Supports for Science and Mathematics Learning in Pre-Kindergarten Dual Language Learners: Designing and Expanding a Professional Development System
SciMath-DLL is an innovative preschool professional development (PD) model that integrates supports for dual language learners (DLLs) with high quality science and mathematics instructional offerings. It engages teachers with workshops, classroom-based coaching, and professional learning communities. Based on initial evidence of promise, the SciMath-DLL project will expand PD offerings to include web-based materials.
The 4-year project, Supports for Science and Mathematics Learning in Pre-Kindergarten Dual Language Learners: Designing and Expanding a Professional Development System (SciMath-DLL), will address a number of educational challenges. Global society requires citizens and a workforce that are literate in science, technology, engineering, and mathematics (STEM), but many U.S. students remain ill prepared in these areas. At the same time, the children who fill U.S. classrooms increasingly speak a non-English home language, with the highest concentration in the early grades. Many young children are also at risk for lack of school readiness in language, literacy, mathematics, and science due to family background factors. Educational efforts to offset early risk factors can be successful, with clear links between high quality early learning experiences and later academic outcomes. SciMath-DLL will help teachers provide effective mathematics and science learning experiences for their students. Early educational support is critical to assure that all students, regardless of socioeconomic or linguistic background, learn the STEM content required to become science and mathematics literate. Converging lines of research suggest that participation in sustained mathematics and science learning activities could enhance the school readiness of preschool dual language learners. Positive effects of combining science inquiry with supports for English-language learning have been identified for older students. For preschoolers, sustained science and math learning opportunities enhance language and pre-literacy skills for children learning one language. Mathematics skills and science knowledge also predict later mathematics, science, and reading achievement. What has not been studied is the extent to which rich science and mathematics experiences in preschool lead to better mathematics and science readiness and improved language skills for preschool DLLs. Because the preschool teaching force is not prepared to support STEM learning or to provide effective supports for DLLs, professional development to improve knowledge and practice in these areas is required before children's learning outcomes can be improved.
SciMath-DLL is an innovative preschool professional development (PD) model that integrates supports for DLLs with high quality science and mathematics instructional offerings. It engages teachers with workshops, classroom-based coaching, and professional learning communities. Development and research activities incorporate cycles of design-expert review-enactment- analysis-redesign; collaboration between researcher-educator teams at all project stages; use of multiple kinds of data and data sources to establish claims; and more traditional, experimental methodologies. Based on initial evidence of promise, the SciMath-DLL project will expand PD offerings to include web-based materials, making the PD more flexible for use in a range of educational settings and training circumstances. An efficacy study will be completed to examine the potential of the SciMath-DLL resources, model, and tools to generate positive effects on teacher attitudes, knowledge, and practice for early mathematics and science and on children's readiness in these domains in settings that serve children learning two languages. By creating a suite of tools that can be used under differing educational circumstances to improve professional knowledge, skill, and practice around STEM, the project increases the number of teachers who are prepared to support children as STEM learners and, thus, the number of children who can be supported as STEM learners.
Researching the Impact of an Online MOOC Designed to Transform Student Engagement and Achievement in Mathematics
This study examines non-cognitive factors, mindsets, cognitive factors, and strategies for learning mathematics, in the context of a MOOC combined with classroom instruction for middle grades students in mathematics. No previous mindset study has researched the impact of mindset messages within mathematics, and the proposed study will add important knowledge to this field.
This project is designed to study a Massively Open Online Course (MOOC), expected to have approximately 2 million students, which will supplement middle grades mathematics classes to understand the impact on students' mathematical learning and engagement in mathematics. The MOOC learning environment, used with school aged children in concert with their regular mathematics course, focuses on helping students to develop positive and productive beliefs, or growth mindsets, about their own potential in mathematics and to teach the students a range of strategies that lead to mathematics success. A better understanding of growth mindsets and learning how to learn mathematics in the context of regular classroom instruction potentially makes important contributions in introducing a new intervention to tens of thousands of students. This contribution is made in concert with providing evidence of impact of using MOOCs coupled with classroom instruction with school aged children on student learning. If the study finds that the mathematics intervention MOOC significantly increases students' achievement and engagement with mathematics, it can be scaled nationally and potentially change the face of mathematics education in the United States.
This study examines non-cognitive factors, mindsets, cognitive factors, and strategies for learning mathematics, in the context of a MOOC combined with classroom instruction for middle grades students in mathematics. No previous mindset study has researched the impact of mindset messages within mathematics, and the proposed study will add important knowledge to this field. The study will also contribute to new knowledge of MOOCs, of their potential as learning opportunities and of the design of innovative pedagogies. Using a blocked randomized control trial of 10,000 students in two California districts, the statistical design employed will enable schools to implement the program across entire classes of students. The study employs measures of pre/post changes in mathematics engagement, mindset, use of mathematics strategies, and mathematics achievement, with close examination of the implications for girls, students of color, students of different socio-economic-status and low achieving students.
Despite the tremendous growth in the availability of mathematics videos online, little research has investigated student learning from them. The goal of this exploratory project is to create, investigate, and provide evidence of promise for a model of online videos that embodies a more expansive vision of both the nature of the content and the pedagogical approach than is currently represented in YouTube-style lessons.
The goal of this exploratory project is to create, investigate, and provide evidence of promise for a model of online videos that embodies a more expansive vision of both the nature of the content and the pedagogical approach than is currently represented in YouTube-style lessons. This goal is pursued through the development and research of videos for two mathematics units--one focused on proportional reasoning at the middle grades level and the other focused on quadratic functions at the high school level, using an approach that could be applied to any STEM content area. The media attention on the Khan Academy and the wide array of massive open online courses has highlighted the internet phenomenon of widespread accessibility to mathematics lessons, which offer many benefits, such as student control of the pace of learning and earlier access to advanced topics than is often possible in public schools. Yet, despite the huge range of topics presented in online videos, there is surprising uniformity in the procedural emphasis of the content and in the expository mode of presentation. Moving beyond the types of videos now used, primarily recorded lectures that replicate traditional classroom experience, this project advances our understanding about how students learn from video and from watching others learn - vicarious learning - as opposed to watching an expert. This project addresses the need for an alternative approach. Rather than relying on an expository style, the videos produced for this project focus on pairs of students, highlighting their dialogue, explanations and alternative conceptions. This alternative has the potential to contribute to learning sciences and to develop a usable tool.
Despite the tremendous growth in the availability of mathematics videos online, little research has investigated student learning from them. This project develops dialogue-intensive videos in which children justify and explain their reasoning, elucidate their own comprehension of mathematical situations, and argue for and against various ideas and strategies. According to Wegerif (2007), such vicarious participation in a dialogic community may help learners take the perspective of another in a discussion, thus "expanding the spaces of learning" through digital technology. Consequently, a major contribution of this proposed work will be a set of four vicarious learning studies. Two qualitative studies investigate the particular meanings and ways of reasoning that learners appropriate from observing the dialogue of the students in the videos, as well as the learning trajectories of vicarious learners for each unit. Two quantitative studies isolate and test the effectiveness of the dialogic and the conceptual components of the model by comparing learning outcome gains for (a) conceptual dialogic versus conceptual expository conditions, and (b) dialogic conceptual versus dialogic procedural conditions. Another mark of the originality of the proposed work is the set of vicarious learning studies that contributes to the emerging literature across several dimensions, by (a) using secondary students rather than undergraduates; (b) exploring longer periods of learning, which is more conducive to deeper understanding; and (c) examining the nature of reasoning that is possible, not just the effectiveness of the approach.
Preparing Urban Middle Grades Mathematics Teachers to Teach Argumentation Throughout the School Year
The objective of this project is to develop a toolkit of resources and practices that will help inservice middle grades mathematics teachers support mathematical argumentation throughout the school year. A coherent, portable, two-year-long professional development program on mathematical argumentation has the potential to increase access to mathematical argumentation for students nationwide and, in particular, to address the needs of teachers and students in urban areas.
The project is an important study that builds on prior research to bring a comprehensive professional development program to another urban school district, The District of Columbia Public Schools. The objective of this full research and development project is to develop a toolkit that provides resources and practices for inservice middle grades mathematics teachers to support mathematical argumentation throughout the school year. Mathematical argumentation, the construction and critique of mathematical conjectures and justifications, is a fundamental disciplinary practice in mathematics that students often never master. Building on a proof of concept of the project's approach ifrom two prior NSF-funded studies, this project expands the model to help teachers support mathematical argumentation all year. A coherent, portable, two-year-long professional development program on mathematical argumentation has the potential to increase access to mathematical argumentation for students nationwide and, in particular, to address the needs of teachers and students in urban areas. Demonstrating this program in the nation's capital will likely attract broad interest and produces important knowledge about how to implement mathematical practices in urban settings. Increasing mathematical argumentation in schools has the potential for dramatic contributions to students' achievement and participation in 21st century workplaces.
Mathematical argumentation is rich discussion in which students take on mathematical authority and co-construct conjectures and justifications. For many teachers, supporting such discourse is challenging; many are most comfortable with Initiate-Respond-Evaluate types of practices and/or have insufficient content understanding. The professional development trains teachers to be disciplined improvisers -- professionals with a toolkit of tools, knowledge, and practices to be deployed creatively and responsively as mathematical argumentation unfolds. This discipline includes establishing classroom norms and planning lessons for argumentation. The model's theory of action has four design principles: provide the toolkit, use simulations of the classroom to practice improvising, support learning of key content, and provide job-embedded, technology-enabled supports for using new practices all year. Three yearlong studies will address design, feasibility, and promise. In Study 1 the team co-designs tools with District of Columbia Public Schools staff. Study 2 is a feasibility study to examine program implementation, identify barriers and facilitators, and inform improvements. Study 3 is a quasi-experimental pilot to test the promise for achieving intended outcomes: expanding teachers' content knowledge and support of mathematical argumentation, and increasing students' mathematical argumentation in the classroom and spoken argumentation proficiency. The studies will result in a yearlong professional development program with documentation of the theory of action, design decisions, pilot data, and instrument technical qualities.
This project will use classroom-based research to teach children about important algebraic concepts and to carefully explore how children come to understand these concepts. The primary goal is to identify levels of sophistication in children's thinking as it develops through instruction. Understanding how children's thinking develops will provide a critical foundation for designing curricula, developing content standards, and informing educational policies.
Algebra is a central concern in school mathematics education. Its historical gatekeeper role in limiting students' career and life choices is well documented. In recent years, the response has been to reframe algebra as a K-12 endeavor. To this end, research on children's algebraic thinking in grades 3-5 shows that students can begin to understand algebraic concepts in elementary grades that they will later explore more formally. However, there is much that is unknown about how children in grades K-2 make sense of algebraic concepts appropriate for their age. This project aims to understand specific ways in which grades K-2 children begin to think algebraically. It will identify how children understand mathematical relationships, how they represent the relationships they notice, and how they use these relationships as building blocks for more sophisticated thinking. The project will use classroom-based research to teach children about important algebraic concepts and to carefully explore how children come to understand these concepts. The primary goal is to identify levels of sophistication in children's thinking as it develops through instruction. Understanding how children's thinking develops will provide a critical foundation for designing curricula, developing content standards, and informing educational policies, all in ways that can help children become successful in algebra and have wider access to STEM-related careers.
While college and career readiness standards point to the role of algebra beginning in kindergarten, the limited research base in grades K-2 restricts algebra's potential in K-2 classrooms. This project will develop cognitive foundations regarding how children learn to generalize, represent, and reason with algebraic relationships. Such findings will inform both the design of new interventions and resources to strengthen algebra learning in grades K-2 and the improvement of educational policies, practices, and resources. The project will use design research to identify: (1) learning trajectories as cognitive models of how grades K-2 children learn to generalize, represent, and reason with algebraic relationships within content dimensions where these practices can occur (e.g., generalized arithmetic); (2) critical junctures in the development of these trajectories; and (3) characteristics of tasks and instruction that facilitate movement along the trajectories. The project's design will include the use of classroom teaching experiments that incorporate: (1) instructional design and planning; (2) ongoing analysis of classroom events; and (3) retrospective analysis of all data sources generated in the course of the experiment. This will allow for the development and empirical validation of hypothesized trajectories in students' understanding of algebraic relationships. This exploratory research will contribute critical early-grade cognitive foundations of K-12 teaching and learning algebra that can help democratize access to student populations historically marginalized by a traditional approach to teaching algebra. Moreover, the project will occur in demographically diverse school districts, thereby increasing the generalizability of findings across settings.
Learning Linkages: Integrating Data Streams of Multiple Modalities and Timescales (Collaborative Research: Sherin)
In this project, researchers will collaborate to enhance understanding of influences on learning, and improve teaching and learning in high school and middle school STEM classes. They will leverage the latest tools for data processing and many different streams of data that can be collected in technology-rich classrooms to (1) identify classroom factors that affect learning and (2) explore how to use that data to automatically track development of students' understanding and capabilities over time.
This Research on Education and Learning (REAL) project arises from an October 2014 Ideas Lab on Data-intensive Research to Improve Teaching and Learning. The intentions of that effort were to (1) bring together researchers from across disciplines to foster novel, transformative, multidisciplinary approaches to using the data in large education-related data sets to create actionable knowledge for improving STEM teaching and learning environments in the medium term; and (2) revolutionize learning in the longer term. In this project, researchers from Carnegie-Mellon University, Wested, Arizona State University, and Northwestern University will collaborate to enhance understanding of influences on learning, and improve teaching and learning in high school and middle school STEM classes. To accomplish this, they will leverage the latest tools for data processing and many different streams of data that can be collected in technology-rich classrooms to (1) identify classroom factors that affect learning and (2) explore how to use that data to automatically track development of students' understanding and capabilities over time.
Two forces are poised to transform research on learning. First, more and more student work is conducted on computers and online, producing vast amounts of learning-related data. At the same time, advances in computing, data mining, and learning analytics are providing new tools for the collection, analysis, and representation of these data. Together, the available data and analytical tools enable smart and responsive systems that personalize learning experiences for individual learners. The PIs aim to collect highly enriched data that go far beyond typical computer data capture, leveraging the latest tools for data processing to generate new insights about STEM teaching and learning. Working to maximize the potential while mitigating the risks of automated data collection and analysis, they will: (1) collect and integrate diverse sources of data including log files, videos, and written artifacts from across eight different two-week enactments of two different computer supported learning environments (one used in middle school math and one in high school science); and (2) compare analyses of log-file data with analyses of integrated datasets to understand the possibilities and limitations in using log-file data for assessment of student learning and proficiency. The collaborators expect their findings will inform both theories and practical recommendations applicable across a wide range of disciplines and settings.
Learning and Sharing the World Best Practices in Math Education: The U.S. National Commission on Mathematics Instruction
To prepare the country's youth more broadly for a globalized world, the U.S. National Commission on Mathematics Instruction (USNCMI) will engage with the international community and assist in improving the state of mathematics education in the country by implementing international education programs, participating in international benchmarking activities, and working closely with other countries and multilateral organizations.
To prepare the country's youth more broadly for a globalized world, the U.S. National Commission on Mathematics Instruction (USNCMI) will engage with the international community and assist in improving the state of mathematics education in the country by implementing international education programs, participating in international benchmarking activities, and working closely with other countries and multilateral organizations. As a commission of the Board of International Scientific Organizations, the USNCMI serves as the liaison to the International Commission on Mathematical Instruction (ICMI), representing the U.S. mathematics education community abroad while learning about the world's best mathematics educational practices. Through a series of local and international activities over the course of three years, the USNCMI will achieve the following goals: (1) advance the U.S. position in the international mathematics education community through continued engagement, leveraging the U.S. strength in research; (2) create opportunities for educators in the U.S. to learn from promising practices in other countries and engage with mathematics educators internationally; and, (3) communicate findings from Goals 1 and 2 to the mathematics education community and policymakers in the United States.
The USNCMI provides the vehicle through which the U.S. National Academy of Sciences (NAS) reaches out to, and coordinates international activities with, the U.S. mathematics education community. Further, it takes advantage of the NAS network to disseminate its national and international interests, activities, and products. The USNCMI will continue to provide effective international representation and participation in meetings that involve learning and sharing the world's best practices in mathematics education. The primary activities of the USNCMI over the next three years are as follows: (1) Participate in ICMI leadership meetings, which provide vision and mission for fostering efforts to improve the quality of mathematics teaching and learning worldwide; (2) Participate in the influential ICMI Studies, which is a document that addresses how to better understand and resolve the challenges that face multidisciplinary and culturally diverse research and development in mathematics education; (3) Provide support for a strong U.S. representation at the next ICMI Congress (ICME-13) and the General Assembly in 2016, which foster collaboration, exchange, and dissemination of ideas and information involving the theory and practice of contemporary mathematical education; (4) Support the U.S. bid to host ICME-14 in Hawaii in 2020, an international meeting that develops a scientific program addressing various aspects of mathematics education; (5) Host and facilitate the U.S.-Finland Workshop, which will discuss current mathematics education policies and best practices in the U.S. and Finland; (6) Hold the Park City Mathematics Institute International Seminar, which invites scholars from different countries to discuss viewpoints and other relevant issues related to mathematics education; and, (7) Disseminate opportunities and products of the USNCMI and ICMI to the U.S. mathematics education community.
Students who fail algebra in the ninth grade are significantly less likely than their peers to graduate from high school on time. This project intends to test a common support strategy for at-risk students that provides an extra period of algebra, commonly known as a "double dose" condition. The Intensified Algebra (IA) is an intervention that addresses both the academic and non-academic needs of students.
Student success in algebra continues to be a problem as many U.S. students are underprepared when they enter high school. Students who fail algebra in the ninth grade are significantly less likely than their peers to graduate from high school on time. This project intends to test a common support strategy for at-risk students that provides an extra period of algebra, commonly known as a "double dose" condition. The Intensified Algebra (IA) is an intervention that addresses both the academic and non-academic needs of students. It is set of cohesive, integrated, and rigorous resources that builds student motivation and confidence. IA uses a blended model of instruction with a strong technology component designed to support the productive use of expanded instructional time that has shown evidence of promise in earlier studies.
This project is intended to rigorously test the impact of IA on student outcomes in a school-level random assignment design involving 6 districts, 55 high schools and over 4,000 9th grade students across two cohorts. Within each district, eligible schools are randomly assigned to either implement IA or to use the school's already established "double dose" algebra course. Analyses will use hierarchical linear models that explicitly take into account the clustering of students within classrooms and classrooms within schools. The study investigates short-term outcomes including end-of-9th grade algebra learning, passing rate for algebra I and attitudes toward mathematics. Longer-term outcomes include subsequent course-taking patterns and performances. The study examines fidelity of implementation and key implementation factors with descriptive and correlational analyses.
Improving Students' Mathematical Proficiency through Formative Assessment: Responding to an Urgent Need in the Common Core Era
The overarching goal of this RAPID project is to contribute to the national goal of improving students' mathematical proficiency by providing information and guidance to mathematics education practitioners and scholars to support a sharpened focus on formative assessment. The project produces, analyzes, and makes available to the field timely information regarding the views and practices of mathematics teacher educators and professional development specialists regarding formative assessment early in the enactment of ambitious standards in mathematics.
The products of this project will be useful to national organizations, their state and local affiliates, and school districts as they plan and offer mathematics professional development to support the implementation of high quality mathematics instruction to meet the urgent national need for smart and effective approaches to support ambitious college and career-ready standards in mathematics. Directing mathematics instruction toward ambitious learning goals is intended to address the critically important national priority of improving students' mathematics achievement. It is widely recognized that successful attainment of the content and practices contained in any ambitious set of learning goals, requires well-designed, smartly delivered, professional development for the nation's mathematics teachers. The information generated from this project is critical to inform nationwide mathematics professional development to support the implementation of ambitious mathematics learning goals. For our nation's teachers and students to attain ambitious learning goals, it is imperative that formative assessment becomes a more prominent feature of mathematics instruction as there is an evidence base that suggests formative assessment positively impacts student learning.
The overarching goal of this RAPID project is to contribute to the national goal of improving students' mathematical proficiency by providing much-needed information and guidance to mathematics education practitioners and scholars to support a sharpened focus on formative assessment. The project produces, analyzes, and makes available to the field timely information regarding the views and practices of mathematics teacher educators and professional development specialists regarding formative assessment early in the enactment of ambitious standards in mathematics. Moreover, it offers a potentially transformative view of formative assessment as integrated with other promising mathematics instructional frameworks, approaches and practices that have already established a strong presence in the mathematics education community and have influenced the instructional practice of many teacher educators and teachers. The project will result in: (a) an in-depth analysis of the responses of mathematics teacher educators and professional development specialists to a recent survey that probed their practices and beliefs related to formative assessment and its intertwined relationships with promising mathematics instructional frameworks, approaches and practices; (b) collaborative work among mathematics teacher educators and professional development specialists to elaborate effective ways to focus on formative assessment in the preparation and continuing education of teachers of mathematics; and (c) a set of design features and principles, along with associated activities, intended to undergird creating and sustaining an approach to mathematics teacher professional development that both attends to critically important instructional practices of formative assessment and links to other promising mathematics instructional frameworks, approaches and practices.
This project investigates the variation in teachers' practice of lesson study to identify effective and scalable design features of lesson study associated with student mathematics achievement growth in Florida. Lesson study is a teacher professional development model in which a group of teachers works collaboratively to plan a lesson, observe the lesson in a classroom with students, and analyze and discuss the student work and understanding in response to the lesson.
This project investigates the variation in teachers' practice of lesson study to identify effective and scalable design features of lesson study associated with student mathematics achievement growth in Florida. Lesson study is a teacher professional development model in which a group of teachers works collaboratively to plan a lesson, observe the lesson in a classroom with students, and analyze and discuss the student work and understanding in response to the lesson. Florida is the first state to promote lesson study as a statewide professional development model for implementing the Common Core State Standards for Mathematics and improving instruction and student achievement. The original lesson study model imported from Japan poses a challenge for implementation and scalability in the United States, and there is emerging evidence that modifications have been made to make it feasible within the constraints of teachers' work schedules and school structures. Thus, there is an urgent need to investigate the variation in lesson study practice and how modified design features of mathematics lesson study are associated with improvement of student mathematics achievement. The research team will conduct a statewide survey of approximately 1,000 teachers in grades 3-8 who are practicing mathematics lesson study during the 2015-2016 academic year. They will examine variations in four design features of lesson study (structure, facilitator, knowledge resources for lesson planning, and research lesson and discussion) and their associated organizational supports. They will examine the relationships between these design features and the original lesson study model, teacher learning, and students' mathematics achievement growth.
This project is designed to advance the scholarship and practice of lesson study by: (1) identifying an effective and scalable model of mathematics lesson study with specific design features that are associated with positive teacher learning experience and improved student mathematics achievement; (2) advancing practical knowledge on how this effective and scalable model of mathematics lesson study can be practiced, based on in-depth case studies of lesson study groups; and (3) contributing to teacher learning principles that can be applied to various professional development programs in mathematics. The project will disseminate evidence regarding the characteristics of an effective and scalable mathematics lesson study model to state and district-level facilitators across the country. The project will also develop a Florida Lesson Study Network (FLSN) to share resources and facilitate communications regarding lesson study practice.