Algebra

Supporting Teachers to Teach Mathematics through Problem Posing

This project aims to support teachers to engage their students in mathematical problem posing (problem-posing-based learning, or P-PBL). P-PBL is a powerful approach to the teaching and learning of mathematics, and provides students with opportunities to engage in authentic mathematical practices.

Lead Organization(s): 
Award Number: 
2101552
Funding Period: 
Sun, 08/01/2021 to Thu, 07/31/2025
Full Description: 

This project aims to support teachers to engage their students in mathematical problem posing (problem-posing-based learning, or P-PBL). P-PBL is a powerful approach to the teaching and learning of mathematics, and provides students with opportunities to engage in authentic mathematical practices. For example, conjecturing in mathematics, a form of problem posing, often plays an important role in solving complex problems, and problem posing is an important component of mathematical modeling. Yet despite its importance, widely used curriculum materials fail to incorporate P-PBL in substantial and consistent ways, leaving teachers with few resources to enact this process. This project will develop problem-posing lessons and illustrative cases of teachers implementing P-PBL that will not only support teachers to develop a vision of what P-PBL looks like and how to implement it in their own classrooms, but will also serve as rich resources for professional development (PD) providers. This project will generate valuable findings about teaching using problem posing for district administrators, mathematics teachers, educators, and researchers as well as curriculum developers and policy makers. The team will develop and pilot a set of 20−30 research-based P-PBL cases that provide critical details for the implementation of P-PBL and reveal “lessons learned” from the development process.

The project promises broader impact on the field of mathematics education as the first goal is to support teachers to teach mathematics through engaging their students in mathematical problem posing. By guiding students to construct and investigate their own problems, P-PBL both helps to create mathematical learning opportunities and develops students’ mathematical agency and positive mathematical identities. A networked improvement community of teachers and researchers will integrate problem posing into daily mathematics instruction and continuously improve the quality of P-PBL through iterative task and lesson design. The intellectual merit of this project is its contribution of new and important insights about teaching mathematics through problem posing. This will be realized through the second project goal which is to longitudinally investigate the promise of supporting teachers to teach with P-PBL for enhancing teachers’ instructional practice and students’ learning. A quasi-experimental design coupled with design-based research methodology and improvement science will be used to understand how, when, and why P-PBL works in practice. Specifically, we plan to follow a sample of 36 teachers and their approximately 3,600 students from six middle schools for multiple years to longitudinally explore the promise of P-PBL for developing teachers’ beliefs about problem posing, their beliefs about P-PBL, and their actual instructional practice. We will also investigate students’ learning as measured by problem-posing performance, problem-solving performance, and mathematics disposition. The findings of the project will add not only to the field’s understanding of the promise of supporting teachers to integrate P-PBL into their mathematics instruction, but also to its understanding of the challenges that teachers face when engaging in a networked improvement community that is focused on improving tasks and lessons by integrating P-PBL.

Practice-Driven Professional Development for Algebra Teachers

This project seeks to develop a personalized, scalable PD approach that centers on and builds from algebra teachers’ practices and individual strengths. The project will focus its PD efforts on instructional actions that are tailored to teachers' existing practice, can be readily adopted, and are easily accessible.

Lead Organization(s): 
Award Number: 
2101508
Funding Period: 
Thu, 07/01/2021 to Mon, 06/30/2025
Full Description: 

Professional development (PD) is a direct attempt to improve the quality of instruction for teachers already in the classroom. Traditional PD is typically costly in terms of time and money, and efforts tend to be delivered as a one-size-fits-all approach. Furthermore, for teachers who adopt novel techniques such as flipped instruction, there may be few resources to support their efforts. This project seeks to develop a personalized, scalable PD approach that centers on and builds from algebra teachers’ practices and individual strengths. The project will focus its PD efforts on instructional actions that are tailored to teachers' existing practice, can be readily adopted, and are easily accessible. The project team have termed such instructional actions high-uptake practices. The project will develop and field test PD materials to support algebra teachers at scale via these high-uptake practices.

In addition to developing the PD materials, the project team will research the efficacy of this PD model in terms of student learning outcomes and teacher instructional practices in approximately 60 algebra classrooms. The main data sources will include teacher observation data, teacher interviews and surveys, student pre/posttests, student surveys, and PD analytics. The research will characterize the immediate and longer term impacts of the PD on teachers’ instructional practices; and characterize the impact of teachers’ participation in the PD on students’ learning outcomes and engagement. The research questions include: 1) In what ways does teachers’ participation in the PD impact their instructional practices? 2) Do students of teachers who participate in the PD demonstrate differential growth in learning outcomes? 3) Do students of teachers who participate in the PD have increased rates of homework completion?; and 4) Do students of teachers who participate in the PD have increased engagement during individual work time? In meeting both our PD development and research aims, this project will contribute knowledge about the effectiveness of an incremental, practice-driven approach to PD and instructional change.

Developing and Researching K-12 Teacher Leaders Enacting Anti-bias Mathematics Education (Collaborative Research: Yeh)

The goal of this project is to study the design and development of community-centered, job-embedded professional development for classroom teachers that supports bias reduction. The project team will partner with three school districts serving racially, ethnically, linguistically, and socio-economically diverse communities, for a two-year professional development program.

Lead Organization(s): 
Award Number: 
2101666
Funding Period: 
Sun, 08/01/2021 to Thu, 07/31/2025
Full Description: 

There is increased recognition that engaging all students in learning mathematics requires an explicit focus on anti-bias mathematics teaching. Teachers, even with positive intentions, have biases, causing them to treat students differently and impacting how they distribute students’ opportunities to learn in K-12 mathematics classrooms. Research is needed to examine models of mathematics teacher professional development that explicitly addresses bias reduction. The goal of this project is to study the design and development of community-centered, job-embedded professional development for classroom teachers that supports bias reduction. The project team will partner with three school districts serving racially, ethnically, linguistically, and socio-economically diverse communities, for a two-year professional development program. The aim is to reduce bias through: analyzing and designing mathematics teaching with colleagues, students, and families to create classrooms and schools based on community-centered mathematics; engaging in anti-bias teaching routines; and building relationships with parents, caretakers, and community members. The project team will study teacher leader professional development, including the professional development model, framework, and tools, along with what teacher leaders across district contexts and grade-levels take up and use in their instructional practice.  This will potentially have wider implications for supporting more equitable mathematics teaching and leadership. Project activities, resources, and tools will be shared with the broader community of mathematics educators and researchers for use in other contexts.

The goal of this two-phase, design based research project is to iteratively design and research teacher leaders’ (TLs) participation in community-centered, job-embedded professional development and investigate their subsequent impact on classrooms, schools, and districts. The project builds on the existing Math Studio professional development model to create a Community Centered Math Studio, integrating the Anti-bias Mathematics Education Framework into the work. The project seeks to understand how the professional development model supports the development of teacher leaders' knowledge, dispositions, and practices for teaching and leading anti-bias mathematics education, and how teachers' subsequent classroom practice can cultivate students' mathematical engagement, discourse, and interests. The project will measure aspects of teacher knowledge and classroom practice by integrating existing classroom observation rubrics and STEM interest surveys to assess the impact on teacher classroom practice and student outcomes. The project will engage 12 TLs and approximately 60 additional teachers working with those TLs in two years of professional development using the Community Centered Math Studio Model to support anti-bias mathematics teaching. Data will be collected for all teachers related to their participation in the professional learning, with six teachers being followed for additional data collection and in-depth case studies. The project's outcomes will contribute to theories of how TLs build adaptive expertise for teaching and leading to reduce bias in classrooms, departments, schools, and districts. In addition, the project will contribute new and adapted research instruments on anti-bias teaching and leading. The research outcomes will add to the growing research base that describes the nature of equitable mathematics teaching in K-12 classrooms and increases access to meaningful mathematics for students, teachers, and communities.

Pandemic Learning Loss in U.S. High Schools: A National Examination of Student Experiences

As a result of the COVID-19 pandemic, schools across much of the U.S. have been closed since mid-March of 2020 and many students have been attempting to continue their education away from schools. Student experiences across the country are likely to be highly variable depending on a variety of factors at the individual, home, school, district, and state levels. This project will use two, nationally representative, existing databases of high school students to study their experiences in STEM education during the COVID-19 pandemic.

Lead Organization(s): 
Award Number: 
2030436
Funding Period: 
Fri, 05/15/2020 to Fri, 04/30/2021
Full Description: 

As a result of the COVID-19 pandemic, schools across much of the U.S. have been closed since mid-March of 2020 and many students have been attempting to continue their education away from schools. Student experiences across the country are likely to be highly variable depending on a variety of factors at the individual, home, school, district, and state levels. This project will use two, nationally representative, existing databases of high school students to study their experiences in STEM education during the COVID-19 pandemic. The study intends to ascertain whether students are taking STEM courses in high school, the nature of the changes made to the courses, and their plans for the fall. The researchers will identify the electronic learning platforms in use, and other modifications made to STEM experiences in formal and informal settings. The study is particularly interested in finding patterns of inequities for students in various demographic groups underserved in STEM and who may be most likely to be affected by a hiatus in formal education.

This study will collect data using the AmeriSpeak Teen Panel of approximately 2,000 students aged 13 to 17 and the Infinite Campus Student Information System with a sample of approximately 2.5 million high school students. The data sets allow for relevant comparisons of student experiences prior to and during the COVID-19 pandemic and offer unique perspectives with nationally representative samples of U.S. high school students. New data collection will focus on formal and informal STEM learning opportunities, engagement, STEM course taking, the nature and frequency of instruction, interactions with teachers, interest in STEM, and career aspirations. Weighted data will be analyzed using descriptive statistics and within and between district analysis will be conducted to assess group differences. Estimates of between group pandemic learning loss will be provided with attention to demographic factors.

This RAPID award is made by the DRK-12 program in the Division of Research on Learning. The Discovery Research PreK-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics by preK-12 students and teachers, through the research and development of new innovations and approaches. 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 the projects.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

 

 

 

 

CAREER: Implementing Mathematical Modeling for Emergent Bilinguals

This project will support teacher capacity for implementing mathematical modeling lessons by engaging teachers in co-planning and co-teaching with researchers skilled in Emergent Bilingual (EB) mathematics instruction. The outcomes of this project will be a framework for teaching mathematical modeling to EB students, teacher professional development materials that can be used widely to support EB mathematics teachers, and a massive open online course (MOOC) for teachers to support their continued learning about teaching mathematics modeling to EB students.

Lead Organization(s): 
Award Number: 
1941668
Funding Period: 
Tue, 09/01/2020 to Sun, 08/31/2025
Full Description: 

This project supports secondary mathematics teachers in teaching mathematical modeling practices to an Emergent Bilingual (EB) population. EB students in linguistically diverse mathematics classrooms are frequently limited to procedural, rote instruction, despite research-based recommendations that suggest that EBs' mathematical and linguistic proficiency can benefit from engaging in complex mathematical tasks based on real-life situations. The project will support teacher capacity for implementing mathematical modeling lessons by engaging teachers in co-planning and co-teaching with researchers skilled in EB mathematics instruction. The project will collect information about the quality of mathematics instruction in modeling lessons, what students learn, and how teachers changed in how they position EB students as knowers and doers of mathematics. The outcomes of this project will be a framework for teaching mathematical modeling to EB students, teacher professional development materials that can be used widely to support EB mathematics teachers, and a massive open online course (MOOC) for teachers to support their continued learning about teaching mathematics modeling to EB students.

The project draws on three important constructs related to teaching mathematics to emergent bilingual (EB) students: research on the mathematics education of EB students; research on mathematical modeling; and positioning theory. Related to mathematics education of EB students, the project supports teachers in enacting high-quality instruction that incldues high cognitive demand tasks, encourages EBs to engage in and explain their problem solving process, and complements that work with linguistic and contextual supports that support EB students' entry into the tasks. Related to mathematical modeling, the project makes use of the conceptualization of modeling as a vehicle for content (as compared to mathematics content of its own), and envisions the use of modeling practices as particularly supportive of EB students' learning of algebra. In particular, the modeling-as-a-vehicle stance invites teachers to engage students in tasks that contain multiple mathematical representations, which has the potential to both build students' conceptual understandings of algebra and to strengthen EBs' language and communication skills in the context of mathematics. With respect to positioning theory, the project seeks to disrupt the finding that secondary mathematics teachers tend underestimate EB students' mathematical abilities due to their English proficiency standards, causing them to choose lower cognitive demand tasks for these students against established research-based recommendations. The project team will engage EB algebra and pre-algebra teachers in Des Moines Public schools in co-planning and co-teaching lessons using mathematical modeling practice. This co-planning and co-teaching activity constitutes in-situ professional development for teachers. Co-planning sessions, co-taught lessons, and regular teacher interviews will be recorded and analyzed for quality of instruction and changes in teacher positioning of EB students. The research team and teachers will co-analyze student learning data from observations and district-administered standardized assessments to better understand the impact of the modeling lessons on students' algebra learning and achievement. Eight teachers will participate in the work over the life of the project, each supporting EB classes of approximately 20 students per teacher. The outcomes of these analyses will guide the development fo a mathematical modeling framework for teaching EBs, teacher professional development materials made available for similar work in other schools and districts, and a massive open online course designed for teachers to develop their skills for teaching secondary mathematics to EB students.

CAREER: Exploring Teacher Noticing of Students' Multimodal Algebraic Thinking

This project investigates and expands teachers' learning to notice in two important ways. First, the research expands beyond teachers' noticing of written and verbal thinking to attend to gesture and other aspects of embodied and multimodal thinking. Second, the project focuses on algebraic thinking and seeks specifically to understand how teacher noticing relates to the content of algebra. Bringing together multimodal thinking and the mathematical ideas in algebra has the potential to support teachers in providing broader access to algebraic thinking for more students.

Award Number: 
1942580
Funding Period: 
Mon, 06/01/2020 to Sat, 05/31/2025
Full Description: 

Effective teachers of mathematics attend to and respond to the substance of students' thinking in supporting classroom learning. Teacher professional development programs have supported teachers in learning to notice students' mathematical thinking and using that noticing to make instructional decisions in the classroom. This project investigates and expands teachers' learning to notice in two important ways. First, the research expands beyond teachers' noticing of written and verbal thinking to attend to gesture and other aspects of embodied and multimodal thinking. Second, the project focuses on algebraic thinking and seeks specifically to understand how teacher noticing relates to the content of algebra. Bringing together multimodal thinking and the mathematical ideas in algebra has the potential to support teachers in providing broader access to algebraic thinking for more students.

To study teacher noticing of multimodal algebraic thinking, this project will facilitate video club sessions in which teachers examine and annotate classroom video. The video will allow text-based and visual annotation of the videos to obtain rich portraits of the thinking that teachers notice as they examine algebra-related middle school practice. The research team will create a video library focused on three main algebraic thinking areas: equality, functional thinking, and proportional reasoning. Clips will be chosen that feature multimodal student thinking about these content areas, and provide moments that would be fruitful for advancing student thinking. Two cohorts of preservice teachers will engage in year-long video clubs using this video library, annotate videos using an advanced technological tool, and engage in reflective interviews about their noticing practices. Follow-up classroom observations will be conducted to see how teachers then notice multimodal algebraic thinking in their classrooms. Materials to conduct the video clubs in other contexts and the curated video library will be made available, along with analyses of the teacher learning that resulted from their implementation.

CAREER: Promoting Equitable and Inclusive STEM Contexts in High School

This project focuses on fostering equitable and inclusive STEM contexts with attention to documenting and reducing adolescents' experiences of harassment, bias, prejudice and stereotyping. This research will contribute to understanding of the current STEM educational climates in high schools and will help to identify factors that promote resilience in the STEM contexts, documenting how K-12 educators can structure their classrooms and schools to foster success of all students in STEM classes.

Award Number: 
1941992
Funding Period: 
Sat, 02/01/2020 to Fri, 01/31/2025
Full Description: 

This project focuses on fostering equitable and inclusive STEM contexts with attention to documenting and reducing adolescents' experiences of harassment, bias, prejudice and stereotyping. An important barrier to persistence in STEM fields for marginalized groups, including women and ethnic minorities, relates to a culture in many STEM organizations, such as academic institutions, that fosters discrimination, harassment and prejudicial treatment of those from underrepresented groups. This research will contribute to understanding of the current STEM educational climates in high schools and will help to identify factors that promote resilience in the STEM contexts, documenting how K-12 educators can structure their classrooms and schools to foster success of all students in STEM classes. Further, this work will explore how to create schools where students stand-up for each other and support each other so that any student who is interested will feel welcome in STEM classes and programs.

This research aims to examine cultures of discrimination and harassment in STEM contexts with attention to: 1) assessing STEM climates in high schools in order to identify the character of discrimination and harassment, 2) understanding how youth think about these instances of bias and discrimination; 3) identifying pathways to resilience for underrepresented youth pursuing STEM interests, and 4) testing an intervention to promote bystander intervention from those who witness discrimination and harassment in STEM contexts. This research will take an intersectional approach recognizing that those who are marginalized by multiple dimensions of their identity may experience STEM contexts differently than those who are marginalized by one dimension of their identity. Because adolescence is a critical developmental period during which youth are forming their attitudes, orientations and lifelong behaviors, this research will attend to issues of bias and discrimination well before individuals enter college STEM classrooms or the STEM workforce: namely, during high school. Further, this work will examine the creation of equitable STEM climates in both college-preparation classes as well as workforce development STEM programs offered though or in partnership with high schools. This research will provide clear evidence to document the current culture of STEM contexts in high schools, using mixed methods, including surveys, qualitative interviews and longitudinal measurement. Further, the project will involve development and implementation of an intervention, which will provide the first test of whether bystander intervention can be fostered in STEM students and will involve training STEM students in key 21st century skills, such as social-cognitive capacities and interpersonal skills, enabling them to speak up and support peers from marginalized backgrounds when they observe discrimination and harassment.

CAREER: Understanding Latinx Students' Stories of Doing and Learning Mathematics

This project characterizes and analyses the developing mathematical identities of Latinx students transitioning from elementary to middle grades mathematics. The central hypothesis of this project is that elementary Latino students' stories can identify how race and language are influential to their mathematical identities and how school and classroom practices may perpetuate inequities.

Lead Organization(s): 
Award Number: 
2036549
Funding Period: 
Mon, 06/01/2020 to Sat, 05/31/2025
Full Description: 

Although the Latino population throughout the United States continues to increase, various researchers have shown that Latino students are often not afforded high quality learning experiences in their mathematics classrooms. As a result, Latino students are underrepresented in higher level mathematics courses and careers involving mathematics. Having a better understanding of Latino students' perspectives and experiences is imperative to improving their opportunities to learn mathematics. Yet, little research has made central Latinos students' perspectives of learning and doing mathematics, especially over a critical period of time like the transition from elementary to middle school. The goal of this study will be to improve mathematics teaching and learning for Latino youth as they move from upper elementary to early middle school mathematics classrooms. The project involves three major parts: investigating the policy, media, and oral histories of Latino families/communities to understand the context for participating Latino students' mathematics education; exploring Latino students' stories about their experiences learning and doing mathematics to understand these students' perspectives; and creating documentary video portraitures (or composite cases) of participants' stories about learning and doing mathematics that can be used in teacher preparation and professional development. Finally, the project will look across the experiences over the duration of the project to develop a framework that can be used to improve Latino students' mathematics education experiences. This project will provide a window into how Latino students may experience inequities and can broaden mathematics educators' views on opportunities to engage Latino students in rigorous mathematics. The project will also broaden the field's understanding of how Latino students racial/ethnic and linguistic identities influence their experiences learning mathematics. It will also identify key factors that impact Latino students' experiences in learning mathematics to pinpoint specific areas where interventions and programs need to be designed and implemented. An underlying assumption of the project is that carefully capturing and understanding Latino students' stories can illuminate the strengths and resilience these students bring to their learning and doing of mathematics.

This research project characterizes and analyses the developing mathematical identities of Latinx students transitioning from elementary to middle grades mathematics. The overarching research question for this study is: What are the developing stories of learning and doing mathematics of Latino students as they transition from elementary to middle school mathematics? To answer this question, this study is divided into three phases: 1) understanding and documenting the historical context by examining policy documents, local newspaper articles, and doing focus group interviews with community members; 2) using ethnographic methods over two years to explore students' stories of learning and doing mathematics and clinical interviews to understand how they think about and construct arguments about mathematics (i.e., measurement, division, and algebraic patterning); and 3) creating video-cases that can be used in teacher education. Traditional ways of teaching mathematics perpetuate images of who can and cannot do mathematics by not acknowledging contributions of other cultures to the mathematical sciences (Gutiérrez, 2017) and the way mathematics has become a gatekeeper for social mobility (Martin, Gholson, & Leonard, 2010; Stinson, 2004). Focusing on Latino students' stories can illuminate teachers' construction of equitable learning spaces and how they define success for their Latino students. The central hypothesis of this project is that elementary Latino students' stories can identify how race and language are influential to their mathematical identities and how school and classroom practices may perpetuate inequities. Finally, the data and video-cases will then be used to develop a conceptual framework for understanding the development of the participating students' developing mathematical identities. This framework will provide an in-depth understanding of the developing racial/ethnic, linguistic, and mathematical identities of the participating Latino students. The educational material developed (e.g. video documentaries, discussion material) from this project will be made available to all interested parties freely through the project website. The distribution of these materials, along with further understanding of Latino students' experiences learning mathematics, will help in developing programs and interventions at the elementary and middle grade level to increase the representation of Latino students in STEM careers. Additionally, identifying the key factors impacting Latino students' experiences in learning mathematics can pinpoint specific areas where interventions and programs still need to be designed and implemented. Future projects could include the assessment of these programs. This project will also inform the development of professional learning experiences for prospective and practicing teachers working with Latino or other marginalized students.

This project was previously funded under award #1941952.

Validation of the Equity and Access Rubrics for Mathematics Instruction (VEAR-MI)

The main goal of this project is to validate a set of rubrics that attend to the existence and the quality of instructional practices that support equity and access in mathematics classes. The project team will clarify the relationships between the practices outlined in the rubrics and aspects of teachers' perspectives and knowledge as well as student learning outcomes.

Award Number: 
1908481
Funding Period: 
Mon, 07/15/2019 to Fri, 06/30/2023
Full Description: 

High-quality mathematics instruction remains uncommon and opportunities for students to develop the mathematical understanding are not distributed equally. This is particularly true for students of color and students for whom English is not their first language. While educational research has made progress in identifying practices that are considered high-quality, little attention has been given to specific instructional practices that support historically marginalized groups of students particularly as they participate in more rigorous mathematics. The main goal is to validate a set of rubrics that attend to the existence and the quality of instructional practices that support equity and access in mathematics classes. In addition, the project team will clarify the relationships between the practices outlined in the rubrics and aspects of teachers' perspectives and knowledge as well as student learning outcomes.

This project will make use of two existing large-scale datasets focusing on mathematics teachers to develop rubrics on mathematics instructional quality. The datasets include nearly 3,000 video-recorded mathematics lessons and student achievement records from students in Grades 3 through 8. The four phases of this research and development project include training material development, an observation and rubric generalizability study, a coder reliability study, and structural analysis. Data analysis plans involve case studies, exploratory and confirmatory factor analyses, and cognitive interviews. 

Developing and Investigating Unscripted Mathematics Videos

This project will use an alternative model for online videos to develop video units that feature the unscripted dialogue of pairs of students. The project team will create a repository of 6 dialogic mathematics video units that target important Algebra 1 and 2 topics for high school and upper middle school students, though the approach can be applied to any STEM topic, for any age level.

Lead Organization(s): 
Award Number: 
1907782
Funding Period: 
Sun, 09/01/2019 to Thu, 08/31/2023
Full Description: 

This project responds to the recent internet phenomenon of widespread accessibility to online instructional videos, which offer many benefits, such as student control of the pace of learning. However, these videos primarily focus on a single speaker working through procedural problems and providing an explanation. While the immense reach of free online instructional videos is potentially transformative, this potential can only be attained if access transcends physical availability to also include entry into important disciplinary understandings and practices, and only if the instructional method pushes past what would be considered outdated pedagogy in any other setting than a digital one. This project will use an alternative model for online videos, originally developed for a previous exploratory project, to develop 6 video units that feature the unscripted dialogue of pairs of students. The project team will use the filming and post-production processes established during the previous grant to create a repository of 6 dialogic mathematics video units that target important Algebra 1 and 2 topics for high school and upper middle school students, though the approach can be applied to any STEM topic, for any age level. They will also conduct 8 research studies to investigate the promise of these unscripted dialogic videos with a diverse population to better understand the vicarious learning process, which refers to learning from video- or audio-taped presentations of other people learning. Additionally, the project team will provide broader access to the project videos and support a variety of users, by: (a) subtitling the videos and checking math task statements for linguistic accessibility; (b) representing diversity of race, ethnicity, and language in both the pool of students who appear in the videos and the research study participants; (c) providing teachers with an array of resources including focus questions to pose in class with each video, printable task worksheets, specific ways to support dialogue about the videos, and alignment of the video content with Common Core mathematics standards and practices; and (d) modernizing the project website and making it functional across a variety of platforms.

The videos created for this project will feature pairs of students (called the talent), highlighting their unscripted dialogue, authentic confusion, and conceptual resources. Each video unit will consist of 7 video lessons (each split into 4-5 short video episodes) meant to be viewed in succession to support conceptual development over time. The project will build upon emerging evidence from the exploratory grant that as students engage with videos that feature peers grappling with complex mathematics, they can enter a quasi-collaborative relationship with the on-screen talent to learn complex conceptual content and engage in authentic mathematical practices. The research focuses on the questions: 1. What can diverse populations of vicarious learners learn mathematically from dialogic videos, and how do the vicarious learners orient to the talent in the videos? 2. What is the nature of vicarious learners' evolving ways of reasoning as they engage with multiple dialogic video lessons over time and what processes are involved in vicarious learning? and, 3. What instructional practices encourage a classroom community to adopt productive ways of reasoning from dialogic videos? To address the first question, the project team will conduct two Learning Outcomes and Orientation Studies, in which they analyze students' learning outcomes and survey responses after they have learned from one of the video units in a classroom setting. Before administering an assessment to a classroom of students, they will first conduct an exploratory Interpretation Study for each unit, in which they link the mathematical interpretations that VLs generate from viewing the project videos with their performance on an assessment instrument. Both types of studies will be conducted twice, once for each of two video units - Exponential Functions and Meaning and Use of Algebraic Symbols. For the second research question, the project team will identify a learning trajectory associated with each of four video units. These two learning trajectories will inform the instructional planning for the classroom studies by identifying what meaningful appropriation can occur, as well as conceptual challenges for VLs. By delivering learning trajectories for two additional units, the project can contribute to vicarious learning theory by identifying commonalities in learning processes evident across the four studies. For the final research question, the project team will investigate how instructors can support students with the instrumental genesis process, which occurs through a process called instrumental orchestration, as they teach the two videos on exponential functions and algebraic symbols.

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