Mathematics

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. 

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

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

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

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

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

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

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

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

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

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

Developing and Investigating Unscripted Mathematics Videos

This project will use an alternative model for online videos to develop video units that feature the unscripted dialogue of pairs of students. The project team will create a repository of 6 dialogic mathematics video units that target important Algebra 1 and 2 topics for high school and upper middle school students, though the approach can be applied to any STEM topic, for any age level.

Lead Organization(s): 
Award Number: 
1907782
Funding Period: 
Sun, 09/01/2019 to Thu, 08/31/2023
Full Description: 

This project responds to the recent internet phenomenon of widespread accessibility to online instructional videos, which offer many benefits, such as student control of the pace of learning. However, these videos primarily focus on a single speaker working through procedural problems and providing an explanation. While the immense reach of free online instructional videos is potentially transformative, this potential can only be attained if access transcends physical availability to also include entry into important disciplinary understandings and practices, and only if the instructional method pushes past what would be considered outdated pedagogy in any other setting than a digital one. This project will use an alternative model for online videos, originally developed for a previous exploratory project, to develop 6 video units that feature the unscripted dialogue of pairs of students. The project team will use the filming and post-production processes established during the previous grant to create a repository of 6 dialogic mathematics video units that target important Algebra 1 and 2 topics for high school and upper middle school students, though the approach can be applied to any STEM topic, for any age level. They will also conduct 8 research studies to investigate the promise of these unscripted dialogic videos with a diverse population to better understand the vicarious learning process, which refers to learning from video- or audio-taped presentations of other people learning. Additionally, the project team will provide broader access to the project videos and support a variety of users, by: (a) subtitling the videos and checking math task statements for linguistic accessibility; (b) representing diversity of race, ethnicity, and language in both the pool of students who appear in the videos and the research study participants; (c) providing teachers with an array of resources including focus questions to pose in class with each video, printable task worksheets, specific ways to support dialogue about the videos, and alignment of the video content with Common Core mathematics standards and practices; and (d) modernizing the project website and making it functional across a variety of platforms.

The videos created for this project will feature pairs of students (called the talent), highlighting their unscripted dialogue, authentic confusion, and conceptual resources. Each video unit will consist of 7 video lessons (each split into 4-5 short video episodes) meant to be viewed in succession to support conceptual development over time. The project will build upon emerging evidence from the exploratory grant that as students engage with videos that feature peers grappling with complex mathematics, they can enter a quasi-collaborative relationship with the on-screen talent to learn complex conceptual content and engage in authentic mathematical practices. The research focuses on the questions: 1. What can diverse populations of vicarious learners learn mathematically from dialogic videos, and how do the vicarious learners orient to the talent in the videos? 2. What is the nature of vicarious learners' evolving ways of reasoning as they engage with multiple dialogic video lessons over time and what processes are involved in vicarious learning? and, 3. What instructional practices encourage a classroom community to adopt productive ways of reasoning from dialogic videos? To address the first question, the project team will conduct two Learning Outcomes and Orientation Studies, in which they analyze students' learning outcomes and survey responses after they have learned from one of the video units in a classroom setting. Before administering an assessment to a classroom of students, they will first conduct an exploratory Interpretation Study for each unit, in which they link the mathematical interpretations that VLs generate from viewing the project videos with their performance on an assessment instrument. Both types of studies will be conducted twice, once for each of two video units - Exponential Functions and Meaning and Use of Algebraic Symbols. For the second research question, the project team will identify a learning trajectory associated with each of four video units. These two learning trajectories will inform the instructional planning for the classroom studies by identifying what meaningful appropriation can occur, as well as conceptual challenges for VLs. By delivering learning trajectories for two additional units, the project can contribute to vicarious learning theory by identifying commonalities in learning processes evident across the four studies. For the final research question, the project team will investigate how instructors can support students with the instrumental genesis process, which occurs through a process called instrumental orchestration, as they teach the two videos on exponential functions and algebraic symbols.

Strengthening Middle School Mathematical Argumentation through Teacher Coaching: Bridging from Professional Development to Classroom Practice

This project is a professional learning experience for middle school teachers to support them in developing five mathematical practices in their teaching focused on mathematical argumentation - creating mathematical arguments, using appropriate tools strategically, looking for and make use of structure, attending to precision, and looking for and express regularity in repeated reasoning.

Lead Organization(s): 
Award Number: 
2000545
Funding Period: 
Mon, 07/01/2019 to Fri, 06/30/2023
Full Description: 

The Bridging Professional Development project is a professional learning experience for middle school teachers to support them in developing five mathematical practices in their teaching focused on mathematical argumentation. These practices are: create mathematical arguments, use appropriate tools strategically, look for and make use of structure, attend to precision, and look for and express regularity in repeated reasoning. Mathematics argumentation is an important component of complex problem solving and supporting students in understanding the why, not just the how, of mathematics. The professional development intervention consists of summer workshop focused on approximations of teaching practice, and coaching during the school year. The coaching component includes face-to-face coaching and a video-based tool that allows teachers and coaches to engage with records of classroom interactions. The project expands the successful Bridging professional development work by adding four additional mathematical practices that relate to argumentation, adding the coaching component, collecting data on students' equitable participation in classroom discussions, and piloting an impact study to determine whether the professional development that includes coaching leads to improved mathematics teaching and learning, and the mechanisms by which that hypothesized improvement occurs.

The Bridging series of professional development projects are built on a theoretical framework that begins with providing teachers with opportunities to engage in meaningful mathematics teaching practices, identify teaching moves that would support students in learning those practices, and to try out those moves with other teachers in approximations of teaching practice. The outcomes of such activity are increased teacher knowledge that can be mobilized in the planning and enactment of lessons, and improved pedagogical moves in the classroom. This in turn is likely to lead to increased student engagement and mathematics achievement. In this award, Bridging adds cycles of coaching to support teachers in translating lessons learned from approximations of practice to the work in their classrooms with students, and to provide ongoing school-year support for implementation. The research components of the project focus on understanding the practice of the coaches, including the design and deployment of coaching training and coaching sessions, as it relates to teachers' abilities to foster stronger student engagement in mathematical practices. The project will recruit 25 teachers at middle schools with experienced mathematics coaches to participate, with teachers directed to select a single focus class for data collection. Case studies will be pursued with six teachers and three coaches that represent diverse backgrounds, experiences, and levels of prior knowledge. Video records of coaching training and sessions will be collected and analyzed, along with lessons plans and teacher-enacted lessons, to determine the influence of the coaching on practice. The study will also investigate the ways in which teacher engagement in the professional developments leads to changes in teacher practice and student outcomes. Video records of practice, written lesson plans, student work, and interviews will be collected and analyzed to determine the impact on teaching practice. Teachers' mathematical knowledge for teaching will also be assessed at key points in the project to assess teacher learning, and student standardized assessment scores and performance assessment outcomes will be collected to assess student learning.

This project was previously funded under award #1907561.

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.

Lead Organization(s): 
Award Number: 
2001116
Funding Period: 
Sun, 09/01/2019 to Wed, 08/31/2022
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.

This project was previously funded under award #1908825.

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