Quantitative

Responding to an Emerging Epidemic through Science Education

This research project will produce curricular materials designed to help students learn about viral epidemics as both a scientific and social issue. It will engage students in scientific modeling of the epidemic and in critical analyses of media and public health information about the virus. This approach helps students connect their classroom learning experiences with their lives beyond school, a key characteristic of science literacy.

Partner Organization(s): 
Award Number: 
2023088
Funding Period: 
Sun, 03/01/2020 to Sun, 02/28/2021
Full Description: 

At this moment, there is global concern about the coronavirus disease 2019 (COVID-19) and its potential to become an epidemic in the U.S. and other countries. Reports of past studies on student understanding of epidemics and how they are taught in school indicate that teachers are reticent to teach the material because the science is unclear given the emerging nature of evidence, or because they don?t understand it well themselves. Curricular resources are limited. Consequently, many students are left on their own to grapple with a potential public health emergency that could affect them and their families. The problem is further complicated by misinformation that may be spread through social media. There is less public understanding about the science of the virus and how it spreads; the risk of being infected; treatment, or, the severity of the illness. This research project will produce curricular materials designed to help students learn about viral epidemics as both a scientific and social issue. It will engage students in scientific modeling of the epidemic and in critical analyses of media and public health information about the virus. This approach helps students connect their classroom learning experiences with their lives beyond school, a key characteristic of science literacy. This project is an example of how science education can be both engaging and relevant.

Researchers at the University of North Carolina and the University of Missouri have been studying how to teach about issues at the crossroads of science and social concerns such as community health; they have developed a framework to build curriculum materials focused on student learning of such complex issues through modeling and inquiry. For this study on the coronavirus disease 2019 (COVID-19); first, the researchers will study student responses to the epidemic in real time, collecting data on student initial understandings and concerns. Then, using this information, they will work with 7 high school science teachers familiar with their framework to build a prototype curriculum unit, and test it in classrooms in 4 high schools selected for their socio-economic and ethnic/racial diversity. The study will gather data on student interest in the epidemic, as well as how students access information about it through various forms of media, and how they vet news reports and social media. The researchers will also use pre- and post-test data to assess student learning. After this initial enactment of the curriculum materials developed to teach about the epidemic, researchers and teachers will revise the curriculum materials to make them more effective. The final products will be a curriculum unit that will be readily available and modifiable for teaching and learning about future epidemics, as well as greater understanding about how students deal with vast amounts of information about societal issues that affect their immediate lives and the science behind them.


 Project Videos

2021 STEM for All Video Showcase

Title: Responding to an Emerging Epidemic through Science Education

Presenter(s): Troy Sadler, Pat Friedrichsen, Li Ke, & Laura Zangori


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.

Design and Implementation of Immersive Representations of Practice

This project will address the potential positive and negative impacts of using 360-degree video for bridging the gap between theory and practice in mathematics instruction by investigating how preservice teachers' tacit and explicit professional knowledge are facilitated using immersive video technology and annotations.

Lead Organization(s): 
Award Number: 
1908159
Funding Period: 
Sun, 09/01/2019 to Wed, 08/31/2022
Full Description: 

Various researchers have documented that a large proportion of preservice teachers (PSTs) demonstrate less sophisticated professional knowledge for teaching both fractions and multiplication/division. Use of representations of practice (i.e., video, animation), and accompanying annotation technology, are effective in improving such professional knowledge, but PSTs continue to demonstrate a lack of precision in attending to or noticing particular mathematics in classroom scenarios. Fortunately, a new technology, 360-degree video, has emerged as a means of training novices for professional practice. This project will address the potential positive and negative impacts of using 360-degree video for bridging the gap between theory and practice in mathematics instruction. Specifically, PSTs demonstrate difficulty in synthesizing explicit knowledge learned in the college classroom with tacit professional knowledge situated in professional practice. The initial pilot of the technology resulted in PSTs demonstrating specific attention to the mathematics. The purpose of the project will be to investigate how PSTs' tacit and explicit professional knowledge are facilitated using immersive video technology and annotations (technologically embedded scaffolds). To do this, the project will examine where and what PSTs attend to when viewing 360-degree videos, both at a single point in the classroom and through incorporating multiple camera-perspectives in the same class. Additionally, the project will examine the role of annotation technology as applied to 360-degree video and the potential for variations in annotation technology. Findings will allow for an improved understanding of how teacher educators may support PSTs' tacit and explicit knowledge for teaching. The project will make video experiences publicly available and the platform used in the project to create these video experiences for teacher educators to use, create, and share 360-degree video experiences.

The project will examine how representations of practice can facilitate preservice teachers' professional knowledge for teaching fractions and multiplication/division. The project will: examine the effect of single versus multiple perspective in PSTs' professional knowledge; examine how PSTs use annotation technology in immersive video experiences, and its effect on PSTs' professional knowledge for teaching fractions and multiplication/division; and design a platform for teacher educators to create their own 360 video immersive experiences. Using an iterative design study process, the project team will develop and pilot single and multi-perspective 360-degree video experiences in grade 3-5 classrooms including developing a computer program to join multiple 360-degree videos. They will also develop an annotation tool to allow PSTs to annotate the single and multi-perspective 360 video experiences. Using a convergent mixed methods design, the project team will analyze the quantitative data using multiple regressions of pre-post data on mathematical knowledge for teaching and survey data on PSTs reported immersion and presence in viewing the videos to compare single and multi-perspective 360-degree video data. They will also qualitatively analyze heat maps generated from eye tracking, written responses from PSTs' noticing prompts, and field notes from implementation to examine the effect of single versus multiple perspectives. The team will use similar methods to examine how PSTs use the annotation technology and its effect. The results of the research and the platform will be widely disseminated.


Project Videos

2021 STEM for All Video Showcase

Title: Immersive Representations of Practice in Teacher Education

Presenter(s): Karl Kosko, Christine Austin, Richard Ferdig, Enrico Gandolfi, Jennifer Heisler, & Maryam Zolfaghari

2020 STEM for All Video Showcase

Title: Use of 360 Video in Elementary Mathematics Teacher Education

Presenter(s): Karl Kosko, Christina Austin, Richard Ferdig, Enrico Gandolfi, Qiang Guan, Jennifer Heisler, Annette Kratcoski, Cheng-Chang Lu, Yuxin Yang, & Maryam Zolfaghari


Crowdsourcing Neuroscience: An Interactive Cloud-based Citizen Science Platform for High School Students, Teachers, and Researchers

This project will develop a cloud-based platform that enables high school students, teachers, and scientists to conduct original neuroscience research in school classrooms.

Lead Organization(s): 
Award Number: 
1908482
Funding Period: 
Thu, 08/01/2019 to Mon, 07/31/2023
Full Description: 

Current priorities in school science education include engaging students in the practices of science as well as the ideas of science. This project will address this priority by developing a cloud-based platform that enables high school students, teachers, and scientists to conduct original neuroscience research in school classrooms. Before students and teachers initiate their own studies using the system, they will participate in existing research studies by contributing their own data and collaborating with researchers using the online, interactive system. When experienced with the system, students and teachers will become researchers by developing independent investigations and uploading them to the interactive platform. Both student-initiated and scientist-initiated proposals will be submitted to the platform, peer-reviewed by students and scientists, revised, and included in the online experimental bank. In addition to conducting their own studies using the platform, scientists will act as educators and mentors by populating the experiment bank with studies that can serve as models for students and provide science content for the educational resource center. This online system addresses a critical need in science education to involve students more fully and authentically in scientific inquiry where they gain experience in exploring the unknown rather than confirming what is already known.

This early stage design and development study is guided by three goals: 1) Develop an open-science citizen science platform for conducting human brain and behavior research in the classroom, 2) Develop a remote neuroscience Student-Teacher-Scientists (STS) partnership program for high schools, and 3) Evaluate the design, development, and implementation of the program and its impacts on students and tachers. In developing this project, the project team will link two quickly emerging trends, one in science education, and one in the sciences. Consistent with current priorities in science education, the project will engage students and their teachers in authentic, active inquiry where they learn scientific practices by using them to conduct authentic inquiry where a search for knowledge is grounded in finding evidence-based answers to original questions. On the science side, students and their science partners will participate in an open science approach by pre-registering their research and committing to an analysis plan before data are collected. In this project, students will primarily be using reaction time and online systems to do research that includes study of their own brain function. The project research is guided by three research questions. How does an online citizen neuroscience STS platform: a) impact students' understanding of, and abilities to apply neuroscience and experimental design concepts? b) Impact students' interests in, and attitudes toward science, including an awareness of science careers and applications? and c) Affect teachers' attitudes towards neuroscience teaching, and the use of inquiry-based strategies? A design-based research approach will be used to iteratively design a sustainable and scalable inquiry-based neuroscience curriculum with teachers as design partners.


 Project Videos

2021 STEM for All Video Showcase

Title: MindHive: A Citizen Science Platform

Presenter(s): Sushmita Sadhukha, Engin Bumbacher, Kim Burgas, Suzanne Dikker, Rebecca Martin, Camillia Matuk, Yury Shevchenko, & Veena Vasudevan


Generalized Embodied Modeling to Support Science through Technology Enhanced Play (Collaborative Research: Danish)

The project will develop and research a new Mixed Reality environment (MR), called GEM-STEP, that leverages play and embodiment as resources for integrating computational modeling into the modeling cycle as part of science instruction for elementary students.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1908632
Funding Period: 
Thu, 08/01/2019 to Sun, 07/31/2022
Full Description: 

The project will develop and research a new Mixed Reality environment (MR), called GEM-STEP, that leverages play and embodiment as resources for integrating computational modeling into the modeling cycle as part of science instruction for elementary students. GEM stands for Generalized Embodied Modeling. Through these embodied, play-as-modeling activities, students will learn the core concepts of science, and the conceptual skills of modeling and systematic measurement. MR environments use new sensing technologies to help transform young children's physical actions during pretend play into a set of symbolic representations and parameters in a science simulation. As students physically move around the classroom, the computer will track their motion and interactions with selected objects and translate their physical activity into a shared display. For example, students pretend they are water particles and work together to model different states of matter. The children see their activity projected onto a computer simulation where a model of a water particle is displayed over the video of themselves. As students collectively reflect upon the nature of a water molecule, they refine their understanding of water as ice, a liquid or a gas. The proposed innovation allows the students to program and revise their own mixed reality simulations as part of their modeling cycle. Embodied and computational modeling will help students to reflect on their models in a unique way that will make their models more computationally accurate and enhance their understanding of the underlying concepts.

The project will research how using the body as a component of the modeling cycle differs from and interacts with the articulation of a scientific model through more structured computational means. The project will investigate the benefits of combining embodiment with computational elements in GEM:STEP by studying the range of concepts that students can learn in this manner. Lessons will be developed to address different disciplinary core ideas, such as states of matter, pollination as a complex system, or decomposition, as well as cross-cutting concepts of systems thinking, and energy/matter flow, all of which link directly to upper elementary science curriculum. Project research will gather data to understand what kinds of models students develop, what learning processes are supported using GEM:STEP, and what learning results. The data will include: (1) documenting and analyzing what students modeled and how accurate the models are; (2) recording student activity using audio and voice to code their activity to document learning processes and to look at how different forms of modeling interact with one another to promote learning; and (3) pre-post content measures to assess learning. All of the software that is developed for GEM:STEP will be made available as Open Source projects, allowing other researchers to build upon and extend this work. The results of the research will be disseminated in academic conferences and peer reviewed journals. The motion tracking software is already available on Github, a popular open-source repository. Once developed, the aim is to implement GEM:STEP in a wide range of classroom contexts, supported by a user-friendly interface, teacher guides, and professional development.

Generalized Embodied Modeling to Support Science through Technology Enhanced Play (Collaborative Research: Enyedy)

The project will develop and research a new Mixed Reality environment (MR), called GEM-STEP, that leverages play and embodiment as resources for integrating computational modeling into the modeling cycle as part of science instruction for elementary students.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1908791
Funding Period: 
Thu, 08/01/2019 to Sun, 07/31/2022
Full Description: 

The project will develop and research a new Mixed Reality environment (MR), called GEM-STEP, that leverages play and embodiment as resources for integrating computational modeling into the modeling cycle as part of science instruction for elementary students. GEM stands for Generalized Embodied Modeling. Through these embodied, play-as-modeling activities, students will learn the core concepts of science, and the conceptual skills of modeling and systematic measurement. MR environments use new sensing technologies to help transform young children's physical actions during pretend play into a set of symbolic representations and parameters in a science simulation. As students physically move around the classroom, the computer will track their motion and interactions with selected objects and translate their physical activity into a shared display. For example, students pretend they are water particles and work together to model different states of matter. The children see their activity projected onto a computer simulation where a model of a water particle is displayed over the video of themselves. As students collectively reflect upon the nature of a water molecule, they refine their understanding of water as ice, a liquid or a gas. The proposed innovation allows the students to program and revise their own mixed reality simulations as part of their modeling cycle. Embodied and computational modeling will help students to reflect on their models in a unique way that will make their models more computationally accurate and enhance their understanding of the underlying concepts.

The project will research how using the body as a component of the modeling cycle differs from and interacts with the articulation of a scientific model through more structured computational means. The project will investigate the benefits of combining embodiment with computational elements in GEM:STEP by studying the range of concepts that students can learn in this manner. Lessons will be developed to address different disciplinary core ideas, such as states of matter, pollination as a complex system, or decomposition, as well as cross-cutting concepts of systems thinking, and energy/matter flow, all of which link directly to upper elementary science curriculum. Project research will gather data to understand what kinds of models students develop, what learning processes are supported using GEM:STEP, and what learning results. The data will include: (1) documenting and analyzing what students modeled and how accurate the models are; (2) recording student activity using audio and voice to code their activity to document learning processes and to look at how different forms of modeling interact with one another to promote learning; and (3) pre-post content measures to assess learning. All of the software that is developed for GEM:STEP will be made available as Open Source projects, allowing other researchers to build upon and extend this work. The results of the research will be disseminated in academic conferences and peer reviewed journals. The motion tracking software is already available on Github, a popular open-source repository. Once developed, the aim is to implement GEM:STEP in a wide range of classroom contexts, supported by a user-friendly interface, teacher guides, and professional development.

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. 


 Project Videos

2021 STEM for All Video Showcase

Title: Supporting Equitable Participation and Access

Presenter(s): Jonee Wilson, Elizabeth Adams, Danielle Moloney, Tiffini Pruitt-Britton, Anna Thorp, Temple Walkowiak, Annie Wilhelm, & Natalia Yanez Castillo


Validity Evidence for Measurement in Mathematics Education (V-M2ED) (Collaborative Research: Bostic)

The purpose of this project is to fully explore the mathematics education literature to synthesize what validity evidence is available for quantitative assessments in mathematics education.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1920621
Funding Period: 
Thu, 08/01/2019 to Wed, 07/31/2024
Full Description: 

As education has shifted more towards data-driven policy and research initiatives in the last several decades, data for policy-related aspects are often expected to be more quantitative in nature.  This has led to the increase in use of more quantitative measures in STEM education, including mathematics education. Unfortunately, evidence regarding the validity and reliability of mathematics education measures is lacking. Furthermore, the evidence for validity for quantitative tools and measures is not conceptualized or defined consistently by researchers in the field. The purpose of this project is to fully explore the mathematics education literature to synthesize what validity evidence is available for quantitative assessments in mathematics education. Drawing on the results of the synthesis study, the researchers will design, curate, and disseminate a repository of quantitative assessments used in mathematics education teaching and research. The researchers will also create materials and online training for a variety of scholars and practitioners to use the repository.

The team will address two main research questions: 1) How might validity evidence related to quantitative assessments used in mathematics education research be categorized and described? and 2) What validity evidence exists for quantitative instruments used in mathematics education scholarship since 2000? Researchers will use a cross-comparative methodology which involves conducting a literature search and then analyzing and categorizing features of instruments. The research team will examine cases (i.e., assessments described in manuscripts) in which quantitative instruments have been used, alongside specific features such as the construct measured, evidence related to sources of validity, and study sample. The team will then design, develop, and deploy a free online digital repository for the categorization of instruments and describe their associated validity evidence.

Validity Evidence for Measurement in Mathematics Education (V-M2ED) (Collaborative Research: Krupa)

The purpose of this project is to fully explore the mathematics education literature to synthesize what validity evidence is available for quantitative assessments in mathematics education.

Partner Organization(s): 
Award Number: 
1920619
Funding Period: 
Thu, 08/01/2019 to Wed, 07/31/2024
Full Description: 

As education has shifted more towards data-driven policy and research initiatives in the last several decades, data for policy-related aspects are often expected to be more quantitative in nature.  This has led to the increase in use of more quantitative measures in STEM education, including mathematics education. Unfortunately, evidence regarding the validity and reliability of mathematics education measures is lacking. Furthermore, the evidence for validity for quantitative tools and measures is not conceptualized or defined consistently by researchers in the field. The purpose of this project is to fully explore the mathematics education literature to synthesize what validity evidence is available for quantitative assessments in mathematics education. Drawing on the results of the synthesis study, the researchers will design, curate, and disseminate a repository of quantitative assessments used in mathematics education teaching and research. The researchers will also create materials and online training for a variety of scholars and practitioners to use the repository.

The team will address two main research questions: 1) How might validity evidence related to quantitative assessments used in mathematics education research be categorized and described? and 2) What validity evidence exists for quantitative instruments used in mathematics education scholarship since 2000? Researchers will use a cross-comparative methodology which involves conducting a literature search and then analyzing and categorizing features of instruments. The research team will examine cases (i.e., assessments described in manuscripts) in which quantitative instruments have been used, alongside specific features such as the construct measured, evidence related to sources of validity, and study sample. The team will then design, develop, and deploy a free online digital repository for the categorization of instruments and describe their associated validity evidence.

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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