This project builds on a prior study that demonstrated increases in students' knowledge of argumentation and their performance on mathematics assessments. The project will extend the use of the argumentation intervention into all eighth grade content areas, with a specific focus on students' learning of reasoning and proof, and contribute to understanding how students' learning about mathematical practices that can help them learn mathematics better.
The project will examine learning in eighth grade mathematics with a specific focus on students' learning of reasoning and proof. The intervention builds on a prior study in algebra that demonstrated increases in students' knowledge of argumentation and their performance on mathematics assessments. This project will extend the use of the argumentation intervention into all eighth grade content areas. The investigators will also address support for teachers in the form of teacher materials that link the argumentation content with mathematics standards and state-wide assessments, and a learning progression to engage students in proving tasks. The project will use assessments of mathematics learning and additional data from teachers and students to understand the impact of the argumentation intervention on teachers and students. The project contributes to understanding how students can learn about mathematical practices, such as proving, that can help them learn mathematics better. A significant contribution will be the definition of aspects of proving and descriptions of student outcomes that can be used to measure how well students have achieved these components of proving. The Discovery Research PreK-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. This project is also supported by NSF's EHR Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field.
The project suggests twelve conceptual pillars that are combined with classroom processes and assessable outcomes to examine the use of argumentation practices in the teaching of eighth grade mathematics content. The investigation of classroom support for argumentation includes research questions that focus on improvement on state-level assessments, students' ability to construct mathematical arguments, and the conceptual progression that supports students' understanding of argumentation and proof. In addition, the study will examine teachers' role in argumentation in the classroom and their perception of potential challenges for classroom implementation. The study will use an experimental design to examine an intervention for mathematical reasoning and proof in eighth grade. The project includes a treatment group of teachers that will participate in professional development including a summer institute followed by instructional coaching over a two year period.
This project will scale up, implement, and assess the efficacy of interventions in K-12 mathematics education based on the well-established Algebra Project (AP) pedagogical framework, which seeks to improve performance and participation in mathematics of students in distressed school districts, particularly low-income students from underserved populations.
Algebra continues to serve as a gatekeeper and potential barrier for high school students. The Algebra Project Mathematics Content and Pedagogy Initiative (APMCPI) will scale up, implement and assess the efficacy of interventions in K-12 mathematics education based on the well-established Algebra Project (AP) pedagogical framework. The APMCPI project team is comprised of four HBCUs (Virginia State University, Dillard University, Xavier University, Lincoln University), the Southern Initiative Algebra Project (SIAP), and four school districts that are closely aligned with partner universities. The purpose of the Algebra Project is to improve performance and participation in mathematics by members of students in distressed school districts, particularly those with a large population of low-income students from underserved populations including African American and Hispanics. The project will provide professional development and implement the Algebra Project in four districts and study the impact on student learning. The research results will inform the nation's learning how to improve mathematics achievement for all children, particularly those in distressed inner-city school districts.
The study builds on a prior pilot project with a 74% increase in students who passed the state exam. In the early stages of this project, teachers in four districts closely associated with the four universities will receive Algebra Project professional development in Summer Teacher Institutes with ongoing support during the academic year, including a community development plan. The professional development is designed to help teachers combine mathematical problem solving with context-rich lessons, which both strengthen and integrate teachers' understanding of key concepts in mathematics so that they better engage their students. The project also will focus on helping teachers establish a framework for mathematically substantive, conceptually-rich and experientially-grounded conversations with students. The first year of the study will begin a longitudinal quasi-experimental, explanatory, mixed-method design. Over the course of the project, researchers will follow cohorts who are in grade-levels 5 through 12 in Year 1 to allow analyses across crucial transition periods - grades 5 to 6; grades 8 to 9; and grades 12 to college/workforce. Student and teacher data will be collected in September of Project Year 1, and in May of each project year, providing five data points for each student and teacher participant. Student data will include student attitude, belief, anxiety, and relationship to mathematics and science, in addition to student learning outcome measures. Teacher data will include content knowledge, attitudes and beliefs, and practices. Qualitative data will provide information on the implementation in both the experimental and control conditions. Analysis will include hierarchical linear modeling and multivariate analysis of covariance.
For this project, researchers will iteratively develop simulations to include sonifications, non-speech sounds that represent visual information, aimed at enhancing accessibility for all learners, but particularly for those with visual impairments to produce sonified simulations, professional development resources, design guidelines and exemplars, and publications.
Students with disabilities often have fewer opportunities for experiential learning, an important component of quality STEM education. Computer based simulations in science can provide valuable opportunities for these students to experience and manipulate natural phenomena related to critical STEM ideas. However, existing simulations remain largely inaccessible to students with visual impairments in particular. Recent advances in technology related to sonification use with simulations can make it possible for these students to have a more complete and authentic experience. Sonification is the use of non-speech sounds, such as musical tones, to represent visual information including data. Such sounds can be manipulated temporally and spatially and can also vary by amplitude and frequency to convey information that is more traditionally displayed visually.
Researchers will iteratively develop five middle school physical science simulations to include sonifications aimed at enhancing accessibility for all learners, but particularly for those with visual impairments. Data collection activities will include focus groups and interviews with students and teachers focused on engagement. The end products of this project will include sonified simulations, professional development resources, design guidelines and exemplars, and publications.
Sensing Science through Modeling: Developing Kindergarten Students' Understanding of Matter and Its Changes
This project will develop a technology-supported, physical science curriculum that will facilitate kindergarten students' conceptual understanding of matter and how matter changes. The results of this investigation will contribute important data on the evolving structure and content of children's physical science models as well as demonstrate children's understanding of matter and its changes.
Despite recent research demonstrating the capacity of young children to engage deeply with science concepts and practices, challenging science curriculum is often lacking in the early grades. This project addresses this gap by developing a technology-supported, physical science curriculum that will facilitate kindergarten students' conceptual understanding of matter and how matter changes. To accomplish these goals, the curriculum will include opportunities for students to participate in model-based inquiry in conjunction with the use of digital probeware and simulations that enable students to observe dynamic visualizations and make sense of the phenomena. To support the capacity of kindergarten teachers, a continuous model of teacher development will be implemented.
Throughout development, the project team will collaborate with kindergarten teachers and more than 300 demographically diverse students across eight classrooms in Massachusetts and Indiana. A design based research approach will be used to iteratively design and revise learning activities, technological tools, and assessments that meet the needs and abilities of kindergarten students and teachers. The project team will: 1) work with kindergarten teachers to modify an existing Grade 2 curricular unit for use with their students; 2) design a parallel curricular unit incorporating technology; 3) evaluate both units for feasibility and maturation effects; and 4) iteratively revise and pilot an integrated unit and assess kindergarten student conceptual understanding of matter and its changes. The results of this investigation will contribute important data on the evolving structure and content of children's physical science models as well as demonstrate children's understanding of matter and its changes.
Strengthening Mathematics Intervention Classes: Identifying and Addressing Challenges to Improve Instruction for Struggling Learners
The purpose of this project is to improve mathematics instruction for struggling learners by focusing on the quality of instruction occurring in mathematics intervention classrooms. The study will focus on how intervention class time is spent, what mathematics content is emphasized, which evidence-based instructional practices are used, and what challenges are faced by teachers.
Given the adoption of more rigorous mathematics standards, U.S. school districts face a pressing need to improve instruction for struggling learners who are not reaching proficiency on standardized assessments. In response to low performance, a common district solution is to add mathematics intervention classes which aim to provide struggling students with time for more intensive and targeted instruction. Researchers have begun to identify effective mathematics intervention practices, but few studies have examined if intervention teachers are actually implementing these approaches with students. Very little is known about how intervention class time is spent, what mathematics content is emphasized, which evidence-based instructional practices are used, and what challenges are faced by teachers.
The purpose of this project is to improve mathematics instruction for struggling learners by focusing on the quality of instruction occurring in mathematics intervention classrooms. The investigators will conduct observations and interviews with teachers and district leaders to understand current practices and challenges. This will be followed by a national survey of 300 teachers to document challenges across the country in terms of providing mathematics intervention. The final aspect of the project involves the design of professional development for mathematics intervention teachers based on the needs identified in the earlier phases of the project.
This project focuses on the creation of the initial functionality for a dynamic microworld, Proportions Playground, designed to support teachers in developing a coherent understanding of proportional reasoning. The Proportions Playground project seeks to both develop a unique pilot software application for the iPad and explore how it supports teachers in developing a coherent, robust definition of proportions.
Proportions are a critical topic in mathematics that is simultaneously complicated and over-simplified in typical instruction. Current research undertaken by the research team suggests that the over-simplification is related to limitations in teachers' understandings of proportional relationships. Presenting proportions in a dynamic environment offers teachers the opportunity to create key developmental understandings related to this area of mathematics. This project focuses on the creation of the initial functionality for a dynamic microworld, Proportions Playground, designed to support teachers in developing a coherent understanding of proportional reasoning. Proportions Playground is conceptualized as a tool for supporting the development of coherent understandings by allowing teachers to interact in concrete ways with otherwise abstract ideas and by allowing teachers easy access to dynamic objects and other representations. It is meant to address the significant limitations for reasoning about the relationships between measurable aspects of two objects as well as in manipulating those relationships. Building from work currently underway, Proportions Playground will explore key areas in which there are opportunities for engaging teachers in the development of a coherent and robust understanding of proportional reasoning that extends beyond the typical "3 given, 1 unknown" proportion problem. This approach attempts to engage teachers in an array of dynamic, visually-rich sets of tasks designed to challenge teachers' preconceptions of proportions and to strengthen their connections between proportions and related areas of mathematics. This project is funded by the Discovery Research PreK-12 (DRK-12) and EHR Core Research (ECR) Programs. the DRK-12 program supports research and development on STEM education innovations and approaches to teaching, learning, and assessment. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field.
The Proportions Playground project seeks to both develop a unique pilot software application for the iPad and explore how it supports teachers in developing a coherent, robust definition of proportions. The software will be designed to support either numeric manipulation (e.g., graphing software) or geometric constructions (e.g., dynamic geometry software). Specifically, for this project the mathematics of interest will include the relationships between similarity and proportion and the nature of covariation. The research will focus on how teachers are developing a robust and coherent understanding of proportions and how the dynamic environment promotes such understandings. Working with six teacher advisors, the project will develop three task sets. Using teaching experiments and individual interviews, results will be used to refine the task sets. The revised task sets will be piloted with 40 teachers. Data will be collected on participants' thinking and any changes seen in the knowledge resources they are using. The researchers will be looking for factors that seem to impact teachers' thinking as well as evidence to support or deny the assertion that the Proportions Playground activities engage teachers in (a) different ways of reasoning about proportions and (b) support them in drawing from a wide array of resources so that coherence may be developed were the teachers to have a prolonged engagement with the tools. The project will rely on Epistemic Network Analysis to identify the connections between knowledge resources.
The purpose of this project is to investigate issues in the design and implementation of effective virtual learning communities (VLCs) for teachers and to examine the relation between teachers' reflective engagement with VLCs and their students' mathematics learning outcomes. Findings from this project will be used to build and share effective ways to support teacher learning online.
U.S. elementary teachers face many challenges. They are asked to teach all subjects to students with different needs and abilities. To do this well, they need good professional learning opportunities. Many teachers look online for such opportunities, but little is known about the quality of those opportunities and how they can be improved to help teachers meet their challenges. The goals of this project are to learn more about how teachers use one popular website for elementary mathematics teachers and how this website and similar ones can be adapted to better support teacher learning. Specifically, the project will (1) interview teachers about their use of the website, (2) investigate how to improve the ways teachers interact with video resources on the site by testing different ways of guiding their attention, and (3) examine how teachers' interactions with these video resources are related to their students' learning of mathematics. Findings from this project will be used to build and share effective ways to support teacher learning online. The project will thus benefit teachers who use the popular website, teachers who use similar websites, researchers who study how teachers learn from such websites, and the students of teachers who learn from such websites.
Video-based learning has been the focus of much professional development research over the past decade. As video-based learning has been found to be effective, many professional developers have taken this learning to scale through the online space. A number of high profile and popular virtual learning communities (VLCs) have emerged to allow teachers to interact with video, but the scant number of studies on the effectiveness of such VLCs show some difficulties in engaging teachers in sustained, reflective professional learning. The purpose of this project is to investigate several major issues in the design and implementation of effective VLCs for teachers and to examine the relation between teachers' reflective engagement with VLCs and their students' mathematics learning outcomes. The investigators propose 3 studies, which build on each other, to address these issues. This project will (1) interview teachers who are members of a popular VLC, to investigate what they learn and how they contribute to community; (2) investigate conditions that impact the posting of reflective commentary about video cases through iterative experiments, as reflective commentary has the potential to build community and to support teacher learning; and (3) investigate the relation between reflective reactions to video cases and student mathematics outcomes. Through these investigations, this project will explore issues that impact the scalability of teachers learning asynchronously from online video. Results will be used to develop guided pathways - a prototype of an innovation that will be based on the results from the research - on one widely used VLC. Thus, this project will provide both a contribution to the field of STEM teacher education research and an immediate, research-based product that can be disseminated to thousands of teachers through an existing VLC.
Improving the Implementation of Rigorous Instructional Materials in Middle-Grades Mathematics: Developing a System of Practical Measures and Routines (Collaborative Research: Smith)
The goal of this project is to improve the implementation of rigorous instructional materials in middle-grades mathematics at scale through a system of practical measures and routines for collecting and using data that both assesses and supports implementation.
The goal of this 5-year research project is to improve the implementation of rigorous instructional materials in middle-grades mathematics at scale. Many projects seek to improve mathematics instruction, but are not able to easily track their efforts at improvement. The primary product of this project will be a system of practical measures and routines for collecting and using data that both assesses and supports the implementation of rigorous instructional materials in middle-grades mathematics. In contrast to research and accountability measures, practical measures are assessments that require little time to administer and can thus be used frequently. The data can be analyzed rapidly so that teachers can receive prompt feedback on their progress, and instructional leaders can use the data to decide where to target resources to support improvement in the quality of instruction and student learning. The system of practical measures and routines will include 1) measures of high-leverage aspects of teachers' instructional practices that have been linked to student learning (e.g., rigor of tasks, quality of students' discourse) and attend to equitable student participation; and 2) measures of high-leverage aspects of key supports for improving the quality of teachers' practice (e.g., quality of professional development; coaching); and 3) a set of routines regarding how to use the resulting data to engage in rapid, improvement efforts. A key principle of the proposed project is that the system of measures and routines can be adapted to a wide range of school and district contexts. This project is supported by the Discovery Research preK-12 (DRK-12) program. The DRK-12 program supports research and development of STEM education innovations and approaches in assessment, learning, and teaching.
The project will establish three research-practice partnerships with five districts, in three different states, that are currently implementing rigorous instructional materials in middle-grades mathematics. Year 1 will focus on the development of a set of practical measures of classroom instruction. Year 2 will focus on testing the use of the classroom measures in the context of supports for teachers' learning, and the development of practical measures of key supports for teachers' learning. Years 3-4 will focus on how the project can "learn our way to scale" (Bryk et al., 2015), which requires strategically implementing measures and routines in increasingly diverse conditions. The project will engage in rapid improvement cycles in which researchers will work alongside district leaders and professional development (PD) facilitators to analyze the data from the measures of both classroom instruction and the quality of support for teacher learning to test the effectiveness of improvements in intended supports for teacher learning and to adjust the design of the support based on data. Across Years 1-4, the project will use recent developments in technology and information visualization to test and improve 1) the collection of practical measures in situ and 2) the design of data representations (or visualizations) that support teachers and leaders to make instructional improvement decisions. In Year 5, the project will conduct formal analyses of the relations between supports for teachers' learning; teachers' knowledge and classroom practices; and student learning.
This project will design and pilot professional development that focuses on developing the confidence, mathematical knowledge, and teaching strategies of paraeducators using classroom activities that they are expected to implement. The planned professional development will enable them to make a greater difference in the classroom, but it will also increase their access to continuing education and workplace opportunities.
Over one million paraeducators (teaching assistants and volunteers) currently assist in classrooms, and another 100,000 are likely to be added in the next ten years. Paraeducators (paras) are often required to teach content, such as mathematics, but there are few efforts to provide them with the knowledge or supervision they need to be effective when working with a range of students, including those with disabilities and for whom English is a second language. The project will focus on developing the confidence, mathematical knowledge, and teaching strategies of paras using classroom activities that they are expected to implement. The planned professional development will enable them to make a greater difference in the classroom, but it will also increase their access to continuing education and workplace opportunities. The work will be conducted in the Boston Public Schools (BPS) and will focus on grades K-3, where the largest numbers of paras are employed. Given the importance of early math learning in predicting mathematical achievement, supporting paras who work in the early grades is particularly important.
The project will design and pilot professional development that supports paraeducator knowledge development and addresses instructional challenges in teaching mathematics. The project will address the following goals: research the current roles of paras in mathematics instruction, the preparation of their collaborating teachers, and the opportunities for collaboration and planning between supervising teachers and paras in BPS; pilot, develop, implement, and research a model for professional development program for paras that targets specific activities they can implement that are key to student learning in number and operation in K-3; document how paras assume new roles that increase student engagement and empower them as mathematical learners; pilot, develop, implement, and research a supervisory component to help teachers set expectations, and structures for debriefing and reflecting along with their paras; and identify next steps for an early stage development study based on our findings. A needs assessment survey will investigate the context in which paras work. The iterative process of design-based research will develop, test, and implement the targeted professional development with paras, measuring how prepared they feel to implement new ideas and how they translate their learning into new pedagogical practices. Crosscase analyses, descriptive statistics, tallies and coded behaviors from observations, and themes from paras, and teacher and administrator interviews will be collected, coded, and analyzed. Furthermore, an efficacy survey will be administered periodically to document longitudinal changes in paras, which will be integrated in the crosscase analyses.
This project addresses the fundamental challenge of how to support teachers to improve their practice. The approach uses a "live mathematics classroom" as a common text for working on practice, where participants are not only watching and discussing but are engaged in developing and learning practice. The project will generate new knowledge regarding ways in which elementary teachers of mathematics can be supported to learn effective teaching practice.
Growing evidence about the powerful effects of skillful teaching on students' learning creates a need to for professional development that impacts teachers' actual practice. Just as other professions (e.g., nursing, social work, law) have centered practitioners' learning in "live" practice with structures that support learning in context, the project will investigate whether and how this can be accomplished in teaching. The approach uses a "live mathematics classroom" as a common text for working on practice, where participants are not only watching and discussing but are engaged in developing and learning practice. The project also explores the following variations in practice-based professional development: (1) on-site and remote participation of teachers; and (2) the addition of supplementary practice-focused professional development. The project will generate new knowledge regarding ways in which elementary teachers of mathematics can be supported to learn effective teaching practice.
This project addresses a fundamental challenge for professional development, that is, how to support teachers to improve their practice. Teachers profit from well-designed opportunities to develop new visions for practice, learn more about students' thinking, or work on specific mathematical topics or tasks. Still, such opportunities are often insufficient to support teachers with the complexity of classroom teaching. These kinds of professional opportunities focus on critical resources for instruction but not on the details of teaching practice itself. This practice-centered professional development is situated within a summer mathematics program for fifth graders. The proposed research will explore the impact on teachers' practice, as well as on their knowledge and dispositions, from participating in these structured ways. Three studies will resolve the following three sets of questions: (1) What do teachers learn from structured participation in the class? Does their participation impact their own teaching practice, and if so, in what ways? (2) Does the setting of the peripheral participation matter? Does this form of participation impact their own teaching practice, and if so, in what ways? (3) Does the addition of professional development focused on a particular teaching practice impact teachers' own practice, and if so, in what ways? How does the addition of professional development focused on a specific instructional practice compare across the in-person and online forms of participation in terms of impact on teachers' own practice? The project will collect and analyze several types of data pre- and post-intervention, including measures of mathematical knowledge for teaching, measures of language for talking about the work of teaching and students, and skill with leading a mathematics discussion, and the mathematical quality of instruction. The project will generate new knowledge related to to organizing professional learning around supports that teachers need to learn practice as well as ways to study their learning of teaching practice.