Mathematics

An Online Reflection and Community-based Instructional Development System for Mathematics Education

The project will create a system of online mathematics teacher professional development modules for middle and high school teachers. Teachers will engage in online, asynchronous, high-quality mathematics learning experiences that mirror research-based productive classroom practices and models of instruction that feature active learning and student collaboration, explanation, and discussion.

Lead Organization(s): 
Award Number: 
2010306
Funding Period: 
Sat, 08/01/2020 to Wed, 07/31/2024
Full Description: 

The project will create a system of online mathematics teacher professional development modules for middle and high school teachers. Teachers will engage in online, asynchronous, high-quality mathematics learning experiences that mirror research-based productive classroom practices and models of instruction that feature active learning and student collaboration, explanation, and discussion. The modules will integrate mathematics content and teaching strategies for teachers. The teachers will work collaboratively using math tasks, their own students' work, and other resources to develop teaching practices to support mathematical problem solving. Developing online environments for teacher development is critical to reaching greater numbers of teachers, providing flexible options for learning, and taking advantage of online opportunities for collaborative learning. In particular, the software will allow teachers to share, comment and discuss mathematical work.

The field of mathematics education needs to understand the development and implementation of online learning modules for mathematics teacher development. This project will create an environment that integrates content and pedagogical knowledge via mathematics-focused modules. The project builds on the Online Asynchronous Collaboration in Mathematics Teacher Education model to create the modules. The project's research questions are about the how the teachers build mathematics knowledge for teaching together online. They also examine teacher reflection on students' mathematical works, teacher collaboration, and reciprocal perspective-taking. Finally, the research examines how shifts in instruction are supported as teachers are learning new practices in the modules. The implementation study will use data such as measures of teacher knowledge, questionnaires, artifacts from the online platform, interviews, and other sources. These will be analyzed using a mixed methods approach to understand teachers' learning, collaboration and use of the modules and to refine the modules themselves. The findings of the study should inform the design of online learning experiences for mathematics teachers, new models for teacher development, and understanding of secondary mathematics teacher knowledge and practice.

Enhancing the Teacher-Curriculum Relationship in Problem-based Mathematics Classrooms by Connecting Teacher and Student Digital Collaborative Environments

The project will create a digital environment for middle school mathematics teachers that is combined with a student collaborative platform for a problem-solving curriculum. The goal is to design and develop the digital collaborative platform so networks of teachers can create, use, and share teaching resources for planning, enactment, and reflection on student thinking.

Lead Organization(s): 
Award Number: 
2007842
Funding Period: 
Sat, 08/01/2020 to Wed, 07/31/2024
Full Description: 

The project will create a digital environment for middle school mathematics teachers to promote collaboration. The digital environment for the teachers links to a student collaborative environment and contains the same problem-based curriculum materials. The environment helps teachers to collaborate and learn from one another. This occurs when teachers plan, teach, and reflect on student learning. The online, digital platform will help teachers work together more easily in networks that might be at different schools. The resources online will include problem-based curriculum materials, classroom artifacts from students, and resources created by teachers. The project will learn about how teachers use resources, collaborate in the digital environment, and support each other through the network. With more curriculum resources being created for online teaching and learning, the project will help understand how mathematics teaching and learning can be best supported.

The design-based research project in mathematics studies a digital, collaborative environment for teachers that is combined with a student collaborative platform for a middle school problem-solving curriculum. The goal is to design and develop the digital collaborative platform so networks of teachers can create, use, and share teaching resources for planning, enactment, and reflection on student thinking. The project will include middle school teachers in the design process. The environment for students enables student thinking to be visible to other students and the teacher. This allows the teacher to archive and then examine student reasoning and thinking. The new environment will allow that work to be shared with other teachers in a professional learning community. The research question is: How do teachers in networks access, generate, use, and share teaching resources (including classroom artifacts) as needed to support mathematics teaching (planning, enactment, and reflection of student thinking)? The project will use teacher interviews and artifacts from the collaborative environment for mixed methods data collection and analysis. Teacher reflection resources will be used to understand how they are thinking about students' mathematical work and how they are using the platform resources.

Broadening Participation in Mathematics for English Learners with Mathematics Difficulties: A Multi-Site Impact Study

The purpose of this project is to rigorously test the efficacy of the Precision Mathematics First-Grade (PM-1) intervention on the mathematics outcomes of English learners (ELs) who face mathematics difficulties (MD). The PM-1 intervention is designed to support students with or at risk for MD in developing a robust understanding of the underlying concepts, problem-solving skills, and vocabulary of early measurement and statistical investigation.

Lead Organization(s): 
Award Number: 
2010550
Funding Period: 
Tue, 09/01/2020 to Sun, 08/31/2025
Full Description: 

Success in mathematics has major implications for student success at the public school and postsecondary levels, as well as contributing to the nation's STEM workforce and economy. While building mathematics literacy is important for all learners, it is especially critical for students most vulnerable for academic risk. Among these at-risk subgroups are English learners (ELs). By definition, ELs are not yet proficient in academic English and often come to school unprepared for the linguistic demands of disciplinary learning. Authentic and engaged content learning activities, such as early mathematics, may comprise the ideal context for acquiring the language and literacy skills ELs need. Research suggests ELs represent the fastest growing subgroup in U.S. schools. Currently, U.S. classrooms serve over five million ELs and estimated projections suggest that up to one in four students in 2025 will be an EL. Considering the rising presence of ELs, there is an urgent need to advance equity and eliminate disparities in STEM education among this group of learners who are often underserved by current practice. Overwhelming evidence suggests that ELs place well short of their non-EL peers in the area of mathematics. Therefore, the purpose of this 5-year Impact Project is to rigorously test the efficacy of the Precision Mathematics First-Grade (PM-1) intervention on the mathematics outcomes of ELs who face mathematics difficulties (MD). PM-1 is an innovative, first-grade, English-based, mathematics intervention focused on state-of-the-art technology and hands-on problem-solving activities, the PM-1 intervention is designed to support students with or at risk for MD in developing a robust understanding of the underlying concepts, problem-solving skills, and vocabulary of early measurement and statistical investigation. This study will examine student response to the PM-1 intervention based on variables such as students' initial mathematics skill levels and proficiency in English, and explore how the rate and quality of mathematics discourse opportunities for ELs may predict gains in mathematics outcomes.

This impact study will investigate the efficacy of the Precision Mathematics First-Grade (PM-1) intervention through a methodologically rigorous randomized controlled trial. The study will utilize a randomized block design, blocking on classrooms and randomly assigning first-grade English learners (ELs) who face mathematics difficulties (MD) within first-grade classrooms to one of two conditions: (a) PM-1 intervention or (b) control (business-as-usual). Approximately 900 ELs from 150 first-grade classrooms will participate. Three research aims will guide this study. Aim 1 will systematically evaluate the average effect of PM-1 on student mathematics achievement; while Aim 2 will investigate differential response to the intervention based on student-level variables, including ELs proficiency in English and pretreatment mathematics performance. In Aim 3, researchers will explore whether the frequency and quality of mathematics discourse opportunities for ELs predicts gains in mathematics achievement. Although random assignment will take place at the student level, students will be assigned to small instructional group formats for intervention delivery. Therefore, the design employs a partially nested mixed-model Time × Condition analyses to evaluate the effect of PM-1 on pretest to posttest gains in mathematics achievement (Aim 1) and differential response to PM-1 based on student characteristics (Aim 2). A random coefficients analysis that nests repeated assessments within students and PM-1 intervention groups will explore whether the rate and quality of mathematics discourse opportunities predicts ELs' gains in mathematics achievement (Aim 3).

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.

Implementation and Efficacy Study of Preschool Math Activities for Numeracy

This project explores how teachers can use activities with young children to develop their knowledge of numbers and patterns. Part of the study examines how much guidance teachers should provide to students. The project also explores the design of resources that are the most likely to be used by preschool teachers and that can be easily incorporated into their teaching of young children.

Lead Organization(s): 
Award Number: 
2010547
Funding Period: 
Wed, 07/15/2020 to Sun, 06/30/2024
Full Description: 

Math games and play engage young children's interest in patterns, numbers and logic. In preschools, there is a critical need for math instruction and learning. Early childhood is an important point for children to learn about mathematics. Children's play-based activities provide natural opportunities for them to explore and learn math topics. This project explores how teachers can use activities with young children to develop their knowledge of numbers and patterns. Part of the study examines how much guidance teachers should provide to students. The project also explores the design of resources that are the most likely to be used by preschool teachers and that can be easily incorporated into their teaching of young children. The study of the use of play-based mathematics activities will support critical early learning of number concepts.

This project will investigate the implementation and efficacy of the preschool math games for mathematics learning. The research would study the materials as used in classrooms by teachers in order to understand how the materials improve early numeracy skills, and whether children's improvement is affected by how the activities are implemented in the classroom. The research questions for the study examine the role of the teacher in providing guidance to children when engaging in the numeracy activities and how the materials influence children's early numeracy skills. The study employs an experimental design to study different implementation pathways. The design would examine the impact of two different instructor types and two levels of guidance for the preschool students when using the activities. Data collected will include measures of children's mathematical knowledge and teachers' pedagogical self-efficacy and content knowledge.

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.

Enhancing Rational Number Instruction for Students with Math Disabilities and Difficulties: Designing Professional Development for Teachers Who Provide Math Intervention

The project will develop and study a professional development program focused on fraction for interventionists who work with grades four and five students with mathematics disabilities and difficulties.

Lead Organization(s): 
Award Number: 
2010038
Funding Period: 
Wed, 07/15/2020 to Sun, 06/30/2024
Full Description: 

The project will develop and study a professional development program focused on fraction for interventionists who work with grades four and five students with mathematics disabilities and difficulties. Mathematics interventions for students with mathematical disabilities are provided by a variety of educators in elementary schools including classroom teachers, special education teachers, mathematics specialists, and paraprofessionals. However, professional development and training to address the needs of students with mathematics disabilities and difficulties varies. This project addresses a need in elementary schools for improved fraction instruction and the professional development for interventionists who work with students. The project would create resources usable by other professional development projects for interventionists. The project will also provide guidance about professional development for other mathematics topics.

The professional development will be focused on fractions concepts, use interactive and hands-on methods for learning, and be relevant because fractions are a critical topic in upper elementary grades. The participants in the student are interventionists who work with grades 4 and 5 students. The project includes a design phase followed by a randomized controlled trial to measure teacher-level outcomes. Measures of instruction, student knowledge and teacher outcomes will be used to understand the promise of the intervention. Interventionist teaching practice and fractions knowledge will be used as the proximal outcomes and will be analyzed using ANCOVAs with the pretest measures serving as the covariates. For distal outcomes related to fourth- and fifth-grade students' fractions achievement, a multi-level model including students and interventionists will be used. As an early stage design and development project, the design is being tested in multiple districts in different states. The project relies on prior research about students' learning of fractions and related teaching approaches. The results should inform professional development for interventionists for students with mathematical disabilities and difficulties. The results also support understanding of professional development that develops teachers' knowledge of content and teaching practice simultaneously.

Creating a Model for Sustainable Ambitious Mathematics Programs in High-Need Settings: A Researcher-Practitioner Collaboration

This project will study a successful, ambitious mathematics reform effort in high-needs secondary schools. The goal is to develop resources and tools to support other high-needs schools and districts in transforming and sustaining  their mathematics programs. The model focuses on the resources required for change and the aspects of the organization that support or constrain change in mathematics teaching and learning.

Lead Organization(s): 
Award Number: 
2010111
Funding Period: 
Sat, 08/01/2020 to Wed, 07/31/2024
Full Description: 

A long-standing challenge in secondary mathematics education is broadening participation in STEM. Reform of schools and districts to support this goal can be challenging to sustain. This implementation and improvement project will study a successful, ambitious mathematics reform effort in high-needs secondary schools. The goal is to develop resources and tools to support other high-needs schools and districts in transforming and sustaining  their mathematics programs. The model focuses on the resources required for change and the aspects of the organization that support or constrain change in mathematics teaching and learning. The project team includes school district partners that have successfully transformed mathematics teaching to better support students' learning.

The project will develop a model for understanding the demands and resources from an organizational perspective that support ambitious mathematics teaching and learning reforms. Demands are requirements for physical resources or efforts that need to be met in the instructional system. Resources are the material, human, instructional, and organizational requirements needed to address demands. The project will develop the model through a collaboration of researchers, professional development leaders, students, teachers, coaches, and administrators to: (1) understand the demands created throughout a school or district when implementing an ambitious secondary mathematics program in a high-need context; (2) identify the resources and organizational dynamics necessary to address the demands and thus sustain the program; and (3) articulate a model for a sustainable ambitious secondary mathematics program in high-need settings that has validity across a range of implementation contexts. To develop the model over multiple iterations, the project will examine the demands and resources related to implementing an ambitious mathematics program, the perspectives of stakeholders, the organizational structure, and the program goals and implementation. The project will also conduct a systematic literature review to bring together findings from the successful district and other research findings. The data collection and analysis process will include interviews, document analysis, collection of artifacts, and observations across four phases of the project.  Participants will include students, teachers, instructional support personnel, and administrators (from schools and the district).

Storytelling for Mathematics Learning and Engagement

This project will collect and curate digital stories of diverse mathematicians sharing stories of their learning within and beyond schools. These short videos will become part of a more extensive digital database of mathematics stories that will be aligned with K-8 mathematics topics and then materials will be developed for teachers to use. The project team will explore the use of mathematics storytelling on K-8 teacher and student mathematics learning and engagement.

Award Number: 
2010276
Funding Period: 
Wed, 07/01/2020 to Fri, 06/30/2023
Full Description: 

Mathematics education in the United States has long been challenged by three key issues this project seeks to address: (a) narrow conceptions of mathematics as a discipline (b) the lack of racially/ethnically diverse role models for mathematics in terms of representation in the public imagination, media, and schools; and (c) a paucity of resources for instruction to harness students' early interest and engagement in mathematics across racial and gender groups. One promising way to expose teachers and students to a variety of images and diversity of models of mathematics is to include images of diverse people telling their stories about their doing and knowing of mathematics. Although storytelling is a natural part of human activity and is used extensively in other elementary school subjects like social studies and language arts, it is not usually found in elementary mathematics. As part of this three-year project, the project team will collect and curate digital stories of diverse mathematicians sharing stories of their learning within and beyond schools. These short videos will become part of a more extensive digital database of mathematics stories that will be aligned with K-8 mathematics topics and then materials will be developed for teachers to use. Throughout this work, the project team will explore the use of mathematics storytelling on K-8 teacher and student mathematics learning and engagement.

This project responds to calls for improved equity and access to rich, rigorous math: to contribute to understanding a more equitable K-12 pedagogy; to disrupt racial inequities in math (and STEM, more broadly) through culturally responsive and inclusive instructional practice; and to enhance teachers' instructional practice. The first phase of the work will involve collecting and curating a set of digital stories told by mathematicians. Then, through two cycles of design and piloting, the project team will work with participating teachers and students to finalize the design of the videos and associated instructional materials. A sample of pilot teachers will be purposefully selected to account for diversity in region, school population, and experience level of teachers. The research team will also design grade-level appropriate research instruments, collect surveys, and conduct interviews to investigate both teachers' and students' conceptions of mathematics, their conceptions of who "belongs" in mathematics, and teachers' instructional practice with the storytelling materials themselves. Their analysis will draw on quantitative and qualitative research methods. For example, they will use narrative inquiry to examine teachers' and students' experiences with the videos. Using the research findings, the project will make available samples of teachers' pedagogical repertoires related to these videos and demonstrate how storytelling can be used as an effective mechanism for mathematics teaching and learning. Products from this project will include a digital database and supporting instructional materials for teachers, school leaders, and professional developers to use. The dissemination of this research will contribute to building models for mathematics education that serve to deepen understanding of mathematics of teachers and students, as well as simultaneously empowering students of all backgrounds, but especially underserved students, to activate and pursue their interests in mathematics.

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.

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