes a treatment group of teachers that will participate in professional development including a summer institute followed by instructional coaching over a two year period.

Systemic Formative Assessment to Promote Mathematics Learning in Urban Elementary Schools

This project builds on the study of the Ongoing Assessment Project's (OGAP) math assessment intervention on elementary teachers and students and combines the intervention with research-based understandings of systemic reform. This project will produce concrete tools, routines, and practices that can be applied to strengthen programs' implementation by ensuring the strategic support of school and district leaders.

Lead Organization(s): 
Award Number: 
1621333
Funding Period: 
Thu, 09/15/2016 to Sat, 02/29/2020
Full Description: 

Districts have long struggled to implement instructional programming in ways that meaningfully and sustainably impact teaching and learning. Systemic education reform is based on the hypothesis that prevailing patterns of incoherence and misalignment in an educational system can send mixed messages to local implementers as they try to respond to various cues and incentives in the environment. Systemic reform seeks to bring alignment to education systems in multiple ways, including consistency across instructional philosophies, alignment across grade levels, and vertical coherence from district to schools to classrooms. This project builds on the Consortium for Policy Research in Education's (CPRE) ongoing, NSF-funded experimental study of the impacts of the Ongoing Assessment Project's (OGAP) math assessment intervention on elementary teachers and students in Philadelphia-area schools. The project will combine the OGAP math intervention with research-based understandings of systemic reform. OGAP is based upon established theory and research demonstrating the impact of teachers' use of ongoing short- and medium-cycle formative assessment on student learning. It combines these understandings with recent research on learning trajectories within mathematics content domains. By bringing to bear the strengths of all three of these areas of research - formative assessment, learning trajectories, and systemic reform - the project promises a significant contribution to the knowledge base about the application of math learning research to classroom instruction on a large scale. This project will produce concrete tools, routines, and practices that can be applied to strengthen programs' implementation by ensuring the strategic support of school and district leaders. This project is funded by the Discovery Research PreK-12 (DRK-12) and EHR Core Research (ECR) Programs. The DRK-12 program supports research and development on STEM education innovations and approaches to teaching, learning, and assessment. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field.

CPRE and the School District of Philadelphia (SDP) will establish a research-practice partnership focused on developing, implementing, refining, and testing a systemic support model to strengthen implementation of the OGAP math intervention in elementary schools. CPRE's current experimental study of OGAP's impacts reveals, preliminarily, statistically significant positive effects on teacher knowledge and student learning. As a result, SDP has decided to expand OGAP into an additional 60 schools in 2016-17. However, the current OGAP study has also revealed weak implementation stemming from a lack of consistent leadership support for the intervention. The project will address this implementation challenge by developing, refining, supporting, and documenting a systemic support component that will accompany OGAP's classroom-level implementation. The systemic supports will be developed by a research-practice partnership between CPRE; SDP; OGAP; the Graduate School of Education at the University of Pennsylvania (PennGSE); and the Philadelphia Education Research Consortium (PERC). The team will use principles of design-based implementation research to iteratively refine and improve the systemic support model. Along with the design and development of the systemic support model, the project will conduct a mixed-methods study of its impacts and roll-out. A three-armed quasi-experimental study will examine the differential impacts of OGAP, with and without systemic supports, and business-as-usual math programming on teacher and student outcomes. A mixed-methods study will examine teacher and administrator experiences in both treatment groups, and will provide feedback to inform the iterative development of the systemic support model.

Building a Next Generation Diagnostic Assessment and Reporting System within a Learning Trajectory-Based Mathematics Learning Map for Grades 6-8

This project will build on prior funding to design a next generation diagnostic assessment using learning progressions and other learning sciences research to support middle grades mathematics teaching and learning. The project will contribute to the nationally supported move to create, use, and apply research based open educational resources at scale.

Award Number: 
1621254
Funding Period: 
Thu, 09/15/2016 to Sat, 08/31/2019
Full Description: 

This project seeks to design a next generation diagnostic assessment using learning progressions and other research (in the learning sciences) to support middle grades mathematics teaching and learning. It will focus on nine large content ideas, and associated Common Core State Standards for Mathematics. The PIs will track students over time, and work within school districts to ensure feasibility and use of the assessment system.

The research will build on prior funding by multiple funding agencies and address four major goals. The partnership seeks to address these goals: 1) revising and strengthening the diagnostic assessments in mathematics by adding new item types and dynamic tools for data gathering 2) studying alternative ways to use measurement models to assess student mathematical progress over time using the concept of learning trajectories, 3) investigating how to assist students and teachers to effectively interpret reports on math progress, both at the individual and the class level, and 4) engineering and studying instructional strategies based on student results and interpretations, as they are implemented within competency-based and personalized learning classrooms. The learning map, assessment system, and analytics are open source and can be used by other research and implementation teams. The project will exhibit broad impact due to the number of states, school districts and varied kinds of schools seeking this kind of resource as a means to improve instruction. Finally, the research project contributes to the nationally supported move to create, use, and apply research based open educational resources at scale.

Geological Models for Explorations of Dynamic Earth (GEODE): Integrating the Power of Geodynamic Models in Middle School Earth Science Curriculum

This project will develop and research the transformational potential of geodynamic models embedded in learning progression-informed online curricula modules for middle school teaching and learning of Earth science. The primary goal of the project is to conduct design-based research to study the development of model-based curriculum modules, assessment instruments, and professional development materials for supporting student learning of (1) plate tectonics and related Earth processes, (2) modeling practices, and (3) uncertainty-infused argumentation practices.

Lead Organization(s): 
Award Number: 
1621176
Funding Period: 
Mon, 08/15/2016 to Fri, 07/31/2020
Full Description: 

This project will contribute to the Earth science education community's understanding of how engaging students with dynamic computer-based systems models supports their learning of complex Earth science concepts regarding Earth's surface phenomena and sub-surface processes. It will also extend the field's understandings of how students develop modeling practices and how models are used to support scientific endeavors. This research will shed light on the role uncertainty plays when students use models to develop scientific arguments with model-based evidence. The GEODE project will directly involve over 4,000 students and 22 teachers from diverse school systems serving students from families with a variety of socioeconomic, cultural, and racial backgrounds. These students will engage with important geoscience concepts that underlie some of the most critical socio-scientific challenges facing humanity at this time. The GEODE project research will also seek to understand how teachers' practices need to change in order to take advantage of these sophisticated geodynamic modeling tools. The materials generated through design and development will be made available for free to all future learners, teachers, and researchers beyond the participants outlined in the project.

The GEODE project will develop and research the transformational potential of geodynamic models embedded in learning progression-informed online curricula modules for middle school teaching and learning of Earth science. The primary goal of the project is to conduct design-based research to study the development of model-based curriculum modules, assessment instruments, and professional development materials for supporting student learning of (1) plate tectonics and related Earth processes, (2) modeling practices, and (3) uncertainty-infused argumentation practices. The GEODE software will permit students to "program" a series of geologic events into the model, gather evidence from the emergent phenomena that result from the model, revise the model, and use their models to explain the dynamic mechanisms related to plate motion and associated geologic phenomena such as sedimentation, volcanic eruptions, earthquakes, and deformation of strata. The project will also study the types of teacher practices necessary for supporting the use of dynamic computer models of complex phenomena and the use of curriculum that include an explicit focus on uncertainty-infused argumentation.

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