Quantitative

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.

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.

Aligning the Science Teacher Education Pathway: A Networked Improvement Community

This project will study the activities of a Networked Improvement Community (NIC) as a vehicle to bridge gaps across four identified steps along the science teacher training and development pathways within local contexts of 8 participating universities. The overarching goal of the project is to strengthen the capacity of universities and school districts to reliably produce teachers of science who are knowledgeable about and can effectively enact the Next Generation Science Standards (NGSS), although prepared in varied organizational contexts.

Award Number: 
1908900
Funding Period: 
Mon, 07/01/2019 to Fri, 06/30/2023
Full Description: 

California State University will study the activities of a Networked Improvement Community (NIC) as a vehicle to bridge gaps across four identified steps along the science teacher training and development pathways within local contexts of 8 participating universities (NIC sites). Networked Improvement Community (NIC) will co-create a shared vision and co-defined research agenda between university researchers, science educators and school district practitioners working together to reform teacher education across a variety of local contexts. By studying outcomes of shared supports and teacher tools for use in multiple steps along the science teacher education pathway, researchers will map variation existing in the system and align efforts across the science teacher education pathway. This process will integrate an iterative nature of educational change in local contexts impacting enactment of the NGSS in both university teacher preparation programs and in school district professional training activities and classrooms.

The overarching goal of the project is to strengthen the capacity of universities and school districts to reliably produce teachers of science who are knowledgeable about and can effectively enact the Next Generation Science Standards (NGSS), although prepared in varied organizational contexts. The project will accomplish this goal 1) leveraging the use of an established Networked Improvement Community, composed of science education faculty from eight university campuses and by 2) improving and studying coherence in the steps along the science teacher education pathway within and across these universities and school districts. The project will use a mixed methods approach to data collection and analysis. Consistent with Improvement Science Theory, research questions will be co-defined by all stakeholders.

Getting Unstuck: Designing and Evaluating Teacher Resources to Support Conceptual and Creative Fluency with Programming

The project will create opportunities for teachers to develop programming content knowledge and new understandings of the creative possibilities in computer science education, thereby increasing opportunities for students to develop conceptual and creative fluency with programming.

Lead Organization(s): 
Award Number: 
1908110
Funding Period: 
Mon, 07/01/2019 to Wed, 06/30/2021
Full Description: 

The project will create opportunities for teachers to develop programming content knowledge and new understandings of the creative possibilities in computer science education, thereby increasing opportunities for students to develop conceptual and creative fluency with programming. K-12 introductory programming experiences are often highly scaffolded, and it can be challenging for students to transition from constrained exercises to open-ended programming activities encountered later in-and out of-school. Teachers can provide critical support to help students solve problems and develop the cognitive, social, and emotional capacities required for conceptually and creatively complex programming challenges. Teachers - particularly elementary and middle school teachers, especially in rural and Title I schools - often lack the programming content knowledge, skills, and practices needed to support deeper and more meaningful programming experiences for students. Professional development opportunities can cultivate teacher expertise, especially when supported by curricular materials that bridge teachers' professional learning and students' classroom learning. This research responds to these needs, addressing key national priorities for increasing access to high-quality K-12 computer science education for all students through teacher professional development.

The project will involve the design and evaluation of (1) an online learning experience for teachers to develop conceptual and creative fluency through short, daily programming prompts (featuring the Scratch programming environment), and (2) educative curricular materials for the classroom (based on the online experience). The online experience and curricular materials will be developed in collaboration with three 4th through 6th-grade rural or Title I teachers. The project will evaluate teacher learning in the online experience using mixed-methods analyses of pre/post-survey data of teachers' perceived expertise and quantitative analyses of teachers' programs and evolving conceptual knowledge. Three additional 4th through 6th-grade teachers will pilot the curricular materials in their classrooms. The six pilot teachers will maintain field journals about their experiences and will participate in interviews, evaluating use of the resources in practice. An ethnography of one teacher's classroom will be developed to further contribute to understandings of the classroom-level resources in action, including students' experiences and learning. Student learning will be evaluated through student interviews and analyses of student projects. Project outcomes will inform how computer science conceptual knowledge and creative fluency can be developed both for teachers and their students' knowledge and fluency that will be critical for students' future success in work and life.

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
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.

CAREER: Expanding Latinxs' Opportunities to Develop Complex Thinking in Secondary Science Classrooms through a Research-Practice Partnership

This project will address the need to educate teachers and students to engage in asking questions, collecting and interpreting data, making claims, and constructing explanations about real-world problems that matter to them. The study will explore ways to enhance youths' learning experiences in secondary school classrooms (grades 6-12) by building a sustainable partnership between researchers and practitioners.

Award Number: 
1846227
Funding Period: 
Mon, 07/01/2019 to Sun, 06/30/2024
Full Description: 

This project will address the need to educate teachers and students to engage in asking questions, collecting and interpreting data, making claims, and constructing explanations about real-world problems that matter to them. Science educators generally agree that science classrooms should provide opportunities for students to advance their thinking by engaging in critical conversations with each other as capable sense-makers. Despite decades of reform efforts and the use of experiential activities in science instruction, research indicates that classroom learning for students remains largely procedural, undemanding, and disconnected from the development of substantive scientific ideas. Furthermore, access to high-quality science instruction that promotes such complex thinking is scarce for students with diverse cultural and linguistic backgrounds. The project goals will be: (1) To design a year-long teacher professional development program; and (2) To study the extent to which the professional development model improves teachers' capacity to plan and implement inclusive science curricula.

This study will explore ways to enhance youths' learning experiences in secondary school classrooms (grades 6-12) by building a sustainable partnership between researchers and practitioners. The work will build on a previous similar activity with one local high school; plans are to expand the existing study to an entire school district over five years. The proposed work will be conducted in three phases. During Phase I, the study will develop a conceptual framework focused on inclusive science curricula, and implement the new teacher professional development program in 3 high schools with 15 science teachers. Phase II will expand to 6 middle schools in the school district with 24 teachers aimed at creating a continuous and sustainable research-practice partnership approach at the district. Phase III will focus on data analysis, assessment of partnership activities, dissemination, and planning a research agenda for the immediate future. The study will address three research questions: (1) Whether and to what extent does participating teachers' capacity of planning and implementing the curriculum improve over time; (2) How and why do teachers show differential progress individually and collectively?; and (3) What opportunities and constraints within schools and the school district shape teachers' development of their capacity to design and implement curricula? To address the research questions, the project will gather information about the quality of planned and implemented curriculum using both qualitative and quantitative data. Main project's outcomes will be: (1) a framework that guides teachers' engagement in planning and implementing inclusive science curricula; and (2) increased knowledge base on teacher learning. An advisory board will oversee the work in progress. An external evaluator will provide formative and summative feedback.

Using Technology to Capture Classroom Interactions: The Design, Validation, and Dissemination of a Formative Assessment of Instruction Tool for Diverse K-8 Mathematics Classrooms

This project will refine, expand, and validate a formative assessment tool called Math Habits Tool (MHT) for kindergarten through 8th grade classrooms. MHT is intended to capture and understand patterns of in-the-moment teacher-student and student-student classroom interactions in ways that can promote more equitable access to high quality math learning experiences for all students.

Lead Organization(s): 
Award Number: 
1814114
Funding Period: 
Sat, 09/15/2018 to Wed, 08/31/2022
Full Description: 

An important aspect of mathematics teaching and learning is the provision of timely and targeted feedback to students and teachers on the teaching and learning processes. However, many of the tools and resources focused on providing such feedback (e.g., formative assessment) are aimed at helping students. However, formative assessment of teaching can be equally transformative for teachers and school leaders and is a key component of improved teacher practice. This project will refine, expand and validate a formative assessment tool called Math Habits Tool (MHT) for kindergarten through 8th grade classrooms. MHT is intended to capture and understand patterns of in-the-moment teacher-student and student-student classroom interactions in ways that can promote more equitable access to high quality math learning experiences for all students. The tablet or computer-based tool is intended for use with teacher leaders, principals, coaches, and others interested in assessing teacher practice in a formative way.

This project will continue the development of the MHT through: (1) the integration of an access component; (2) analysis of videos collected during prior studies covering a diverse set of classrooms across the K-8 spectrum; (2) a validation study using validity-argument approach; and (3) the development, piloting, and refinement of professional development modules that will guide math educators, researchers, and practitioners in using the MHT effectively as a formative assessment of instruction. The revised MHT will be validated through analyses of video data from a range of K-8 classrooms with varying demographics and contexts such as socio-economic status, language backgrounds, gender, school settings (e.g., urban, rural, suburban), and race, with particular attention to increasing accessibility to mathematics learning by students who are traditionally underserved, including emergent bilingual students. The data analysis plan involves video coding with multiple checks on reliability, dimensionality analysis with optimal scaling, correlation analysis, and hierarchical linear modeling.

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