Mathematics

Teaching Students to Reason about Variation and Covariation in Data: What Do We Know and What Do We Need to Find Out?

The purpose of this project is to gather, analyze, and synthesize mathematics and science education research studies published from 1988 to the present that have investigated different approaches to supporting students in grades 6-14 in learning to analyze, interpret, and reason about data.

Lead Organization(s): 
Award Number: 
1920119
Funding Period: 
Mon, 07/01/2019 to Wed, 06/30/2021
Full Description: 

Because data are so much a part of modern life, making sense of data is a skill that benefits all members of society. Reasoning about data has been described as one of the most important cognitive activities and making sense of data is essential for a public's informed civic participation. But the public's ability to make sense of data is not what it should be. There is an important role for educators to play in supporting students' ability (and ultimately the public's ability) to be savvy consumers of data. But education researchers lack a coherent vision of the current best practices for supporting students in analyzing, interpreting, and reasoning about data. Existing research focused on supporting students in learning to analyze, interpret, and reason about data tends to reside in silos by grade band and by math or science domain. The purpose of this project is to gather, analyze, and synthesize mathematics and science education research studies published from 1988 to the present that have investigated different approaches to supporting students in grades 6-14 in learning to analyze, interpret, and reason about data. The researchers will carefully examine the nature of each education intervention and what the researchers found in each case, looking for patterns across studies. The findings of this study can inform mathematics and science education developers in the production of instructional programs for teachers and students.

The researchers will gather, analyze, and synthesize studies in mathematics and science education from 1988 to the present that examine instruction related to variation and covariation in data. The team will first conduct a descriptive synthesis including a wide array of studies (qualitative, single group pre/post, and experimental/quasi-experimental) and examine the nature of interventions in the field. Next, researchers will conduct a statistical meta-regression of experiments and quasi-experiments using Robust Variance Estimation (RVE) to examine how effect size estimates from primary studies depend on intervention characteristics, study design, outcomes of interest, and demographic characteristics of participants in the studies. The project will help researchers across math and science education build on each other's work and ultimately develop and refine highly effective approaches for supporting students in the life-long skill of making sense of data in a complex world.

Invigorating Statistics Teacher Education Through Professional Online Learning (InSTEP)

This project seeks to strengthen the teaching of statistics and data science in grades 6-12 through the design and implementation of an online professional learning environment for teachers. The professional learning environment aims to support in-service teachers in developing stronger content knowledge related to statistics, and knowledge of how to effectively teach statistics in their classrooms.

Project Email: 
Award Number: 
1908760
Funding Period: 
Thu, 08/01/2019 to Mon, 07/31/2023
Project Evaluator: 
Full Description: 

Implementing meaningful statistics education in middle and high schools has been a persistent challenge in the United States. Statistics and data science are critical domains for STEM careers and the general data literacy of the citizenry. This project seeks to strengthen the teaching of statistics and data science in grades 6-12 through the design and implementation of an online professional learning environment for teachers. The professional learning environment aims to support in-service teachers in developing stronger content knowledge related to statistics, and knowledge of how to effectively teach statistics in their classrooms. The project will also evaluate a model of professional development that integrates personalized online learning and microcredentialing (earning small-scale certifications) to better understand its effectiveness in supporting teacher learning. The project will draw from previous work to assemble online modules that engage teachers in doing high-quality statistics and data science tasks, the analysis of video of teachers' and students' work with those tasks, learning a pedagogical framework for teachers to implement the tasks, and exploring guidelines for identifying and developing high-quality statistics and data science tasks. The project will study teacher learning through the use of these modules, and the pathways that teachers choose through them to understand the effectiveness of the model.

The project builds on previous work by the investigators to develop research-based teacher professional development modules that support learning about statistics and statistics education in grades 6-12. Materials currently developed include a series of microcredentials with design features consistent with research on effective teacher professional development. They include opportunities for teachers to engage with statistics content appropriate to the target grade levels they teach, active learning opportunities that engage them with teachers in similar contexts, and a coherent focus that builds on the knowledge and experience teachers bring to the table. The project will take place in iterative phases, beginning with focus groups of middle and high school teachers and district leaders based on first drafts of the materials. This will be followed by cognitive interviews with teachers who engage in the microcredential ecosystem which will inform modifications to the system. Following this phase, cohorts of teachers (25 in the first cohort, 75 in the second) will participate in scaffolded professional development engagement with the materials, and will be assessed with respect to changes in their knowledge and practice. The project will assess changes in teacher knowledge using reliable and valid measures of statistics knowledge and practice. Data will be collected from the online platform regarding teacher engagement and usage to better understand usage and pathways through the materials. The professional learning platform will be made available as a free and open online source at the close of the project.

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Learning Trajectories as a Complete Early Mathematics Intervention: Achieving Efficacies of Economies at Scale

The purpose of this project is to test the efficacy of the Learning and Teaching with Learning Trajectories (LT2) program with the goal of improving mathematics teaching and thereby increasing young students' math learning. LT2 is a professional development tool and a curriculum resource intended for teachers to be used to support early math instruction and includes the mathematical learning goal, the developmental progression, and relevant instructional activities.

Lead Organization(s): 
Award Number: 
1908889
Funding Period: 
Mon, 07/01/2019 to Sun, 06/30/2024
Full Description: 

U.S. proficiency in mathematics continues to be low and early math performance is a powerful predictor of long-term academic success and employability. However, relatively few early childhood degree programs have any curriculum requirements focused on key mathematics topics. Thus, teacher professional development programs offer a viable and promising method for supporting and improving teachers' instructional approaches to mathematics and thus, improving student math outcomes. The purpose of this project is to test the efficacy of the Learning and Teaching with Learning Trajectories (LT2) program with the goal of improving mathematics teaching and thereby increasing young students' math learning. LT2 is a professional development tool and a curriculum resource intended for teachers to be used to support early math instruction. The LT2 program modules uniquely include the mathematical learning goal, the developmental progression, and relevant instructional activities. All three aspects are critical for high-quality and coherent mathematics instruction in the early grades.

This project will address the following research questions: 1) What are the medium-range effects of LT2 on student achievement and the achievement gap? 2) What are the short- and long-term effects of LT2 on teacher instructional approach, beliefs, and quality? and 3) How cost effective is the LT2 intervention relative to the original Building Blocks intervention? To address the research questions, this project will conduct a multisite cluster randomized experimental design, with 90 schools randomly assigned within school districts to either experimental or control groups. Outcome measures for the approximately 250 kindergarten classrooms across these districts will include the Research-based Elementary Math Assessment, observations of instructional quality, a questionnaire focused on teacher beliefs and practices, in addition to school level administrative data. Data will be analyzed using multi-level regression models to determine the effect of the Learning Trajectories intervention on student learning.

Developing and Validating Early Assessments of College Readiness: Differential Effects for Underrepresented Groups, Optimal Timing of Assessments, and STEM-Specific Indicators

This purpose of this project is to develop and validate a range of assessments with a focus on academic preparedness for higher education. The team will explore relevant qualities of assessments such as their differential predictive validity to ensure they are appropriate for underrepresented groups, the optimal grade level to begin assessing readiness, and measures that are most appropriate for predicting STEM-specific readiness.

Project Email: 
Award Number: 
1908630
Funding Period: 
Mon, 07/15/2019 to Wed, 06/30/2021
Project Evaluator: 
Full Description: 

One third of all college freshmen are academically unprepared for entry-level college coursework and require remedial course. That figure is much higher at many colleges. The problem is more acute in STEM disciplines, particularly among students from underrepresented ethnic groups and low socioeconomic status families. This purpose of this project is to develop and validate a range of assessments with a focus on academic preparedness for higher education. The team will explore relevant qualities of assessments such as their differential predictive validity to ensure they are appropriate for underrepresented groups, the optimal grade level to begin assessing readiness, and measures that are most appropriate for predicting STEM-specific readiness.

This project will use two recent and complementary large-scale, nationally representative federal databases: the High School Longitudinal Study of 2009 and the Education Longitudinal Study of 2002. Factor analysis will be used to develop composite variables of college readiness and multilevel regression will be used to develop predictive models on a range of college outcomes to test the predictive validity of composite and individual predictors. The models will be extended to conduct multiple group analyses to test for differential prediction for students from underrepresented groups. The project intends to promote 1) the use of a wider range of assessments of academic preparedness, 2) the use of measures that are more sensitive for assessing college readiness from underrepresented groups and among STEM majors, 3) earlier assessment using indicators and models with predictive validity and 4) progress monitoring of college readiness by providing a detailed example of how that can be developed and implemented. Findings will also raise student, parental, teacher, and other school personnel awareness of the range of factors relevant for preparing students for college.

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Reasoning Language for Teaching Secondary Algebra

This project proposes to study the teaching and learning of algebra in grades 7-9, with a specific focus on the ways in which classroom language explicitly describes properties of and relationships among algebraic objects. The project seeks to investigate the bi-directional relationship between reasoning-rich algebraic discourse and the mathematical meanings students hold for core algebraic concepts such as equations, the equation-solving process, and functions.

Project Email: 
Award Number: 
1908825
Funding Period: 
Sun, 09/01/2019 to Wed, 08/31/2022
Project Evaluator: 
Full Description: 

Decades of research have demonstrated that stronger mathematics classroom discourse, along with the use and connection of multiple mathematical representations, correlates positively with gains in student learning. This relationship is particularly salient in algebra, where diversifying the representations available to students can provide important supports for the development of conceptual understanding. The Reasoning Language for Teaching Secondary Algebra (ReLaTe-SA) project proposes to study the teaching and learning of algebra in grades 7-9, with a specific focus on the ways in which classroom language explicitly describes properties of and relationships among algebraic objects. The project seeks to investigate the bi-directional relationship between reasoning-rich algebraic discourse and the mathematical meanings students hold for core algebraic concepts such as equations, the equation-solving process, and functions. With a focus on the teacher, ReLaTe-SA will analyze classroom narratives about algebraic concepts and procedures and provide an 80-hour professional development program designed to support teachers in developing stronger explanations of algebraic objects, their properties, and their relationships.

The ReLaTe-SA project will investigate three aspects of teacher discourse practice related to algebra. First, the project will study the discourse and discourse routines that teachers use to explain algebraic objects, their properties, and their relationships. This will be accomplished through the development and deployment of an assessment called the Survey of Algebraic Language and Reasoning to identify teachers' discursive routines and narratives in the context of algebra. The instrument asks teachers to interpret student work and explanations by describing the student's mathematical reasoning and underlying mathematical understandings. Second, the project will support potential growth in teachers' algebraic discourse practices through an 80-hour professional development intervention focused on discourse in algebra. The impact of this intervention will be measured by changes to teachers' response patterns on the Survey of Algebraic Language and Reasoning, analyses of teachers' work within the professional development, and the analysis of classroom observations after the professional development has concluded. Third, the project will seek to understand the ways in which teachers develop lessons that explicitly focus on the development of students' algebraic reasoning and discourse. This goal will be realized through analyses of the tasks, plans, and implementations of mathematics lessons in participating teachers' classrooms. Three cohorts of 12 teachers each will be recruited for the project. Based on the results of this exploratory project, the team intends to follow up with a larger-scale study of the professional development and its impact on the teaching and learning of algebra.

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Building a Teacher Knowledge Base for the Implementation of High-Quality Instructional Resources through the Collaborative Investigation of Video Cases (Collaborative Research: Murray)

This project will address the pressing national need to generate shared, practice-based knowledge about how to implement freely available, high-quality instructional resources (mathematics formative assessment lessons) that have been shown to produce significant gains in student learning outcomes. It will expand a professional development model (Analyzing Instruction in Mathematics using the Teaching for Robust Understanding Framework (AIM-TRU)) that supports teacher learning about effective lesson implementation.

Lead Organization(s): 
Award Number: 
1908319
Funding Period: 
Mon, 07/01/2019 to Fri, 06/30/2023
Full Description: 

This project will address the pressing national need to generate shared, practice-based knowledge about how to implement freely available, high-quality instructional resources (mathematics formative assessment lessons) that have been shown to produce significant gains in student learning outcomes. It will expand a professional development model (Analyzing Instruction in Mathematics using the Teaching for Robust Understanding Framework (AIM-TRU)) that supports teacher learning about effective lesson implementation. The backbone of AIM-TRU is a growing, open repository of video cases available to teachers and teacher educators across the U.S. who use or are interested in using the lessons. The repository will include tools such as a facilitator's guide to support teachers and teacher educators to engage in the model and collaboratively investigate the video cases. Consequently, the work will have the potential to engage teachers and teacher educators in improving mathematics education at scale. Because the video cases will capture implementation and ideas for improving instruction in schools serving populations who are underrepresented in mathematics, AIM-TRU will serve to improve mathematics education equitably.

Research questions focus on what teachers learn about high-quality mathematics instruction and instructional materials within a community of practice, and how that learning influences their teaching. In AIM-TRU, teachers engage in the collaborative investigation of video cases utilizing a shared repertoire that includes questioning protocols adapted from the Teaching for Robust Understanding (TRU) framework. This framework articulates five dimensions of classroom instruction that are necessary and sufficient to support students in becoming powerful mathematical thinkers. This affords teachers opportunities to use the TRU dimensions as lenses to diagnose common problems of practice that arise in implementation, and propose innovations and theories for improving instruction that can be tested in real classrooms and documented in new video cases. Analytic tools will be used from frame analysis to produce empirical evidence of what teachers are learning about instruction and instructional materials along the five dimensions of TRU. These data will be mapped to a random sample of video recordings of participating teachers' instruction, scored using the TRU Math Rubric, in order to link learning outcomes from the professional development to changes in instruction. Addressing these research questions will provide a deeper understanding and empirical evidence of learning within teacher collectives, the pressing national need to develop mechanisms to produce collective professional knowledge for teaching, and further efforts to understand the types of knowledge required for effective teaching.

Building a Teacher Knowledge Base for the Implementation of High-Quality Instructional Resources through the Collaborative Investigation of Video Cases (Collaborative Research: Jabon)

This project will address the pressing national need to generate shared, practice-based knowledge about how to implement freely available, high-quality instructional resources (mathematics formative assessment lessons) that have been shown to produce significant gains in student learning outcomes. It will expand a professional development model (Analyzing Instruction in Mathematics using the Teaching for Robust Understanding Framework (AIM-TRU)) that supports teacher learning about effective lesson implementation.

Lead Organization(s): 
Award Number: 
1908311
Funding Period: 
Mon, 07/01/2019 to Fri, 06/30/2023
Full Description: 

This project will address the pressing national need to generate shared, practice-based knowledge about how to implement freely available, high-quality instructional resources (mathematics formative assessment lessons) that have been shown to produce significant gains in student learning outcomes. It will expand a professional development model (Analyzing Instruction in Mathematics using the Teaching for Robust Understanding Framework (AIM-TRU)) that supports teacher learning about effective lesson implementation. The backbone of AIM-TRU is a growing, open repository of video cases available to teachers and teacher educators across the U.S. who use or are interested in using the lessons. The repository will include tools such as a facilitator's guide to support teachers and teacher educators to engage in the model and collaboratively investigate the video cases. Consequently, the work will have the potential to engage teachers and teacher educators in improving mathematics education at scale. Because the video cases will capture implementation and ideas for improving instruction in schools serving populations who are underrepresented in mathematics, AIM-TRU will serve to improve mathematics education equitably.

Research questions focus on what teachers learn about high-quality mathematics instruction and instructional materials within a community of practice, and how that learning influences their teaching. In AIM-TRU, teachers engage in the collaborative investigation of video cases utilizing a shared repertoire that includes questioning protocols adapted from the Teaching for Robust Understanding (TRU) framework. This framework articulates five dimensions of classroom instruction that are necessary and sufficient to support students in becoming powerful mathematical thinkers. This affords teachers opportunities to use the TRU dimensions as lenses to diagnose common problems of practice that arise in implementation, and propose innovations and theories for improving instruction that can be tested in real classrooms and documented in new video cases. Analytic tools will be used from frame analysis to produce empirical evidence of what teachers are learning about instruction and instructional materials along the five dimensions of TRU. These data will be mapped to a random sample of video recordings of participating teachers' instruction, scored using the TRU Math Rubric, in order to link learning outcomes from the professional development to changes in instruction. Addressing these research questions will provide a deeper understanding and empirical evidence of learning within teacher collectives, the pressing national need to develop mechanisms to produce collective professional knowledge for teaching, and further efforts to understand the types of knowledge required for effective teaching.

Building a Teacher Knowledge Base for the Implementation of High-Quality Instructional Resources through the Collaborative Investigation of Video Cases (Collaborative Research: Wilson)

This project will address the pressing national need to generate shared, practice-based knowledge about how to implement freely available, high-quality instructional resources (mathematics formative assessment lessons) that have been shown to produce significant gains in student learning outcomes. It will expand a professional development model (Analyzing Instruction in Mathematics using the Teaching for Robust Understanding Framework (AIM-TRU)) that supports teacher learning about effective lesson implementation.

Lead Organization(s): 
Award Number: 
1908185
Funding Period: 
Mon, 07/01/2019 to Fri, 06/30/2023
Full Description: 

This project will address the pressing national need to generate shared, practice-based knowledge about how to implement freely available, high-quality instructional resources (mathematics formative assessment lessons) that have been shown to produce significant gains in student learning outcomes. It will expand a professional development model (Analyzing Instruction in Mathematics using the Teaching for Robust Understanding Framework (AIM-TRU)) that supports teacher learning about effective lesson implementation. The backbone of AIM-TRU is a growing, open repository of video cases available to teachers and teacher educators across the U.S. who use or are interested in using the lessons. The repository will include tools such as a facilitator's guide to support teachers and teacher educators to engage in the model and collaboratively investigate the video cases. Consequently, the work will have the potential to engage teachers and teacher educators in improving mathematics education at scale. Because the video cases will capture implementation and ideas for improving instruction in schools serving populations who are underrepresented in mathematics, AIM-TRU will serve to improve mathematics education equitably.

Research questions focus on what teachers learn about high-quality mathematics instruction and instructional materials within a community of practice, and how that learning influences their teaching. In AIM-TRU, teachers engage in the collaborative investigation of video cases utilizing a shared repertoire that includes questioning protocols adapted from the Teaching for Robust Understanding (TRU) framework. This framework articulates five dimensions of classroom instruction that are necessary and sufficient to support students in becoming powerful mathematical thinkers. This affords teachers opportunities to use the TRU dimensions as lenses to diagnose common problems of practice that arise in implementation, and propose innovations and theories for improving instruction that can be tested in real classrooms and documented in new video cases. Analytic tools will be used from frame analysis to produce empirical evidence of what teachers are learning about instruction and instructional materials along the five dimensions of TRU. These data will be mapped to a random sample of video recordings of participating teachers' instruction, scored using the TRU Math Rubric, in order to link learning outcomes from the professional development to changes in instruction. Addressing these research questions will provide a deeper understanding and empirical evidence of learning within teacher collectives, the pressing national need to develop mechanisms to produce collective professional knowledge for teaching, and further efforts to understand the types of knowledge required for effective teaching.

Building Students' Data Literacy through the Co-design of Curriculum by Mathematics and Art Teachers (Collaborative Research: Matuk)

This project aims to enact and study the co-design of classroom activities by mathematics and visual arts teachers to promote middle school students' data literacy.

Lead Organization(s): 
Award Number: 
1908557
Funding Period: 
Mon, 07/01/2019 to Wed, 06/30/2021
Full Description: 

The aim of this project is to enact and study a process in which middle school teachers of mathematics and visual arts co-design and teach activities that combine math and art to teach data science. Many existing efforts to promote data literacy are grounded in mathematical concepts of central tendency and variation, and typically are narrowly focused in single subject domains. Taking an art-based perspective on data science has the potential to promote student relevance, accessibility, engagement, reasoning, and meaning-making with data science. Moreover, visualization technology has advanced to a degree that the relation between the information in data and visual aesthetic can be leveraged easily. To explore the opportunity this offers, research on this project will examine how to equip teachers to develop such interdisciplinary pedagogical approaches to cultivate their students' data literacy. This exploratory project will provide support for 12 teachers during summer workshops and during the school year as these teachers implement their co-designed units in their classrooms. The work addresses the following questions: (1) How do we support effective co-design of data literacy units among art teachers, mathematics teachers, and researchers? (2) How are teachers able to use the unit materials in their classrooms to engage students in data literacy? And (3) How does an art-based approach support students' data literacy? Answers to these questions will build an understanding of how to support interdisciplinary curriculum design collaborations among researchers and teachers. They will also show how art-integrated, maker-oriented activities can support middle school learners' data literacy development; and how to design technologies that are accessible and powerful to teachers and learners in these interdisciplinary environments.

Through summer workshops and year-round design collaborations, the project will iteratively design, test and refine four units for middle school classrooms, including activities, tools, and assessments, to promote students' data literacy. Data will be collected from co-design sessions as well as classroom-enactments, and will include observations, video/audio recordings, student- and teacher-generated artifacts, and pre and post assessments of students' knowledge and self-efficacy. Mixed methods analyses of these data, and syntheses of findings across participants, classroom enactments, and project years, will explore effective ways to support co-design among art teachers, mathematics teachers, and researchers; and the impact of art-integrated activities on students' data literacy. This project will reach 12 teachers and their students across 6 New York city schools. By building capacity and knowledge about how to initiate and sustain teachers' interdisciplinary curriculum collaborations, the project will have broader impact. Refined project materials, including pedagogical approaches, toolkits and adaptable classroom activities, will be disseminated to facilitate classroom adoption by other educators who wish to undertake similar art-integrated data literacy curriculum design collaborations, and will thus ultimately broaden participation in data science among diverse youth within and beyond New York City.

Building Students' Data Literacy through the Co-design of Curriculum by Mathematics and Art Teachers (Collaborative Research: Vacca)

The aim of this project is to enact and study a process in which middle school teachers of mathematics and visual arts co-design and teach activities that combine math and art to teach data science.

Lead Organization(s): 
Award Number: 
1908142
Funding Period: 
Mon, 07/01/2019 to Wed, 06/30/2021
Full Description: 

The aim of this project is to enact and study a process in which middle school teachers of mathematics and visual arts co-design and teach activities that combine math and art to teach data science. Many existing efforts to promote data literacy are grounded in mathematical concepts of central tendency and variation, and typically are narrowly focused in single subject domains. Taking an art-based perspective on data science has the potential to promote student relevance, accessibility, engagement, reasoning, and meaning-making with data science. Moreover, visualization technology has advanced to a degree that the relation between the information in data and visual aesthetic can be leveraged easily. To explore the opportunity this offers, research on this project will examine how to equip teachers to develop such interdisciplinary pedagogical approaches to cultivate their students' data literacy. This exploratory project will provide support for 12 teachers during summer workshops and during the school year as these teachers implement their co-designed units in their classrooms. The work addresses the following questions: (1) How do we support effective co-design of data literacy units among art teachers, mathematics teachers, and researchers? (2) How are teachers able to use the unit materials in their classrooms to engage students in data literacy? And (3) How does an art-based approach support students' data literacy? Answers to these questions will build an understanding of how to support interdisciplinary curriculum design collaborations among researchers and teachers. They will also show how art-integrated, maker-oriented activities can support middle school learners' data literacy development; and how to design technologies that are accessible and powerful to teachers and learners in these interdisciplinary environments.

Through summer workshops and year-round design collaborations, the project will iteratively design, test and refine four units for middle school classrooms, including activities, tools, and assessments, to promote students' data literacy. Data will be collected from co-design sessions as well as classroom-enactments, and will include observations, video/audio recordings, student- and teacher-generated artifacts, and pre and post assessments of students' knowledge and self-efficacy. Mixed methods analyses of these data, and syntheses of findings across participants, classroom enactments, and project years, will explore effective ways to support co-design among art teachers, mathematics teachers, and researchers; and the impact of art-integrated activities on students' data literacy. This project will reach 12 teachers and their students across 6 New York city schools. By building capacity and knowledge about how to initiate and sustain teachers' interdisciplinary curriculum collaborations, the project will have broader impact. Refined project materials, including pedagogical approaches, toolkits and adaptable classroom activities, will be disseminated to facilitate classroom adoption by other educators who wish to undertake similar art-integrated data literacy curriculum design collaborations, and will thus ultimately broaden participation in data science among diverse youth within and beyond New York City.

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