Achievement/Growth

Developing Leaders, Transforming Practice in K-5 Mathematics: An Examination of Models for Elementary Mathematics Specialists (Collaborative Research: Rigelman)

This project will study the Developing Leaders Transforming Practice (DLTP) intervention, which aims to develop teacher leaders, improve teachers' instructional practices, and increase student mathematics understanding and achievement.

Lead Organization(s): 
Award Number: 
1906682
Funding Period: 
Sun, 09/01/2019 to Thu, 08/31/2023
Project Evaluator: 
RMC Research
Full Description: 

Minimal rigorous research has been conducted on the effect of various supports for quality mathematics instruction and providing guidance on the development and use of Elementary Mathematics Specialists (EMSs) on student achievement. Portland Public Schools (PPS), Portland State University, and RMC Research Corporation will study the Developing Leaders Transforming Practice (DLTP) intervention, which aims to improve teachers' instructional practices, increase student mathematics understanding and achievement. The project team will evaluate the efficacy and use of EMSs by testing four implementation models that consider the various ways EMSs are integrated into schools. DLTP builds on EMS research, investigating EMSs both as elementary mathematics teachers and coaches by articulating four models and examining their efficacy for both student and teacher learning. This study has the potential to provide benefits both within and beyond PPS as it informs the preparation and use of EMSs. Determining which model is best in certain contexts provides a focus for the expansion of mathematics support.

DLTP enhances the research base by examining the effect of teacher PD on student achievement through a rigorous quasi-experimental design. The project goals will be met by addressing 4 research questions: 1) What is the effect of the intervention on teacher leadership?; 2) What is the effect of the intervention on teachers' use of research-based instructional practices?; 3) What is the effect of the intervention on a school's ability to sustain ongoing professional learning for teachers?; and 4) What is the effect of the intervention on student mathematics achievement? Twelve elementary schools in PPS will select elementary teachers to participate in the DLTP and adopt an implementation model that ranges from direct to diffuse engagement with students: elementary mathematics teacher, grade level coach, grade-level and building-level coach, or building-level coach. The research team will conduct 4 major studies that include rigorous quasi-experimental designs and a multi-method approach to address the research questions: leadership study, instructional practices study, school study, and student achievement study. Several tools will be created by the project - a leadership rubric designed to measure changes in EMS mathematics leadership because of the project and a 5-part teacher survey designed capture EMS leadership skills, pedagogical content knowledge, use of research-based practices, and school climate for mathematics learning as well as implementation issues.

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.

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.

Developing the Science Comprehensive Online Learning Platform for Rural School Science Teacher Development

This project will develop, evaluate, and compare the effectiveness of newly-designed online learning platform with traditional face-to-face PD in supporting rural high school science teachers' implementation of an existing biology curriculum aligned with the Next Generation Science Standards (NGSS).

Lead Organization(s): 
Award Number: 
1908937
Funding Period: 
Sun, 09/01/2019 to Wed, 08/31/2022
Full Description: 

Rural school districts in the US face unique challenges: isolation in small farm communities, significant distances between communities, minimal funding, and low teacher salaries. They also serve high numbers of diverse and low-income students, who deserve equitable access to high quality science learning opportunities. Effective online professional development (PD) is needed for teachers working in isolated rural communities where high quality face-to-face PD may be economically impractical for districts to offer. This project will develop, evaluate, and compare the effectiveness of newly-designed online learning platform with traditional face-to-face PD in supporting rural high school science teachers' implementation of an existing biology curriculum aligned with the Next Generation Science Standards (NGSS). The online learning platform will be modeled after successful face-to-face PD features: (1) job-embedded - learning occurs within the context of teachers' classroom instruction, (2) collaborative - teachers share experiences in implementing new practices, and (3) content-specific - teachers develop disciplinary content and instructional practices that support students' understanding of science. Once developed and refined, the online PD platform can be used broadly across other contexts and content areas.

Over a three year period, this project will develop, evaluate, and then compare an online PD platform for supporting rural science teachers in implementing the Towards High School Biology (THSB) curriculum with a traditional face-to-face PD. In year one, the research team will iteratively develop the online platform and adapt the already developed face-to-face PD for implementing THSB to an online format. Utilizing Curator, a social learning platform developed by HT2Labs, project researchers will embed teacher learning that is situated with their own classroom contexts, is asynchronously and synchronously collaborative, and is focused on the THSB curriculum content. In years two and three, forty eight rural middle-school science educators will be recruited from southwest Kansas and randomly assigned to online PD (treatment) or face-to-face PD (comparison). Using mixed methodology, the project will examine if differences exist between the conditions in regards to teacher content knowledge, teacher self-efficacy in using new practices, teacher classroom practices, and student learning outcomes. It is hypothesized that there should be no differences between conditions in fostering successful implementation of evidence-based science practices and student outcomes, demonstrating the success of an online modality to support deep conceptual change in teachers' instructional practices. Furthermore, lessons learned in developing and investigating a science comprehensive online learning platform can inform application to other disciplinary content (e.g., physics, chemistry, Earth and space sciences) and across other grade level and school contexts.

 

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.

Case Studies of a Suite of Next Generation Science Instructional, Assessment, and Professional Development Materials in Diverse Middle School Settings

This project addresses a gap between vision and implementation of state science standards by designing a coordinated suite of instructional, assessment and teacher professional learning materials that attempt to enact the vision behind the Next Generation Science Standards. The study focuses on using state-of-the-art technology to create an 8-week long, immersive, life science field experience organized around three investigations.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
2125844
Funding Period: 
Mon, 07/01/2019 to Sun, 12/31/2023
Full Description: 

New state science standards are ambitious and require important changes to instructional practices, accompanied by a coordinated system of curriculum, assessment, and professional development materials. This project addresses a gap between vision and implementation of such standards by designing a coordinated suite of instructional, assessment and teacher professional learning materials that attempt to enact the vision behind the Next Generation Science Standards. The study focuses on the design of such materials using state-of-the-art technology to create an 8-week long, immersive, life science field experience organized around three investigations. Classes of urban students in two states will collect data on local insect species with the goal of understanding, sharing, and critiquing environmental management solutions. An integrated learning technology system, the Learning Navigator, draws on big data to organize student-gathered data, dialogue, lessons, an assessment information. The Learning Navigator will also amplify the teacher's role in guiding and fostering next generation science learning. This project advances the field through an in-depth exploration of the goals for the standards documents. The study begins to address questions about what works when, where, and for whom in the context of the Next Generation Science Standards.

The project uses a series of case studies to create, test, evaluate and refine the system of instructional, assessment and professional development materials as they are enacted in two distinct urban school settings. It is designed with 330 students and 22 teachers in culturally, racially and linguistically diverse, under-resourced schools in Pennsylvania and California. These schools are located in neighborhoods that are economically challenged and have students who demonstrate patterns of underperformance on state standardized tests. It will document the process of team co-construction of Next Generation Science-fostering instructional materials; develop assessment tasks for an instructional unit that are valid and reliable; and, track the patterns of use of the instructional and assessment materials by teachers. The study will also record if new misconceptions are revealed as students develop Next Generation Science knowledge,  comparing findings across two diverse school locations in two states. Data collection will include: (a) multiple types of data to establish validity and reliability of educational assessments, (b) the design, evaluation and use of a classroom observation protocol to gather information on both frequency and categorical degree of classroom practices that support the vision, and (c) consecutive years of ten individual classroom enactments through case studies analyzed through cross-case analyses. This should lead to stronger and better developed understandings about what constitutes strong Next Generation Science learning and the classroom conditions, instructional materials, assessments and teacher development that foster it.

This project was previously funded under award #1907944.

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.

Improving Grades 6-8 Students' Mathematics Achievement in Modeling and Problem Solving through Effective Sequencing of Instructional Practices

This project will provide structured and meaningful scaffolds for teachers in examining two research-based teaching strategies hypothesized to positively impact mathematics achievement in the areas of mathematical modeling and problem solving. The project investigates whether the order in which teachers apply these practices within the teaching of mathematics content has an impact on student learning.

Project Email: 
Lead Organization(s): 
Award Number: 
1907840
Funding Period: 
Mon, 07/01/2019 to Fri, 06/30/2023
Project Evaluator: 
Kurt Steuck
Full Description: 

The Researching Order of Teaching project will provide structured and meaningful scaffolds for teachers in examining two research-based teaching strategies hypothesized to positively impact mathematics achievement in the areas of mathematical modeling and problem solving. The first strategy, Explicit Attention to Concepts (EAC), is a set of practices that draw students' attention specifically to mathematical concepts in ways that extend beyond memorization, procedures, or application of skills. This strategy may include teachers asking students to connect multiple mathematical representations, compare solution strategies, discuss mathematical reasoning underlying procedures, or to identify a main mathematical idea in a lesson and how it fits into the broader mathematical landscape. The second strategy, Student Opportunities to Struggle (SOS), entails providing students with time and space to make sense of graspable content, overcoming confusion points, stimulating personal sense-making, building perseverance, and promoting openness to challenge. This strategy may include teachers assigning problems with multiple solution strategies, asking students to look for patterns and make conjectures, encouraging and promoting discourse around confusing or challenging ideas, and asking students for extended mathematical responses. This project investigates whether the order in which teachers apply these practices within the teaching of mathematics content has an impact on student learning. This study builds on previous work that had identified an interaction between the EAC and SOS instructional strategies, and associated teacher reporting of stronger use of the practices with higher student mathematics achievement.

The project will have four key design features. First, the project will adopt and extend the research-based EAC/SOS conceptual framework, and explicitly responds to the call for further research on the interactions. Second, the project will focus on the mathematical areas of modeling and problem solving, two complex and critical competencies for all students in the middle grades. Third, the project will position teachers as collaborators in the research with needed expertise. Finally, the project will make use of research methods from crossover clinical trials to implementation in classrooms. The project aims to identify the affordances and constraints of the EAC/SOS framework in the design and development of instructional practices, to identify student- and teacher-level factors associated with changes in modeling and problem solving outcomes, to analyze teachers' implementations EAC and SOS in teaching modeling and problem solving and to associate those implementation factors with student achievement changes, and to determine whether the ordering of these two strategies correlates with differences in achievement. The project will collect classroom observation data and make use of existing tools to obtain reliable and valid ratings of the EAC and SOS strategies in action.The design of the study features a randomized 2 x 2 cluster crossover trial with a sample of teachers for 80% power. The project builds on existing state infrastructure and relationships with a wide array of school districts in the context of professional development, and aims to create a formal Teacher-Researcher Alliance for Investigating Learning as a part of the project work.

Using Animated Contrasting Cases to Improve Procedural and Conceptual Knowledge in Geometry

This project aims to support stronger student outcomes in the teaching and learning of geometry in the middle grades through engaging students in animated contrasting cases of worked examples. The project will design a series of animated geometry curricular materials on a digital platform that ask students to compare different approaches to solving the same geometry problem. The study will measure changes in students' procedural and conceptual knowledge of geometry after engaging with the materials and will explore the ways in which teachers implement the materials in their classrooms.

Award Number: 
1907745
Funding Period: 
Thu, 08/01/2019 to Sun, 07/31/2022
Full Description: 

This project aims to support stronger student outcomes in the teaching and learning of geometry in the middle grades through engaging students in animated contrasting cases of worked examples. Animated contrasting cases are a set of two worked examples for the same geometry problem, approached in different ways. The animations show the visual moves and annotations students would make in solving the problems. Students are asked to compare and discuss the approaches. This theoretically-grounded approach extends the work of cognitive scientists and mathematics educators who have shown this approach supports strong student learning in algebra. The project will design a series of animated geometry curricular materials on a digital platform that ask students to compare different approaches to solving the same geometry problem. The study will measure changes in students' procedural and conceptual knowledge of geometry after engaging with the materials and will explore the ways in which teachers implement the materials in their classrooms. This work is particularly important as geometry is an understudied area in mathematics education, and national and international assessments at the middle school level consistently identify geometry as a mathematics content area in which students score the lowest.

This project draws on prior work that documents the impact of comparison on students' learning in algebra. Providing students with opportunities to compare multiple strategies is recommended by a range of mathematics policy documents, as research has shown this approach promotes flexibility and enhances conceptual knowledge and procedural fluency. More specifically, the approach allows students to compare the effectiveness and efficiency of mathematical arguments in the context of problem solving. An initial pilot study on non-animated contrasting cases in geometry shows promise for the general approach and suggests that animating the cases has the potential for stronger student learning gains. This study will examine the extent to which the animated cases improve students' conceptual and procedural knowledge of geometry and identify factors that relate to changes in knowledge. The project team will develop 24 worked example contrasting cases based on design principles from the prior work in algebra. The materials will be implemented in four treatment classrooms in the first cycle, revised, and then implemented in eight treatment classrooms. Students' written work will be collected along with data on the nature of the classroom discussions and small-group interviews with students. Teachers' perspectives on lessons will also be collected to support revision and strengthening of the materials. Assessments of students' geometry knowledge will be developed using measures with demonstrated validity and reliability to measure changes in student learning.

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