Middle School

Building a Teacher Knowledge Base for the Implementation of High-Quality Instructional Resources through the Collaborative Investigation of Video Cases (Collaborative Research: Wilson)

This project will address the pressing national need to generate shared, practice-based knowledge about how to implement freely available, high-quality instructional resources (mathematics formative assessment lessons) that have been shown to produce significant gains in student learning outcomes. It will expand a professional development model (Analyzing Instruction in Mathematics using the Teaching for Robust Understanding Framework (AIM-TRU)) that supports teacher learning about effective lesson implementation.

Lead Organization(s): 
Award Number: 
1908185
Funding Period: 
Mon, 07/01/2019 to Fri, 06/30/2023
Full Description: 

This project will address the pressing national need to generate shared, practice-based knowledge about how to implement freely available, high-quality instructional resources (mathematics formative assessment lessons) that have been shown to produce significant gains in student learning outcomes. It will expand a professional development model (Analyzing Instruction in Mathematics using the Teaching for Robust Understanding Framework (AIM-TRU)) that supports teacher learning about effective lesson implementation. The backbone of AIM-TRU is a growing, open repository of video cases available to teachers and teacher educators across the U.S. who use or are interested in using the lessons. The repository will include tools such as a facilitator's guide to support teachers and teacher educators to engage in the model and collaboratively investigate the video cases. Consequently, the work will have the potential to engage teachers and teacher educators in improving mathematics education at scale. Because the video cases will capture implementation and ideas for improving instruction in schools serving populations who are underrepresented in mathematics, AIM-TRU will serve to improve mathematics education equitably.

Research questions focus on what teachers learn about high-quality mathematics instruction and instructional materials within a community of practice, and how that learning influences their teaching. In AIM-TRU, teachers engage in the collaborative investigation of video cases utilizing a shared repertoire that includes questioning protocols adapted from the Teaching for Robust Understanding (TRU) framework. This framework articulates five dimensions of classroom instruction that are necessary and sufficient to support students in becoming powerful mathematical thinkers. This affords teachers opportunities to use the TRU dimensions as lenses to diagnose common problems of practice that arise in implementation, and propose innovations and theories for improving instruction that can be tested in real classrooms and documented in new video cases. Analytic tools will be used from frame analysis to produce empirical evidence of what teachers are learning about instruction and instructional materials along the five dimensions of TRU. These data will be mapped to a random sample of video recordings of participating teachers' instruction, scored using the TRU Math Rubric, in order to link learning outcomes from the professional development to changes in instruction. Addressing these research questions will provide a deeper understanding and empirical evidence of learning within teacher collectives, the pressing national need to develop mechanisms to produce collective professional knowledge for teaching, and further efforts to understand the types of knowledge required for effective teaching.

Getting Unstuck: Designing and Evaluating Teacher Resources to Support Conceptual and Creative Fluency with Programming

The project will create opportunities for teachers to develop programming content knowledge and new understandings of the creative possibilities in computer science education, thereby increasing opportunities for students to develop conceptual and creative fluency with programming.

Lead Organization(s): 
Award Number: 
1908110
Funding Period: 
Mon, 07/01/2019 to Wed, 06/30/2021
Full Description: 

The project will create opportunities for teachers to develop programming content knowledge and new understandings of the creative possibilities in computer science education, thereby increasing opportunities for students to develop conceptual and creative fluency with programming. K-12 introductory programming experiences are often highly scaffolded, and it can be challenging for students to transition from constrained exercises to open-ended programming activities encountered later in-and out of-school. Teachers can provide critical support to help students solve problems and develop the cognitive, social, and emotional capacities required for conceptually and creatively complex programming challenges. Teachers - particularly elementary and middle school teachers, especially in rural and Title I schools - often lack the programming content knowledge, skills, and practices needed to support deeper and more meaningful programming experiences for students. Professional development opportunities can cultivate teacher expertise, especially when supported by curricular materials that bridge teachers' professional learning and students' classroom learning. This research responds to these needs, addressing key national priorities for increasing access to high-quality K-12 computer science education for all students through teacher professional development.

The project will involve the design and evaluation of (1) an online learning experience for teachers to develop conceptual and creative fluency through short, daily programming prompts (featuring the Scratch programming environment), and (2) educative curricular materials for the classroom (based on the online experience). The online experience and curricular materials will be developed in collaboration with three 4th through 6th-grade rural or Title I teachers. The project will evaluate teacher learning in the online experience using mixed-methods analyses of pre/post-survey data of teachers' perceived expertise and quantitative analyses of teachers' programs and evolving conceptual knowledge. Three additional 4th through 6th-grade teachers will pilot the curricular materials in their classrooms. The six pilot teachers will maintain field journals about their experiences and will participate in interviews, evaluating use of the resources in practice. An ethnography of one teacher's classroom will be developed to further contribute to understandings of the classroom-level resources in action, including students' experiences and learning. Student learning will be evaluated through student interviews and analyses of student projects. Project outcomes will inform how computer science conceptual knowledge and creative fluency can be developed both for teachers and their students' knowledge and fluency that will be critical for students' future success in work and life.

Building Students' Data Literacy through the Co-design of Curriculum by Mathematics and Art Teachers (Collaborative Research: Vacca)

The aim of this project is to enact and study a process in which middle school teachers of mathematics and visual arts co-design and teach activities that combine math and art to teach data science.

Project Email: 
Lead Organization(s): 
Award Number: 
1908142
Funding Period: 
Mon, 07/01/2019 to Wed, 06/30/2021
Project Evaluator: 
Full Description: 

The aim of this project is to enact and study a process in which middle school teachers of mathematics and visual arts co-design and teach activities that combine math and art to teach data science. Many existing efforts to promote data literacy are grounded in mathematical concepts of central tendency and variation, and typically are narrowly focused in single subject domains. Taking an art-based perspective on data science has the potential to promote student relevance, accessibility, engagement, reasoning, and meaning-making with data science. Moreover, visualization technology has advanced to a degree that the relation between the information in data and visual aesthetic can be leveraged easily. To explore the opportunity this offers, research on this project will examine how to equip teachers to develop such interdisciplinary pedagogical approaches to cultivate their students' data literacy. This exploratory project will provide support for 12 teachers during summer workshops and during the school year as these teachers implement their co-designed units in their classrooms. The work addresses the following questions: (1) How do we support effective co-design of data literacy units among art teachers, mathematics teachers, and researchers? (2) How are teachers able to use the unit materials in their classrooms to engage students in data literacy? And (3) How does an art-based approach support students' data literacy? Answers to these questions will build an understanding of how to support interdisciplinary curriculum design collaborations among researchers and teachers. They will also show how art-integrated, maker-oriented activities can support middle school learners' data literacy development; and how to design technologies that are accessible and powerful to teachers and learners in these interdisciplinary environments.

Through summer workshops and year-round design collaborations, the project will iteratively design, test and refine four units for middle school classrooms, including activities, tools, and assessments, to promote students' data literacy. Data will be collected from co-design sessions as well as classroom-enactments, and will include observations, video/audio recordings, student- and teacher-generated artifacts, and pre and post assessments of students' knowledge and self-efficacy. Mixed methods analyses of these data, and syntheses of findings across participants, classroom enactments, and project years, will explore effective ways to support co-design among art teachers, mathematics teachers, and researchers; and the impact of art-integrated activities on students' data literacy. This project will reach 12 teachers and their students across 6 New York city schools. By building capacity and knowledge about how to initiate and sustain teachers' interdisciplinary curriculum collaborations, the project will have broader impact. Refined project materials, including pedagogical approaches, toolkits and adaptable classroom activities, will be disseminated to facilitate classroom adoption by other educators who wish to undertake similar art-integrated data literacy curriculum design collaborations, and will thus ultimately broaden participation in data science among diverse youth within and beyond New York City.

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Building Students' Data Literacy through the Co-design of Curriculum by Mathematics and Art Teachers (Collaborative Research: Silander)

The aim of this project is to enact and study a process in which middle school teachers of mathematics and visual arts co-design and teach activities that combine math and art to teach data science.

Award Number: 
1908030
Funding Period: 
Mon, 07/01/2019 to Wed, 06/30/2021
Full Description: 

The aim of this project is to enact and study a process in which middle school teachers of mathematics and visual arts co-design and teach activities that combine math and art to teach data science. Many existing efforts to promote data literacy are grounded in mathematical concepts of central tendency and variation, and typically are narrowly focused in single subject domains. Taking an art-based perspective on data science has the potential to promote student relevance, accessibility, engagement, reasoning, and meaning-making with data science. Moreover, visualization technology has advanced to a degree that the relation between the information in data and visual aesthetic can be leveraged easily. To explore the opportunity this offers, research on this project will examine how to equip teachers to develop such interdisciplinary pedagogical approaches to cultivate their students' data literacy. This exploratory project will provide support for 12 teachers during summer workshops and during the school year as these teachers implement their co-designed units in their classrooms. The work addresses the following questions: (1) How do we support effective co-design of data literacy units among art teachers, mathematics teachers, and researchers? (2) How are teachers able to use the unit materials in their classrooms to engage students in data literacy? And (3) How does an art-based approach support students' data literacy? Answers to these questions will build an understanding of how to support interdisciplinary curriculum design collaborations among researchers and teachers. They will also show how art-integrated, maker-oriented activities can support middle school learners' data literacy development; and how to design technologies that are accessible and powerful to teachers and learners in these interdisciplinary environments.

Through summer workshops and year-round design collaborations, the project will iteratively design, test and refine four units for middle school classrooms, including activities, tools, and assessments, to promote students' data literacy. Data will be collected from co-design sessions as well as classroom-enactments, and will include observations, video/audio recordings, student- and teacher-generated artifacts, and pre and post assessments of students' knowledge and self-efficacy. Mixed methods analyses of these data, and syntheses of findings across participants, classroom enactments, and project years, will explore effective ways to support co-design among art teachers, mathematics teachers, and researchers; and the impact of art-integrated activities on students' data literacy. This project will reach 12 teachers and their students across 6 New York city schools. By building capacity and knowledge about how to initiate and sustain teachers' interdisciplinary curriculum collaborations, the project will have broader impact. Refined project materials, including pedagogical approaches, toolkits and adaptable classroom activities, will be disseminated to facilitate classroom adoption by other educators who wish to undertake similar art-integrated data literacy curriculum design collaborations, and will thus ultimately broaden participation in data science among diverse youth within and beyond New York City.

Improving Grades 6-8 Students' Mathematics Achievement in Modeling and Problem Solving through Effective Sequencing of Instructional Practices

This project will provide structured and meaningful scaffolds for teachers in examining two research-based teaching strategies hypothesized to positively impact mathematics achievement in the areas of mathematical modeling and problem solving. The project investigates whether the order in which teachers apply these practices within the teaching of mathematics content has an impact on student learning.

Project Email: 
Lead Organization(s): 
Award Number: 
1907840
Funding Period: 
Mon, 07/01/2019 to Fri, 06/30/2023
Full Description: 

The Researching Order of Teaching project will provide structured and meaningful scaffolds for teachers in examining two research-based teaching strategies hypothesized to positively impact mathematics achievement in the areas of mathematical modeling and problem solving. The first strategy, Explicit Attention to Concepts (EAC), is a set of practices that draw students' attention specifically to mathematical concepts in ways that extend beyond memorization, procedures, or application of skills. This strategy may include teachers asking students to connect multiple mathematical representations, compare solution strategies, discuss mathematical reasoning underlying procedures, or to identify a main mathematical idea in a lesson and how it fits into the broader mathematical landscape. The second strategy, Student Opportunities to Struggle (SOS), entails providing students with time and space to make sense of graspable content, overcoming confusion points, stimulating personal sense-making, building perseverance, and promoting openness to challenge. This strategy may include teachers assigning problems with multiple solution strategies, asking students to look for patterns and make conjectures, encouraging and promoting discourse around confusing or challenging ideas, and asking students for extended mathematical responses. This project investigates whether the order in which teachers apply these practices within the teaching of mathematics content has an impact on student learning. This study builds on previous work that had identified an interaction between the EAC and SOS instructional strategies, and associated teacher reporting of stronger use of the practices with higher student mathematics achievement.

The project will have four key design features. First, the project will adopt and extend the research-based EAC/SOS conceptual framework, and explicitly responds to the call for further research on the interactions. Second, the project will focus on the mathematical areas of modeling and problem solving, two complex and critical competencies for all students in the middle grades. Third, the project will position teachers as collaborators in the research with needed expertise. Finally, the project will make use of research methods from crossover clinical trials to implementation in classrooms. The project aims to identify the affordances and constraints of the EAC/SOS framework in the design and development of instructional practices, to identify student- and teacher-level factors associated with changes in modeling and problem solving outcomes, to analyze teachers' implementations EAC and SOS in teaching modeling and problem solving and to associate those implementation factors with student achievement changes, and to determine whether the ordering of these two strategies correlates with differences in achievement. The project will collect classroom observation data and make use of existing tools to obtain reliable and valid ratings of the EAC and SOS strategies in action.The design of the study features a randomized 2 x 2 cluster crossover trial with a sample of teachers for 80% power. The project builds on existing state infrastructure and relationships with a wide array of school districts in the context of professional development, and aims to create a formal Teacher-Researcher Alliance for Investigating Learning as a part of the project work.

Using Animated Contrasting Cases to Improve Procedural and Conceptual Knowledge in Geometry

This project aims to support stronger student outcomes in the teaching and learning of geometry in the middle grades through engaging students in animated contrasting cases of worked examples. The project will design a series of animated geometry curricular materials on a digital platform that ask students to compare different approaches to solving the same geometry problem. The study will measure changes in students' procedural and conceptual knowledge of geometry after engaging with the materials and will explore the ways in which teachers implement the materials in their classrooms.

Award Number: 
1907745
Funding Period: 
Thu, 08/01/2019 to Sun, 07/31/2022
Full Description: 

This project aims to support stronger student outcomes in the teaching and learning of geometry in the middle grades through engaging students in animated contrasting cases of worked examples. Animated contrasting cases are a set of two worked examples for the same geometry problem, approached in different ways. The animations show the visual moves and annotations students would make in solving the problems. Students are asked to compare and discuss the approaches. This theoretically-grounded approach extends the work of cognitive scientists and mathematics educators who have shown this approach supports strong student learning in algebra. The project will design a series of animated geometry curricular materials on a digital platform that ask students to compare different approaches to solving the same geometry problem. The study will measure changes in students' procedural and conceptual knowledge of geometry after engaging with the materials and will explore the ways in which teachers implement the materials in their classrooms. This work is particularly important as geometry is an understudied area in mathematics education, and national and international assessments at the middle school level consistently identify geometry as a mathematics content area in which students score the lowest.

This project draws on prior work that documents the impact of comparison on students' learning in algebra. Providing students with opportunities to compare multiple strategies is recommended by a range of mathematics policy documents, as research has shown this approach promotes flexibility and enhances conceptual knowledge and procedural fluency. More specifically, the approach allows students to compare the effectiveness and efficiency of mathematical arguments in the context of problem solving. An initial pilot study on non-animated contrasting cases in geometry shows promise for the general approach and suggests that animating the cases has the potential for stronger student learning gains. This study will examine the extent to which the animated cases improve students' conceptual and procedural knowledge of geometry and identify factors that relate to changes in knowledge. The project team will develop 24 worked example contrasting cases based on design principles from the prior work in algebra. The materials will be implemented in four treatment classrooms in the first cycle, revised, and then implemented in eight treatment classrooms. Students' written work will be collected along with data on the nature of the classroom discussions and small-group interviews with students. Teachers' perspectives on lessons will also be collected to support revision and strengthening of the materials. Assessments of students' geometry knowledge will be developed using measures with demonstrated validity and reliability to measure changes in student learning.

Developing Organizational Capacity to Improve K-8 Mathematics Teaching and Learning

This project will develop and test a leadership model to improve K-8 mathematics teaching and learning by involving stakeholders across the K-8 spectrum. The project will support teachers, teacher leaders, and administrators in collectively identifying and addressing problems of practice in the teaching and learning of mathematics, and in turn develop plans to improve school and district organizational capacities to support stronger mathematics teaching.

Award Number: 
1907681
Funding Period: 
Mon, 07/01/2019 to Sun, 06/30/2024
Full Description: 

The Developing Organizational Capacity to Improve K-8 Mathematics Teaching and Learning is a 4-year implementation and improvement project. The project will develop and test a leadership model to improve K-8 mathematics teaching and learning by involving stakeholders across the K-8 spectrum. The project will support teachers, teacher leaders, and administrators in collectively identifying and addressing problems of practice in the teaching and learning of mathematics, and in turn develop plans to improve school and district organizational capacities to support stronger mathematics teaching. At the heart of the project is the Elementary Mathematics Leadership (EML) model, which is designed to improve stakeholder understandings of effective math teaching practices. The EML model involves collaboratively identifying classroom-based problems of practice with school and district personnel, designing and implementing professional development aligned with the problems of practice, and iterating those cycles of development, implementation, and revision to assess the model's effectiveness.

The EML model operates at the teacher, school, and district level using a design-based implementation research approach. At the district level, leadership teams in conjunction with researchers will identify problems of practice for which work on those problems will lead to a more coherent mathematics instruction in the district. Following this, professional development and coaching at the teacher level will be designed and implemented to target the problem of practice, with a focus on big ideas within the Common Core State Standards for Mathematics. This phase of the model also includes professional development aimed at school leaders and district administrators to strengthen organizational capacity to support and lead change related to the problem of practice. The final phase of the model calls on researchers, district, and school personnel to engage in an annual redesign of the intervention, making use of data gathered during the school year and evidence about what is happening in classrooms. This design acknowledges the broader policy context in which schools and districts operate as they work towards instructional change. To evaluate the effectiveness of the overall EML model, the project will collect a wide variety of data, including student achievement outcomes using standardized tests; assessments of teachers' mathematical knowledge, instructional practices, and efficacy measures; and measures of leader, administrator, and organizational capacities to support high-quality mathematics instruction. Four districts will be recruited to participate, enacting the model in pairs with a staggered start for one pair of districts to be able to measure treatment effects, using a variation of a switching replications design. Classroom practice and teacher outcomes will be assessed using a variety of MKT assessments, the Mathematical Quality of Instruction (MQI), and the Instructional Quality Assessment (IQA). School level outcomes will be collected via a leadership assessment and interview data, and district level outcomes will be assessed through the use of interview and documentary data. Analysis will include a statistical analysis of the EML model using hierarchical linear modeling, MANOVA/ANOVA, and regression as appropriate at the level of students and teachers, and qualitative analysis and descriptive statistics will be used at the school and district level due to small sample size.

Environmental Innovation Challenges: Teaching and Learning Science Practices in the Context of Complex Earth Systems

This project will engage teams of students and teachers of grades 7-12 in four competitive Challenges to design innovative strategies for carbon mitigation in areas such as transportation, agriculture or energy use. The project expands the typical boundaries of schools by enabling teams of students in multiple locations to collaborate in model-based reasoning through online discussion forums, using social media, and crowdsourcing ideas to construct possible solutions to environmental challenges. Project research will examine the impacts of the project on student learning and engagement.

Project Email: 
Lead Organization(s): 
Award Number: 
1908117
Funding Period: 
Thu, 08/01/2019 to Mon, 07/31/2023
Project Evaluator: 
Full Description: 

Current priorities in science education include efforts to engage students in scientific reasoning and using the knowledge and practices of science to understand natural phenomena and constructively respond to local and global challenges. This project responds to these priorities by engaging teams of students and teachers of grades 7-12 in four competitive Challenges to design innovative strategies for carbon mitigation in areas such as transportation, agriculture or energy use. The project expands the typical boundaries of schools by enabling teams of students in multiple locations to collaborate in model-based reasoning through online discussion forums, using social media, and crowdsourcing ideas to construct possible solutions to environmental challenges. Project research will examine the impacts of the project on student learning and engagement.

This early stage Design and Development study is guided by the hypothesis that competitive challenges supported by social media and crowdsourcing will engage a diverse array of students in sustained and meaningful scientific inquiry. Over a period of four years, the project will design and refine four Challenges that will engage approximately 1,000 students of ages 13-17. Project research is guided by three overarching questions related to the design of the Challenges, the influence of school contextual factors, and student learning and self-efficacy. The questions are: (1) How do features of the challenge environment support the work of teams, and the participation of students from communities historically underserved in STEM? (2) What structures within the school ecosystem support or raise obstacles to team work? And (3) Does participation in a Challenge result in the intended student outcomes. Intended outcomes include: a) Learning of basic concepts related to the science of the project focus; b) Engagement in learning disciplinary core ideas, cross-cutting concepts and science and engineering practices; c) Persistence in completing a Challenge; and d) self-efficacy in STEM. Students and their teachers will cross disciplinary boundaries as they choose concepts from chemistry, engineering, mathematics, biology, and social science to support their innovations.Teachers, students, staff members and advisors will comment and provide quidance to the teams on a range of issues through crowdsourcing. Design research will be used to examine how features of the Challenge environment supports the work of teachers and teams, and implementation research will focus on participant learning at the individual and team levels. The project will engage at least 25 teams of 3-4 students each, and researchers will track team activity during all phases of the Challenge process. A mixture of qualitative and quantitative analyses will be used to examine outcomes, and data for girls and others from underserved populations will be disaggregated for separate analyses.

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CAREER: Expanding Latinxs' Opportunities to Develop Complex Thinking in Secondary Science Classrooms through a Research-Practice Partnership

This project will address the need to educate teachers and students to engage in asking questions, collecting and interpreting data, making claims, and constructing explanations about real-world problems that matter to them. The study will explore ways to enhance youths' learning experiences in secondary school classrooms (grades 6-12) by building a sustainable partnership between researchers and practitioners.

Award Number: 
1846227
Funding Period: 
Mon, 07/01/2019 to Sun, 06/30/2024
Full Description: 

This project will address the need to educate teachers and students to engage in asking questions, collecting and interpreting data, making claims, and constructing explanations about real-world problems that matter to them. Science educators generally agree that science classrooms should provide opportunities for students to advance their thinking by engaging in critical conversations with each other as capable sense-makers. Despite decades of reform efforts and the use of experiential activities in science instruction, research indicates that classroom learning for students remains largely procedural, undemanding, and disconnected from the development of substantive scientific ideas. Furthermore, access to high-quality science instruction that promotes such complex thinking is scarce for students with diverse cultural and linguistic backgrounds. The project goals will be: (1) To design a year-long teacher professional development program; and (2) To study the extent to which the professional development model improves teachers' capacity to plan and implement inclusive science curricula.

This study will explore ways to enhance youths' learning experiences in secondary school classrooms (grades 6-12) by building a sustainable partnership between researchers and practitioners. The work will build on a previous similar activity with one local high school; plans are to expand the existing study to an entire school district over five years. The proposed work will be conducted in three phases. During Phase I, the study will develop a conceptual framework focused on inclusive science curricula, and implement the new teacher professional development program in 3 high schools with 15 science teachers. Phase II will expand to 6 middle schools in the school district with 24 teachers aimed at creating a continuous and sustainable research-practice partnership approach at the district. Phase III will focus on data analysis, assessment of partnership activities, dissemination, and planning a research agenda for the immediate future. The study will address three research questions: (1) Whether and to what extent does participating teachers' capacity of planning and implementing the curriculum improve over time; (2) How and why do teachers show differential progress individually and collectively?; and (3) What opportunities and constraints within schools and the school district shape teachers' development of their capacity to design and implement curricula? To address the research questions, the project will gather information about the quality of planned and implemented curriculum using both qualitative and quantitative data. Main project's outcomes will be: (1) a framework that guides teachers' engagement in planning and implementing inclusive science curricula; and (2) increased knowledge base on teacher learning. An advisory board will oversee the work in progress. An external evaluator will provide formative and summative feedback.

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.

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