Early State/Exploratory

Online Practice Suite: Practice Spaces, Simulations and Virtual Reality Environments for Preservice Teachers to Learn to Facilitate Argumentation Discussions in Math and Science

This project will develop, pilot, and refine a set of coordinated and complementary activities that teacher education programs can use in both online and face-to-face settings to provide practice-based opportunities for preservice teachers to develop their ability to facilitate argumentation-focused discussions in mathematics and science.

Lead Organization(s): 
Award Number: 
2037983
Funding Period: 
Sat, 08/15/2020 to Mon, 07/31/2023
Full Description: 

In teacher education it is widely acknowledged that learning to teach requires that preservice teachers have robust, authentic, and consistent opportunities to engage in the work of teaching—ideally across different contexts, with diverse student populations, and for varied purposes—as they hone their instructional practice. Practice teaching experiences in K-12 classrooms, such as field placements and student teaching, are the most widely used approaches to provide these opportunities. In an ideal world these experiences are opportunities for preservice teachers to observe and work closely with mentor teachers and try out new instructional strategies with individual, small groups, and whole classes of K-12 students. While these experiences are critical to supporting preservice teachers' learning, it can be difficult to help preservice teachers transition from university classrooms to field placements in ways that provide them with opportunities to enact ambitious instructional strategies. This need is particularly acute in mathematics and science education, where classrooms that model strong disciplinary discourse and argumentation are not always prevalent. This challenge is amplified by the COVID-19 pandemic environment; with schools and universities across the nation operating online, many preservice teachers will miss out on opportunities to practice teaching both within their courses and in K-12 classrooms. To address this urgent challenge in STEM education, project researchers will develop, pilot, and refine a set of coordinated and complementary activities that teacher education programs can use in both online and face-to-face settings to provide practice-based opportunities for preservice teachers to develop their ability to facilitate argumentation-focused discussions in mathematics and science, a critical teaching practice in these content areas. The practice-based activities include: (1) interactive, online digital games that create targeted practice spaces to engage preservice teachers to respond to students' content-focused ideas and interactions; (2) facilitating group discussions with upper elementary or middle school student avatars in a simulated classroom using performance-based tasks; and (3) an immersive virtual reality whole-classroom environment that allows for verbal, textual and non-verbal interactions between a teacher avatar and 24 student avatars. The online practice suite, made up of these activities along with supports to help teacher educators use them effectively, represents not just an immediate remedy to the challenge of COVID-19, but a rich and flexible set of resources with the potential to support and improve teacher preparation well beyond the COVID-19 challenge.

This study will use design-based research to create this integrated system of practice teaching opportunities. This approach will involve developing and refining the individual practice activities, the integrated online practice suite, and the teacher educator support materials by working with a teacher educator community of practice and engaging up to 20 teacher educators and 400 preservice teachers in multiple rounds of tryouts and piloting during the three-year project. The project will proceed in three phases: a first phase of small-scale testing, a second phase trying the materials with teacher educators affiliated with the project team, and a third phase piloting materials with a broader group of mathematics and science teacher educators. Data sources include surveys of preservice teachers' background characteristics, perceptions of the practice activities, beliefs about content instruction, perceptions about preparedness to teach, and understanding of argumentation and discussion, videos and/or log files of their performances for each practice teaching activity, and scores on their practice teaching performances. The project team will also observe the in-class instructional activities prior to and after the use of each practice teaching activity, conduct interviews with teacher educators, and collect instructional logs from the teacher educators and instructional artifacts used to support preservice teachers' learning. Data analysis will include pre and post comparisons to examine evidence of growth in preservice math and science teachers' beliefs, perceptions, understanding, and teaching performance. The project team will also build a series of analytic memos to describe how each teacher educator used the online practice suite within the mathematics or science methods course and the factors and decisions that went into that each use case. Then, they will describe and understand how the various uses and adaptations may be linked to contextual factors within these diverse settings. Findings will be used to produce empirically and theoretically grounded design principles and heuristics for these types of practice-based activities to support teacher learning.

Co-learning Math Teaching Project: Collaborative Structures to Support Learning to Teach across the Professional Teaching Continuum

This project will design and study an innovative model of collaborative learning for pre-service and experienced secondary mathematics teachers that focuses on equitable mathematics teaching practices that include understanding students' knowledge, math understandings, and experiences they bring to the classroom.

Lead Organization(s): 
Award Number: 
2010634
Funding Period: 
Sun, 11/01/2020 to Thu, 10/31/2024
Full Description: 

An ongoing challenge for the preparation of new mathematics teachers is creating quality experiences in classrooms for student teaching. The project will design and study an innovative model of collaborative learning for pre-service and experienced secondary mathematics teachers. Multiple pre-service teachers will collaborate in the same secondary mathematics teacher's classroom for their field placements. The partnership between the school and the university will allow for professional development for the pre-service teachers and the experienced teachers. A particular focus of the project will be equity in mathematics teaching and learning. Developing equitable mathematics teaching practices includes better understanding students' knowledge, math understandings, and experiences they bring to the classroom. Improving the student teaching experience may improve retention in the teaching profession and help pre-service teachers be better prepared for their first years of teaching.

This is an exploratory project about mathematics teaching and teacher development in field experiences for pre-service teachers. The project introduces collaborative learning structures for pre-service teacher education that focus on equitable mathematics teaching practices. The collaborative learning structures include both the cooperating teacher and multiple pre-service teachers working in the same classroom. The project will use a design-based research model to systematically study the process of co-learning and the critical features of collaborative learning structures as they are designed to support co-learning between novice and experienced teachers. Multiple universities are included in the project in order to compare the model in different settings. The project will use Math Studio as a model for the teachers to focus on a lesson taught by one teacher but the group plans, observes, and reflects about the lesson together. A facilitator or math coach supports the group's work during the Math Studio process. The project has two research questions. First, how do pre-service teachers and cooperating teachers co-learn? More specifically, what vision, dispositions, understandings and practices of justification and generalization does each teacher develop during their time together? How does each teacher's vision, dispositions, understandings, and practices of mathematics teaching shift during their time together? Second, what are the design characteristics of the collaborative learning structures that support or inhibit pre-service teachers and cooperating teachers in learning? The qualitative study will collect video recordings and artifacts from the Math Studio, assessments of math teaching practices, and data from the leadership team in order to compare the model's implementation at different sites. The data analysis will occur iteratively throughout the project to refine the coding framework to describe learning and shifts in teacher practice.

Exploring Changes in Teachers' Engineering Design Self-Efficacy and Practice through Collaborative and Culturally Relevant Professional Development

In this project, investigators from the University of North Dakota develop, evaluate, and implement an on-going, collaborative professional development program designed to support teachers in teaching engineering design to 5th-8th grade students in rural and Native American communities.

Lead Organization(s): 
Award Number: 
2010169
Funding Period: 
Fri, 01/01/2021 to Sun, 12/31/2023
Full Description: 

Promoting diverse, inclusive and equitable participation in engineering design education at the elementary and middle school levels is important for a number of reasons. In addition to benefits of a diverse STEM workforce to industry and the economy, youth are better able to make informed decisions about pursuing STEM degrees and STEM career pathways and youth are able to develop critical thinking and problem solving skills that allow them to be creative and innovative problem solvers. However, for youth to participate in inclusive and equitable engineering design experiences in elementary and middle schools settings, teachers need opportunities to develop engineering content knowledge, pedagogical content knowledge, and strategies for culturally-relevant teaching. In this project, investigators from the University of North Dakota develop, evaluate, and implement an on-going, collaborative professional development program designed to support teachers in teaching engineering design to 5th-8th grade students in rural and Native American communities.

The project advances the understanding of teacher training in K-12 engineering education and more specifically culturally-relevant engineering design education for 5th-8th grade students. The program design is guided by principles from Bandura's Social Learning Theory, Gladson-Billing's culturally-relevant teaching, and Gay's cultural-responsive teaching. The project combines promising, but often isolated, elements from previous engineering education professional development to give teachers a) pedagogical and content knowledge, b) culturally-relevant pedagogy that is inclusive of indigenous students, c) a supportive professional learning community, d) examples of project-based engineering problems implemented in real classrooms, e) extended scaffolded practice with their own classroom engineering tasks, and f) on-going support. The program is designed for teachers in rural and tribal schools with curricular materials developed collaboratively with community input to specifically address their community's unique needs. The project research team, guided by a diverse advisory board, will collect both quantitative and qualitative data in the forms of surveys, interviews, and videotaped observations to determine if and how the project is affecting classroom engineering instruction and pedagogy, as well as the sense of competence and self-efficacy of the teacher participants. The classroom engineering tasks created through this project, especially those developed to be specifically relevant to Native American and rural student populations, will be promoted and made available to other teachers through a project website, teaching practice journals, and teacher conferences.

Exploring COVID and the Effects on U.S. Education: Evidence from a National Survey of American Households

This study aims to understand parents' perspectives on the educational impacts of COVID-19 by leveraging a nationally representative, longitudinal study, the Understanding America Study (UAS). The study will track educational experiences during the summer of 2020 and into the 2020-21 school year and analyze outcomes overall and for key demographic groups of interest.

Award Number: 
2037179
Funding Period: 
Wed, 07/15/2020 to Wed, 06/30/2021
Full Description: 

The COVID-19 epidemic has been a tremendous disruption to the education of U.S. students and their families, and early evidence suggests that this disruption has been unequally felt across households by income and race/ethnicity. While other ongoing data collection efforts focus on understanding this disruption from the perspective of students or educators, less is known about the impact of COVID-19 on children's prek-12 educational experiences as reported by their parents, especially in STEM subjects. This study aims to understand parents' perspectives on the educational impacts of COVID-19 by leveraging a nationally representative, longitudinal study, the Understanding America Study (UAS). The study will track educational experiences during the summer of 2020 and into the 2020-21 school year and analyze outcomes overall and for key demographic groups of interest.

Since March of 2020, the UAS has been tracking the educational impacts of COVID-19 for a nationally representative sample of approximately 1,500 households with preK-12 children. Early results focused on quantifying the digital divide and documenting the receipt of important educational serviceslike free meals and special education servicesafter COVID-19 began. This project will support targeted administration of UAS questions to parents about students' learning experiences and engagement, overall and in STEM subjects, data analysis, and dissemination of results to key stakeholder groups. Findings will be reported overall and across key demographic groups including ethnicity, disability, urbanicity, and socioeconomic status. The grant will also support targeted research briefs addressing pressing policy questions aimed at supporting intervention strategies in states, districts, and schools moving forward. Widespread dissemination will take place through existing networks and in collaboration with other research projects focused on understanding the COVID-19 crisis. All cross-sectional and longitudinal UAS data files will be publicly available shortly after conclusion of administration so that other researchers can explore the correlates of, and outcomes associated with, COVID-19.

Incorporating Professional Science Writing into High School STEM Research Projects

The goal of this project is to expand high school student participation in the peer-review process and in publishing in JEI, a science journal dedicated to mentoring pre-college students through peer-reviewed publication. By publishing pre-college research in an open access website, the project will build understanding of how engaging in these activities can change high school students' perceptions and practices of scientific inquiry.

Lead Organization(s): 
Award Number: 
2010333
Funding Period: 
Wed, 07/15/2020 to Fri, 06/30/2023
Project Evaluator: 
Maya Patel
Full Description: 

This exploratory project addresses important challenge of incorporating disciplinary literacy practices in scientific inquiry projects of high school students. The project will incorporate the peer-review process and publication in the Journal of Emerging Investigators (JEI). The Next Generation Science Standards emphasize constructs from disciplinary literacy such as engaging in argument from evidence, and evaluating and communicating information. However, there are few resources available to students and teachers that integrate these constructs in authentic forms that reflect the practices of professional scientists. High school student learners engage in scientific inquiry, but rarely participate in authentic forms of communication, forms that are reflective of how scientists communicate and participate in the primary literature of their fields. The project has three aims: 1) Generate knowledge of the impact of peer-review and publication on perceptions and skills of scientific inquiry and STEM identity, 2) Generate knowledge of how participation in peer-review and publication are impacted by contextual factors (differences in mentors and research contexts), and 3) Develop JEI field-guides across a range of contexts in which students conduct their research.

The goal of the project is to expand high school student participation in the peer-review process and in publishing in JEI, a science journal dedicated to mentoring pre-college students through peer-reviewed publication. By publishing pre-college research in an open access website, the project will build understanding of how engaging in these activities can change high school students' perceptions and practices of scientific inquiry. The project will investigate how participation in peer-reviewed publications will have an impact on student learning by administering a set of pre- and post-surveys to students who submit a paper to JEI. The project will expand student participation in JEI via outreach to teachers in under-resourced and remote areas by delivering virtual and in-person workshops which will serve to demystify peer review and publication, and explore ways to integrate these processes into existing inquiry projects. Other efforts will focus on understanding how student contextual experiences can impact their learning of scientific inquiry. These student experiences include the location of the project (school, home, university lab), the type of mentor they have, and how they became motivated to pursue publication of their research. The project will recruit students from under-resourced schools in New York through a collaboration with MathForAmerica and from rural areas through outreach with STEM coordinators in the Midwest. The resources created will be disseminated directly on the JEI website.

Assessing College-Ready Computational Thinking (Collaborative Research: Wilson)

The goal of this project is to develop learning progressions and assessment items targeting computational thinking. The items will be used for a test of college-ready critical reasoning skills and will be integrated into an existing online assessment system, the Berkeley Assessment System Software.

Award Number: 
2010314
Funding Period: 
Tue, 09/01/2020 to Sat, 08/31/2024
Full Description: 

Because of the growing need for students to be college and career ready, high-quality assessments of college readiness skills are in high demand. To realize the goal of preparing students for college and careers, assessments must measure important competencies and provide rapid feedback to teachers. It is necessary to go beyond the limits of multiple-choice testing and foster the skills and thinking that lie at the core of college and career ready skills, such as computational thinking. Computational thinking is a set of valuable skills that can be used to solve problems, design systems, and understand human behavior, and is thus essential to developing a more STEM-literate public. Computational thinking is increasingly seen as a fundamental analytical skill that everyone, not just computer scientists, can use. The goal of this project is to develop learning progressions and assessment items targeting computational thinking. The items will be used for a test of college-ready critical reasoning skills and will be integrated into an existing online assessment system, the Berkeley Assessment System Software.

The project will address a set of research questions focused on 1) clarifying computational thinking constructs, 2) usability, reliability of validity of assessment items and the information they provide, 3) teachers' use of assessments, and 4) relationships to student performance. The study sample of 2,700 used for the pilot and field tests will include all levels of students in 10th through 12th grade and first year college students (both community college and university level). The target population is students in schools which are implementing the College Readiness Program (CRP) of the National Mathematics and Science Institute. In the 2020-21 academic year 54 high schools across 11 states (CA, GA, FL, ID, LA, NC, NM, OH, TX, VA, and WA) will participate. This will include high school students in Advanced Placement classes as well as non-Advanced Placement classes.  The team will use the BEAR Assessment System to develop and refine assessment materials. This system is an integrated approach to developing assessments that seeks to provide meaningful interpretations of student work relative to cognitive and developmental goals. The researchers will gather empirical evidence to develop and improve the assessment materials, and then gather reliability and validity evidence to support their use. In total, item response data will be collected from several thousand students. Student response data will be analyzed using multidimensional item response theory models.

Learning to Teach During COVID-19: Leveraging Simulated Classrooms as Practice-based Spaces for Preservice Elementary Teachers within Online Teacher Education Courses

The COVID-19 pandemic has significantly disrupted the ability of teacher education programs to place their teacher candidates in typical K-12 teaching settings as a part of learning to teach. This project examines how simulated classroom field experiences for preservice teachers can be implemented in online and emergency remote teacher education courses.

Lead Organization(s): 
Award Number: 
2032179
Funding Period: 
Mon, 06/15/2020 to Mon, 05/31/2021
Full Description: 

School-based field experiences are a critical part of preservice teacher education. The COVID-19 pandemic has significantly disrupted the ability of teacher education programs to place their teacher candidates in typical K-12 teaching settings as a part of learning to teach. This project examines how simulated classroom field experiences for preservice teachers can be implemented in online and emergency remote teacher education courses. Elementary mathematics and science teacher educators are provided with opportunities to engage their preservice teachers in practice-based spaces using mixed-reality simulated classroom environments. These simulations are real-time lessons with animated student avatars that are voiced by an interactor who is responding to the teacher's lesson in real time in ways that represent authentic student thinking. This project aims to develop support materials for integrating simulated field experiences into elementary mathematics and science teacher education courses. The research will seek to understand what preservice teachers learn about teaching from these experiences, how teacher educators integrate the simulated field experiences into coursework, and how such simulated experiences can be integrated in remote, online courses in ways that support preservice teacher learning.

This project advances knowledge through the development and deployment of simulation-based tools that develop preservice elementary teachers' abilities to teach mathematics and science. Preservice teachers use performance tasks to deliver instruction in the simulated classroom. The project develops support materials for teacher educators to integrate this work into online and/or emergency remote teacher education courses (in response to COVID-19) in ways that support engagement in ambitious teaching practice. The project assesses impact on preservice teachers' ambitious teaching practice through artifacts of the simulated classroom practice, including observations and recordings of the simulated interactions and preservice teacher surveys and assessments of their use of ambitious teaching practices. The project evaluates the ways in which teacher educators integrate the simulated field experience into their emergency remote teacher education courses through surveys and interviews. The research addresses the immediate COVID-19 pandemic challenges in providing field experiences for students and provides long-term support for the ongoing challenge of finding field experience settings that are conducive to preparing highly-qualified elementary mathematics and science teachers.

Exploring Early Childhood Teachers' Abilities to Identify Computational Thinking Precursors to Strengthen Computer Science in Classrooms

This project will explore PK-2 teachers' content knowledge by investigating their understanding of the design and implementation of culturally relevant computer science learning activities for young children. The project team will design a replicable model of PK-2 teacher professional development to address the lack of research in early computer science education.

Lead Organization(s): 
Award Number: 
2006595
Funding Period: 
Tue, 09/01/2020 to Thu, 08/31/2023
Full Description: 

Strengthening computer science education is a national priority with special attention to increasing the number of teachers who can deliver computer science education in schools. Yet computer science education lacks the evidence to determine how teachers come to think about computational thinking (a problem-solving process) and how it could be integrated within their day-to-day classroom activities. For teachers of pre-kindergarten to 2nd (PK-2) grades, very little research has specifically addressed teacher learning. This oversight challenges the achievement of an equitable, culturally diverse, computationally empowered society. The project team will design a replicable model of PK-2 teacher professional development in San Marcos, Texas, to address the lack of research in early computer science education. The model will emphasize three aspects of teacher learning: a) exploration of and reflection on computer science and computational thinking skills and practices, b) noticing and naming computer science precursor skills and practices in early childhood learning, and c) collaborative design, implementation and assessment of learning activities aligned with standards across content areas. The project will explore PK-2 teachers' content knowledge by investigating their understanding of the design and implementation of culturally relevant computer science learning activities for young children. The project includes a two-week computational making and inquiry institute focused on algorithms and data in the context of citizen science and historical storytelling. The project also includes monthly classroom coaching sessions, and teacher meetups.

The research will include two cohorts of 15 PK-2 teachers recruited from the San Marcos Consolidated Independent School District (SMCISD) in years one and two of the project. The project incorporates a 3-phase professional development program to be run in two cycles for each cohort of teachers. Phase one (summer) includes a 2-week Computational Making and Inquiry Institute, phase two (school year) includes classroom observations and teacher meetups and phase three (late spring) includes an advanced computational thinking institute and a community education conference. Research and data collection on impacts will follow a mixed-methods approach based on a grounded theory design to document teachers learning. The mixed-methods approach will enable researchers to triangulate participants' acquisition of new knowledge and skills with their developing abilities to implement learning activities in practice. Data analysis will be ongoing, interweaving qualitative and quantitative methods. Qualitative data, including field notes, observations, interviews, and artifact assessments, will be analyzed by identifying analytical categories and their relationships. Quantitative data includes pre to post surveys administered at three-time points for each cohort. Inter-item correlations and scale reliabilities will be examined, and a repeated measures ANOVA will be used to assess mean change across time for each of five measures. Project results will be communicated via peer-reviewed journals, education newsletters, annual conferences, family and teacher meetups, and community art and culture events, as well as on social media, blogs, and education databases.

Enhancing Energy Literacy through Place-based Learning: Using the School Building to Link Energy Use with Earth Systems

This exploratory project will design, pilot, and evaluate a 10-weeek, energy literacy curriculum unit for a program called Energy and Your Environment (EYE). In the EYE curriculum, students will study energy use and transfer in their own school buildings. They will explore how Earth systems supply renewable and nonrenewable energy, and how these energy sources are transformed and transferred from Earth systems to a school building to meet its daily energy requirements.

Lead Organization(s): 
Award Number: 
2009127
Funding Period: 
Tue, 09/01/2020 to Thu, 08/31/2023
Full Description: 

Student understanding of energy concepts about Earth systems and human-built systems require grappling with current societal issues related to resource use and management, energy sources, climate impacts, and sustainability. These relationships are challenging for students and underdeveloped in many science curriculum frameworks. This exploratory project will design, pilot, and evaluate a 10-weeek, energy literacy curriculum unit for a program called Energy and Your Environment (EYE). In the EYE curriculum, students will study energy use and transfer in their own school buildings. They will explore how Earth systems supply renewable and nonrenewable energy, and how these energy sources are transformed and transferred from Earth systems to a school building to meet its daily energy requirements. Learning about complex ideas in a place that is common to both students and teachers provides a means for deeper understanding and application of energy use and exchange. The research team includes researchers in biology and in architecture with an emphasis on natural resources and the environment. The researchers will work with four middle school science teachers to develop a curriculum unit that requires deep understanding of energy-systems models, but that will also be designed to apply to the school system and community. This is place-based learning aligned with the Next Generation Science Standards to foster energy literacy, modeling of energy use and flow, and systems thinking.

The research questions for this study will ask about students' ability to construct and explain models about energy use and exchange, as well as about teachers' use of the newly developed instructional materials. The research team will collaborate with 4 middle school teachers to design and test the unit in their classrooms. Data collection includes students' drawn models of the energy systems in use in their school building, student and teacher interviews, classroom observations, and teacher questionnaires. Student understanding of the learning goals will be assessed through a learning performance on energy modeling, and an accompanying rubric to score student models and explanations. After an initial implementation of the unit in classrooms, the following summer, researchers and teachers will meet to revise the curriculum materials. Then, teachers new to the curriculum unit will participate in the professional development required to teach the EYE unit. They will introduce the revised unit to their students in the next year, as researchers collect data and evaluate student learning for the revised curriculum materials. Overall, the project intends to include about 600 middle school students.

Paving the Way for Fractions: Identifying Foundational Concepts in First Grade (Collaborative Research: Newcombe)

The goal of this project is to investigate the extent to which individual differences in informal fraction-related knowledge in first-grade children are associated with short- and longer-term fractions and math outcomes, and to see whether there is a causal link between level of informal fraction-related knowledge and the ability to profit from fractions instruction that directly builds on this knowledge.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
2000424
Funding Period: 
Mon, 06/01/2020 to Fri, 05/31/2024
Full Description: 

Although fractions represent a crucial topic in early childhood education, many students develop only a tenuous grasp of fraction concepts, even after several years of fraction instruction that is aligned with current standards. The goal of this project, led by a team of researchers at the University of Delaware and Temple University, is to answer important questions about the informal understandings of fractions young children have before they come to school and what their relations are to fraction learning in more formal instructional settings. Proficiency with fractions dramatically increases the likelihood of students succeeding in math, which in turn increases participation in the STEM workforce. Importantly, large individual differences in fraction understandings are apparent at the start of fractions instruction in the intermediate grades. Early fraction misunderstandings cascade into more severe math weaknesses in later grades, especially when instruction may shift abruptly from whole numbers to fractions. There is a critical need to understand the roots of individual differences that arise before formal instruction takes place. Young children possess important informal fraction understandings before they come to school, but the range of these abilities and their role in formal fraction learning and development is not well understood. The goal of this project is: a) to investigate the extent to which individual differences in informal fraction-related knowledge in first-grade children are associated with short- and longer-term fractions and math outcomes; and b) to see whether there is a causal link between level of informal fraction-related knowledge and the ability to profit from fractions instruction that directly builds on this knowledge. The findings from the project hold promise for informing early childhood educators how fractions can be incorporated in the first-grade curriculum in new and meaningful ways. Though the findings should be beneficial to all students, the project will specifically target members of groups underrepresented in STEM fields, including ethnic and racial minority and low-income students.

The project design includes both an observational study and an experimental study. The observational study will: (1) document individual differences in informal fraction-related knowledge in first grade; (2) determine concurrent relations between this informal knowledge and general cognitive and whole number competencies; and (3) examine whether informal fraction-related knowledge at the beginning of first grade uniquely predicts math outcomes at the end. The experimental study will explore the extent to which first graders' informal and formal fraction concepts can be affected by training. The researchers will test whether training on the number line, which is continuous and closely aligned with the mental representation of the magnitude of all real numbers, will help students capitalize on their informal fraction understandings of proportionality, scaling, and equal sharing as well as their experience with integers to learn key fraction concepts. Together, the synergistic studies will pinpoint the role informal fraction knowledge in learning key fraction concepts. All data will be collected in Delaware schools serving socioeconomically and ethnically diverse populations of students. Primary measures include assessments of informal fraction knowledge (proportional reasoning, spatial scaling, equal sharing), executive functioning, vocabulary, whole number knowledge, whole number/fraction number line estimation, formal fraction knowledge, and broad mathematics achievement (calculation, fluency, applied problems).

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