Measurement

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. 

Young Mathematicians: Expanding an Innovative and Promising Model Across Learning Environments to Promote Preschoolers' Mathematics Knowledge

The goal of this design and development project is to address the critical need for innovative resources that transform the mathematics learning environments of preschool children from under-resourced communities by creating a cross-context school-home intervention.

Award Number: 
1907904
Funding Period: 
Mon, 07/01/2019 to Fri, 06/30/2023
Full Description: 

Far too many children in the U.S. start kindergarten lacking the foundational early numeracy skills needed for academic success. This project contributes to the goal of enhancing the learning and teaching of early mathematics in order to build a STEM-capable workforce and STEM-literate citizenry, which are both crucial to our nation's prosperity and competitiveness. Preparation for the STEM-workforce must start early, as young children's mathematics development undergirds cognitive development, building brain architecture, and supporting problem-solving, puzzling, and persevering, while strongly impacting and predicting future success in school. Preschool children from low socio-economic backgrounds are particularly at risk, as their mathematics knowledge may be up to a full year behind their middle-income peers. Despite agreements about the importance of mathematics-rich interactions for young children's learning and development, most early education teachers and families are not trained in evidence-based methods that can facilitate these experiences, making preschool learning environments (such as school and home) a critical target for intervention. The benefit of this project is that it will develop a robust model for a school-based intervention in early mathematics instruction. The model has the potential to broaden participation by providing instructional materials that support adult-child interaction and engagement in mathematics, explicitly promoting school-home connections in mathematics, and addressing educators' and families' attitudes toward mathematics while promoting children's mathematical knowledge and narrowing opportunity gaps.

The goal of this design and development project is to address the critical need for innovative resources that transform the mathematics learning environments of preschool children from under-resourced communities by creating a cross-context school-home intervention. To achieve this goal, qualitative and quantitative research methodologies will be employed, integrating data from multiple sources and stakeholders. Specifically, the project will: (1) engage in a materials design and development process that includes an iterative cycle of design, development, and implementation, collaborating with practitioners and families in real-world settings; (2) collect and analyze data from at least 40 Head Start classrooms, implementing the mathematics materials to ensure that the classroom and family mathematics materials and resources are engaging, usable, and comprehensible to preschoolers, teachers, and families; and (3) conduct an experimental study that will measure the impact of the intervention on preschool children's mathematics learning. The researchers will analyze collected data using hierarchical linear regression modeling to account for the clustering of children within classrooms. The researchers will also use a series of regression models and multi-level models to determine whether the intervention promotes student outcomes and whether it supports teachers' and families' positive attitudes toward mathematics.

Science, Technology, Engineering and Mathematics Teaching in Rural Areas Using Cultural Knowledge Systems

This project will collaborate with Indigenous communities to create educational resources serving Inupiaq middle school students and their teachers. The Cultural Connections Process Model (CCPM) will formalize, implement, and test a process model for community-engaged educational resource development for Indigenous populations. The project will contribute to a greater understanding of effective natural science teaching and science career recruitment of minority students.

Award Number: 
1812888
Funding Period: 
Sat, 09/01/2018 to Tue, 08/31/2021
Full Description: 

The Cultural Connections Process Model (CCPM) will formalize, implement, and test a process model for community-engaged educational resource development for Indigenous populations. The project will collaborate with Indigenous communities to create educational resources serving Inupiaq middle school students and their teachers. Research activities take place in Northwest Alaska. Senior personnel will travel to rural communities to collaborate with and support participants. The visits demonstrate University of Alaska Fairbanks's commitment to support pathways toward STEM careers, community engagement in research, science teacher recruitment and preparation, and STEM career awareness for Indigenous and rural pre-college students. Pre-service teachers who access to the resources and findings from this project will be better prepared to teach STEM to Native students and other minorities and may be more willing to continue careers as science educators teaching in settings with Indigenous students. The project will contribute to a greater understanding of effective natural science teaching and science career recruitment of minority students. The project's participants and the pre-college students they teach will be part of the pipeline into science careers for underrepresented Native students in Arctic communities. The project will build on partnerships outside of Alaska serving other Indigenous populations and will expand outreach associated with NSF's polar science investments.

CCPM will build on cultural knowledge systems and NSF polar research investments to address science themes relevant to Inupiat people, who have inhabited the region for thousands of years. An Inupiaq scholar will conduct project research and guide collaboration between Indigenous participants and science researchers using the Inupiaq research methodology known as Katimarugut (meaning "we are meeting"). The project research and development will engage 450 students in grades 6-8 and serves 450 students (92% Indigenous) and 11 teachers in the remote Arctic. There are two broad research hypotheses. The first is that the project will build knowledge concerning STEM research practices by accessing STEM understandings and methodologies embedded in Indigenous knowledge systems; engaging Indigenous communities in project development of curricular resources; and bringing Arctic science research aligned with Indigenous priorities into underserved classrooms. The second is that classroom implementation of resources developed using the CCPM will improve student attitudes toward and engagement with STEM and increase their understandings of place-based science concepts. Findings from development and testing will form the basis for further development, broader implementation and deeper research to inform policy and practice on STEM education for underrepresented minorities and on rural education.

Prospective Elementary Teachers Making for Mathematical Learning

This study takes an innovative approach to documenting how teacher knowledge can be enhanced by incorporating a design experience into pre-service mathematics education. Teachers will use digital and fabrication technologies (e.g., 3D printers and laser cutters) to design and use manipulatives for K-6 mathematics learning. The goals of the project include describing how this experience influences the prospective teachers' knowledge and identities while creating curriculum for teacher education.

Lead Organization(s): 
Award Number: 
1812887
Funding Period: 
Sat, 09/01/2018 to Mon, 08/31/2020
Full Description: 

What teachers know and believe is central to what they can do in classrooms. This study takes an innovative approach to documenting how teacher knowledge can be enhanced by incorporating a design experience into pre-service mathematics education. The study's participating prospective teachers will use digital and fabrication technologies (e.g., 3D printers and laser cutters) to design and use manipulatives for K-6 mathematics learning. The goals of the project include describing how this experience influences the prospective teachers' knowledge and identities while creating curriculum for teacher education. Also, because more schools and students have access to 3D fabrication capabilities, teacher education can utilize these capabilities to prepare teachers to take advantage of these resources. Prior research by the team demonstrated how the process of making a manipulative can support prospective teachers in learning about mathematics and how to teach elementary mathematics concepts. The project will generate resources for other elementary teacher education programs and research about how prospective elementary teachers learn mathematics for teaching.

The project includes three research questions. First, what forms of knowledge are brought to bear as prospective elementary teachers make new manipulatives and write corresponding tasks to support the teaching and learning of mathematics? Second, how does prospective elementary teachers' knowledge for teaching mathematics develop as they make new manipulatives and write tasks to support the teaching and learning of mathematics? Third, as prospective elementary teachers make new manipulatives and write tasks to support the teaching and learning of mathematics, how do they see themselves in relation to the making, the mathematics, and the mathematics teaching? The project will employ a design-based research methodology with cycles of design, enactment, analysis and redesign to create curriculum modules for teacher education focused on making mathematics manipulatives. Data collection will include video recording of class sessions, participant observation, field notes, artifacts from the participants' design of manipulatives, and assessments of mathematical knowledge for teaching. A qualitative analysis will use multiple frameworks from prior research on mathematics teacher knowledge and identity development.

Integrating Chemistry and Earth Science

This project will design, develop, and test a new curriculum unit for high school chemistry courses that is organized around the question, "How does chemistry shape where I live?" The new unit will integrate relevant Earth science data, scientific practices, and key urban environmental research findings with the chemistry curriculum to gain insights into factors that support the approach to teaching and learning advocated by current science curriculum standards.

Award Number: 
1721163
Funding Period: 
Tue, 08/15/2017 to Wed, 07/31/2019
Full Description: 

This Integrating Chemistry and Earth science (ICE) project will design, develop, and test a new curriculum unit for high school chemistry courses that is organized around the question, "How does chemistry shape where I live?" The new unit will integrate relevant Earth science data, scientific practices, and key urban environmental research findings with the chemistry curriculum to gain insights into factors that support the approach to teaching and learning advocated by current science curriculum standards. The overarching goal of the project is to develop teacher capacity to teach and evaluate student abilities to use the practices of scientists and concepts from Earth science and chemistry to understand important phenomena in their immediate, familiar environments. The project has the potential to serve as a model for how to make cutting edge science directly accessible to all students. The project is a collaborative effort that engages scientists, science education researchers, curriculum developers, school curriculum and instruction leaders, and science teachers in the longer term challenge of infusing Earth science concepts and practices across the core high school science courses.

Current guidelines and standards for science education promote learning that engages students in three interrelated dimensions: disciplinary core ideas, scientific practices, and crosscutting ideas. This project is guided by the hypothesis that when provided sustained opportunities to engage in three-dimensional learning experiences, in an integrated Earth science and chemistry context, students will improve in their ability to demonstrate the coordination of disciplinary core ideas, scientific practices, and crosscutting concepts when solving problems and developing explanations related to scientific phenomena. This project will employ a design based research approach, and during the two development-enactment-analysis-and-redesign cycles, the project team will collect student assessment data, teacher interview data, observational data from lessons, teacher surveys, and reflective teacher logbooks. These collected data will provide information about how teachers implement the lessons, what students do during the lessons, and what students learn from them that will lead to better design and a better understanding of student learning. This information will be used to inform the modification of lessons from cycle to cycle, and to inform the professional development materials for teachers. The research agenda for the project is guided by the following questions: 1. What are the design features of ICE lessons that support teachers in enacting three-dimensional instruction within the context of their classroom? 2. What are the design features of embedded three-dimensional assessments that yield useful classroom data for teachers and researchers regarding their students' abilities to integrate core ideas, scientific practices, and crosscutting concepts? 3. What is the nature of student learning related to disciplinary core ideas, scientific practices, and crosscutting concepts that results from students' engagement in ICE lesson sets? 4. What differences emerge in student engagement and learning outcomes for ICE lessons that incorporate local phenomena or data sets as compared to lessons that do not? 5. What contextual factors (i.e., school context, administrative support, time constraints, etc.) influence teachers' implementation of three-dimensional instruction embedded within ICE lessons?


Project Videos

2019 STEM for All Video Showcase

Title: Integrating Chemistry and Earth Science (ICE)

Presenter(s): Alan Berkowitz, Vonceil Anderson, Bess Caplan, Kevin Garner, & Jonathon Grooms


CAREER: Designing and Enacting Mathematically Captivating Learning Experiences for High School Mathematics

This project explores how secondary mathematics teachers can plan and enact learning experiences that spur student curiosity, captivate students with complex mathematical content, and compel students to engage and persevere (referred to as "mathematically captivating learning experiences" or "MCLEs"). The study will examine how high school teachers can design lessons so that mathematical content itself is the source of student intrigue, pursuit, and passion.

Lead Organization(s): 
Award Number: 
1652513
Funding Period: 
Wed, 02/15/2017 to Mon, 01/31/2022
Full Description: 

This design and development project explores how secondary mathematics teachers can plan and enact learning experiences that spur student curiosity, captivate students with complex mathematical content, and compel students to engage and persevere (referred to as "mathematically captivating learning experiences" or "MCLEs"). This study is important because of persistent disinterest by secondary students in mathematics in the United States. This study will examine how high school teachers can design lessons so that mathematical content itself is the source of student intrigue, pursuit, and passion. To do this, the content within mathematical lessons (both planned and enacted) is framed as mathematical stories and the felt tension between how information is revealed and withheld from students as the mathematical story unfolds is framed as its mathematical plot. The Mathematical Story Framework (Dietiker, 2013, 2015) foregrounds both the coherence (does the story make sense?) and aesthetic (does it stimulate anticipation for what is to come, and if so, how?) dimensions of mathematics lessons. The project will generate principles for lesson design usable by teachers in other settings and exemplar lessons that can be shared.

Specifically, this project draws from prior curriculum research and design to (a) develop a theory of teacher MCLE design and enactment with the Mathematical Story Framework, (b) increase the understanding(s) of the aesthetic nature of mathematics curriculum by both researchers and teachers, and (c) generate detailed MCLE exemplars that demonstrate curricular coherence, cognitive demand, and aesthetic dimensions of mathematical lessons. The project is grounded in a design-based research framework for education research. A team of experienced high school teachers will design and test MCLEs (four per teacher) with researchers through three year-long cycles. Prior to the first cycle, data will be collected (interview, observations) to record initial teacher curricular strategies regarding student dispositions toward mathematics. Then, a professional development experience will introduce the Mathematical Story Framework, along with other curricular frameworks to support the planning and enacting of lessons (i.e., cognitive demand and coherence). During the design cycles, videotaped observations and student aesthetic measures (surveys and interviews) for both MCLEs and a non-MCLEs (randomly selected to be the lesson before or after the MCLE) will be collected to enable comparison. Also, student dispositional measures, collected at the beginning and end of each cycle, will be used to learn whether and how student attitudes in mathematics change over time. Of the MCLEs designed and tested, a sample will be selected (based on aesthetic and mathematical differences) and developed into models, complete with the rationale for and description of aesthetic dimensions.

Building a Next Generation Diagnostic Assessment and Reporting System within a Learning Trajectory-Based Mathematics Learning Map for Grades 6-8

This project will build on prior funding to design a next generation diagnostic assessment using learning progressions and other learning sciences research to support middle grades mathematics teaching and learning. The project will contribute to the nationally supported move to create, use, and apply research based open educational resources at scale.

Award Number: 
1621254
Funding Period: 
Thu, 09/15/2016 to Sat, 08/31/2019
Full Description: 

This project seeks to design a next generation diagnostic assessment using learning progressions and other research (in the learning sciences) to support middle grades mathematics teaching and learning. It will focus on nine large content ideas, and associated Common Core State Standards for Mathematics. The PIs will track students over time, and work within school districts to ensure feasibility and use of the assessment system.

The research will build on prior funding by multiple funding agencies and address four major goals. The partnership seeks to address these goals: 1) revising and strengthening the diagnostic assessments in mathematics by adding new item types and dynamic tools for data gathering 2) studying alternative ways to use measurement models to assess student mathematical progress over time using the concept of learning trajectories, 3) investigating how to assist students and teachers to effectively interpret reports on math progress, both at the individual and the class level, and 4) engineering and studying instructional strategies based on student results and interpretations, as they are implemented within competency-based and personalized learning classrooms. The learning map, assessment system, and analytics are open source and can be used by other research and implementation teams. The project will exhibit broad impact due to the number of states, school districts and varied kinds of schools seeking this kind of resource as a means to improve instruction. Finally, the research project contributes to the nationally supported move to create, use, and apply research based open educational resources at scale.

CAREER: Multilevel Mediation Models to Study the Impact of Teacher Development on Student Achievement in Mathematics

This project will develop a comprehensive framework to inform and guide the analytic design of teacher professional development studies in mathematics. An essential goal of the research is to advance a science of teaching and learning in ways that traverse both research and education.

Lead Organization(s): 
Award Number: 
1552535
Funding Period: 
Thu, 09/01/2016 to Tue, 08/31/2021
Full Description: 

This is a Faculty Early Career Development Program (CAREER) project. The CAREER program is a National Science Foundation-wide activity that offers the most prestigious awards in support of junior faculty who exemplify the role of teacher-scholars through outstanding research, excellent education and the integration of education and research. The intellectual merit and broader impacts of this study lie in two complementary contributions of the project. First, the development of the statistical framework for the design of multilevel mediation studies has significant potential for broad impact because it develops a core platform that is transferable to other STEM (science, technology, engineering, and mathematics) education areas and STEM disciplines. Second, the development of software and curricular materials to implement this framework further capitalize on the promise of this work because it distributes the results in an accessible manner to diverse sets of research and practitioner groups across STEM education areas and STEM disciplines. Together, the components of this project will substantially expand the scope and quality of evidence generated through mathematics professional development and, more generally, multilevel mediation studies throughout STEM areas by increasing researchers' capacity to design valid and comprehensive studies of the theories of action and change that underlie research programs.

This project will develop a comprehensive framework to inform and guide the analytic design of teacher professional development studies in mathematics. The proposed framework incorporates four integrated research and education components: (1) develop statistical formulas and tools to guide the optimal design of experimental and non-experimental multilevel mediation studies in the presence of measurement error, (2) develop empirical estimates of the parameters needed to implement these formulas to design teacher development studies in mathematics, (3) develop free and accessible software to execute this framework, and (4) develop training materials and conduct workshops on the framework to improve the capacity of the field to design effective and efficient studies of teacher development. An essential goal of the research is to advance a science of teaching and learning in ways that traverse both research and education.

Collaborative Math: Creating Sustainable Excellence in Mathematics for Head Start Programs

This project will adapt and study a promising and replicable teacher professional development (PD) intervention, called Collaborative Math (CM), for use in early childhood programs. Prepared as generalists, preschool teachers typically acquire less math knowledge in pre-service training than their colleagues in upper grades, which reduces their effectiveness in teaching math. To address teacher PD needs, the project will simultaneously develop teacher content knowledge, confidence, and classroom practice by using a whole teacher approach.

Lead Organization(s): 
Award Number: 
1503486
Funding Period: 
Tue, 09/01/2015 to Sat, 08/31/2019
Full Description: 

This project was submitted to the Discovery Research K-12 (DRK-12) program that seeks to significantly enhance the learning and teaching of science, technology, engineering, and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models, and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. The project will adapt and study a promising and replicable teacher professional development (PD) intervention, called Collaborative Math (CM), for use in early childhood programs. CM content will focus on nine topics emphasized in preschool mathematics, including sets, number sense, counting, number operations, pattern, measurement, data analysis, spatial relationships, and shape. These concepts are organized around Big Ideas familiar in early math, are developmentally appropriate and foundational to a young child's understanding of mathematics. The project addresses the urgent need for improving early math instruction for low-income children. Prepared as generalists, preschool teachers typically acquire less math knowledge in pre-service training than their colleagues in upper grades, which reduces their effectiveness in teaching math. To address teacher PD needs, the project will simultaneously develop teacher content knowledge, confidence, and classroom practice by using a whole teacher approach. Likewise, the project will involve teachers, teacher aides, and administrators through a whole school approach in PD, which research has shown is more effective than involving only lead teachers. Through several phases of development and research, the project will investigate the contributions of project components on increases in teacher knowledge and classroom practices, student math knowledge, and overall implementation. The project will impact approximately 200 Head Start (HS) teaching staff, better preparing them to provide quality early math experiences to more than 3,000 HS children during the project period. Upon the completion of the project, a range of well-tested CM materials such as resource books and teaching videos will be widely available for early math PD use. Assessment tools that look at math knowledge, attitudes, and teacher practice will also be available. 

The project builds on Erikson Institute research and development work in fields of early math PD and curriculum. Over a 4-year span, project development and research will be implemented in 4 phases: (1) adapting the existing CM and research measures for HS context; (2) conducting a limited field study of revised CM in terms of fidelity and director, teacher/aide, and student outcomes, and study of business as usual (BAU) comparison groups; (3) a study of the promise of the intervention promise with the phase 3 BAU group (who offered baseline in phase 2) and (4) a test of the 2nd year sustainability intervention with phase 3 treatment group. The teacher and student measures are all published, frequently used measures in early childhood education and will be piloted and refined prior to full implementation. The project is a partnership between Erikson, SRI, and Chicago Head Start programs. Project research and resources will be widely disseminated to policy makers, researchers, and practitioners.

TRUmath and Lesson Study: Supporting Fundamental and Sustainable Improvement in High School Mathematics Teaching (Collaborative Research: Schoenfeld)

Given the changes in instructional practices needed to support high quality mathematics teaching and learning based on college and career readiness standards, school districts need to provide professional learning opportunities for teachers that support those changes. The project is based on the TRUmath framework and will build a coherent and scalable plan for providing these opportunities in high school mathematics departments, a traditionally difficult unit of organizational change.

Award Number: 
1503454
Funding Period: 
Wed, 07/01/2015 to Sun, 06/30/2019
Full Description: 

Given the changes in instructional practices needed to support high quality mathematics teaching and learning based on college and career readiness standards, school districts need to provide professional learning opportunities for teachers that support those changes. The project will build a coherent and scalable plan for providing these opportunities in high school mathematics departments, a traditionally difficult unit of organizational change. Based on the TRUmath framework, characterizing the five essential dimensions of powerful mathematics classrooms, the project brings together a focus on curricular materials that support teaching, Lesson Study protocols and materials, and a professional learning community-based professional development model. The project will design and revise professional development and coaching guides and lesson study mathematical resources built around the curricular materials. The project will study changes in instructional practice and impact on student learning. By documenting the supports used in the Oakland Unified School District where the research and development will be conducted, the resources can be used by other districts and in similar work by other research-practice partnerships.

This project hypothesizes that the quality of classroom instruction can be defined by five dimensions - quality of the mathematics; cognitive demand of the tasks; access to mathematics content in the classroom; student agency, authority, and identity; and uses of assessment. The project will use an iterative design process to develop and refine a suite of tool, including a conversation guide to support productive dialogue between teachers and coaches, support materials for building site-based professional learning materials, and formative assessment lessons using Lesson Study as a mechanism to enact reforms of these dimensions. The study will use a pre-post design and natural variation to student the relationships between these dimensions, changes in teachers' instructional practice, and student learning using hierarchical linear modeling with random intercept models with covariates. Qualitative of the changes in teachers' instructional practices will be based on coding of observations based on the TRUmath framework. The study will also use qualitative analysis techniques to identify themes from surveys and interviews on factors that promote or hinder the effectiveness of the intervention.

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