Mathematics

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.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1418020
Funding Period: 
Mon, 09/01/2014 - Thu, 08/31/2017
Full Description: 

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 Linkages: Integrating Data Streams of Multiple Modalities and Timescales (Collaborative Research: Sherin)

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. 

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1445104
Funding Period: 
Mon, 09/15/2014 - Thu, 08/31/2017
Full Description: 

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.

Learning and Sharing the World Best Practices in Math Education: The U.S. National Commission on Mathematics Instruction

Intensified Algebra Efficacy Study

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.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1418267
Funding Period: 
Fri, 08/01/2014 - Tue, 07/31/2018
Full Description: 

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.

Intensified Algebra Efficacy Study

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.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1439366
Funding Period: 
Sun, 06/15/2014 - Sun, 05/31/2015
Full Description: 

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.

Improving Students' Mathematical Proficiency through Formative Assessment: Responding to an Urgent Need in the Common Core Era

Identifying an Effective and Scalable Model of Lesson Study

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.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1417585
Funding Period: 
Fri, 08/01/2014 - Mon, 07/31/2017
Full Description: 

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.

Identifying an Effective and Scalable Model of Lesson Study

From Elementary Generalist to Mathematics Specialist: Examining Teacher Practice and Student Outcomes in Departmental and Self-Contained Models

This research investigates student mathematics learning outcomes at the elementary level in relation to teacher expertise (elementary teachers with math specialist certification versus generally prepared elementary teachers) and school organization (departmentalized versus self-contained mathematics classrooms). Findings will provide evidence of the impact of content-specific teacher expertise and a departmentalized school organizational model that offers students access to well-qualified teachers of mathematics with no additional staffing costs.

Lead Organization(s): 
Award Number: 
1414438
Funding Period: 
Fri, 08/01/2014 - Tue, 07/31/2018
Full Description: 

This research investigates student mathematics learning outcomes at the elementary level in relation to teacher expertise (elementary teachers with math specialist certification versus generally prepared elementary teachers) and school organization (departmentalized versus self-contained mathematics classrooms). University of Missouri researchers will organize and facilitate the research in multiple Missouri public and private school sites. Findings will provide evidence of the impact of content-specific teacher expertise and a departmentalized school organizational model that offers students access to well-qualified teachers of mathematics with no additional staffing costs. To investigate the impact of teacher expertise and school organization on student learning experimental, quasi-experimental, and qualitative designs are employed. Specifically, 80 teachers who have earned state certification as Elementary Mathematics Specialists (hereafter, "EMS teachers") will be selected to participate in the study. Employing a randomized experimental design, half of the EMS teachers will be assigned to teach in a departmental model (Condition 1) in their school, teaching two or more sections of grade 4 mathematics. The other half will remain in generalist (hereafter, self-contained) positions (Condition 2) in their school, teaching all regular subjects to a single class of students. A comparison group of 40 non-EMS teachers with self-contained teaching assignments (Condition 3) will be selected from the same schools in Condition 2. The Smarter Balanced assessment will provide a baseline measure of students' prior achievement in grade 3 and also a measure of the mathematics achievement of grade 4 students taught by the 120 teachers in the study. The project team will analyze student-level mathematics scores linked with specific teachers.

Improving student achievement in mathematics at the elementary level is particularly challenging due to the way elementary students are generally organized for instruction (e.g., one teacher responsible for teaching all subjects to 25-30 students). Because elementary teachers must be knowledgeable about many content areas, they rarely study mathematics in depth, even though there is a growing body of evidence showing the impact of specialized mathematical knowledge for teaching on student learning outcomes. This study carefully researches an alternative model, where elementary teachers with special training in mathematics teaching and learning are assigned more than one single class of students for mathematics instruction. Findings from the research will provide evidence about the impact of both certification as an elementary mathematics specialist and teaching in a departmental assignment on student learning. The results will help school and district leaders better plan for assignment of staff to provide all students with access to high quality mathematics instruction.

From Elementary Generalist to Mathematics Specialist: Examining Teacher Practice and Student Outcomes in Departmental and Self-Contained Models

Developing and Testing the Internship-inator, a Virtual Internship in STEM Authorware System

The Internship-inator is an authorware system for developing and testing virtual internships in multiple STEM disciplines. In a virtual internship, students are presented with a complex, real-world STEM problem for which there is no optimal solution. Students work in project teams to read and analyze research reports, design and perform experiments using virtual tools, respond to the requirements of stakeholders and clients, write reports and present and justify their proposed solutions. 

Award Number: 
1418288
Funding Period: 
Mon, 09/01/2014 - Fri, 08/31/2018
Full Description: 

Ensuring that students have the opportunities to experience STEM as it is conducted by scientists, mathematicians and engineers is a complex task within the current school context. This project will expand access for middle and high school students to virtual internships, by enabling STEM content developers to design and customize virtual internships. The Internship-inator is an authorware system for developing and testing virtual internships in multiple STEM disciplines. In a virtual internship, students are presented with a complex, real-world STEM problem for which there is no optimal solution. Students work in project teams to read and analyze research reports, design and perform experiments using virtual tools, respond to the requirements of stakeholders and clients, write reports and present and justify their proposed solutions. The researchers in this project will work with a core development network to develop and refine the authorware, constructing up to a hundred new virtual internships and a user group of more than 70 STEM content developers. The researchers will iteratively analyze the performance of the authorware, focusing on optimizing the utility and the feasibility of the system to support virtual internship development. They will also examine the ways in which the virtual internships are implemented in the classroom to determine the quality of the STEM internship design and influence on student learning.

The Intership-inator builds on over ten years of NSF support for the development of Syntern, a platform for deploying virtual internships that has been used in middle schools, high schools, informal science programs, and undergraduate education. In the current project, the researchers will recruit two waves of STEM content developers to expand their current core development network. A design research perspective will be used to examine the ways in which the developers interact with the components of the authorware and to document the influence of the virtual internships on student learning. The researchers will use a quantitative ethnographic approach to integrate qualitative data from surveys and interviews with the developers with their quantitative interactions with the authorware and with student use and products from pilot and field tests of the virtual internships. Data-mining and learning analytics will be used in combination with hierarchical linear modeling, regression techniques and propensity score matching to structure the quasi-experimental research design. The authorware and the multiple virtual internships will provide researchers, developers, and teachers a rich learning environment in which to explore and support students' learning of important college and career readiness content and disciplinary practices. The findings of the use of the authorware will inform STEM education about the important design characteristics for authorware that supports the work of STEM content and curriculum developers.

Developing and Testing the Internship-inator, a Virtual Internship in STEM Authorware System

Teaching STEM with Robotics: Design, Development, and Testing of a Research-based Professional Development Program for Teachers

Using design-based research, with teachers as design partners, the project will create and refine project-based, hands-on robotics curricula such that science and math content inherent in robotics and related engineering design practices are learned. To provide teachers with effective models to capitalize on robotics for elucidating science and math concepts, a design-based Professional Development program will be built using principles of technological, pedagogical, and content knowledge (TPACK).

Lead Organization(s): 
Award Number: 
1417769
Funding Period: 
Mon, 09/01/2014 - Fri, 08/31/2018
Full Description: 

Offering meaningful and motivating engineering contexts, such as robotics, within science and math courses constitutes a compelling strategy to address the Next Generation Science Standards and the Common Core State Standards for Math while enhancing science and math learning for all students. Using design-based research, with teachers as design partners, the project will create and refine project-based, hands-on curricula such that science and math content inherent in robotics and related engineering design practices are learned. To provide teachers with effective models to capitalize on robotics for elucidating science and math concepts, a design-based Professional Development program will be built using principles of technological, pedagogical, and content knowledge (TPACK). To ensure that teachers are well prepared, research-based practices and features of effective Professional Development will be adopted. Experts in robotics, engineering, education, curriculum design, and assessment--with experience in K-12 education, training, and outreach--have formed an interdisciplinary team to make robotics central to and sustainable in middle school science and math classrooms.

The research questions addressed in this project are qualitative in nature as appropriate for design research questions. The methodologies include teacher needs assessment, teachers' perceptions of robotics, pre and post testing, classroom observations, and surveys. Examples of the research questions are:

What characteristics of robotics promote effective learning of middle school science and math?

What elements of Professional Development engender teachers' TPACK of robotics and link it with classroom science and math?

What are student prerequisites to effectively use robotics in science and math learning?

What are the gains in students' STEM engagement, interest, persistence, and career awareness?

The robotics curriculum will include physical science used in robot performance expectations and motion stability. Additionally the curriculum will include the engineering design process consisting of problem definition, solution development, and design improvement. Robotics provides opportunities to support science and engineering practices of the Next Generation Science Standards such as developing and using models, planning and conducting investigations, designing solutions, and analyzing and interpreting data. The project will be aimed at middle school students and will provide substantial teacher professional development to implement the new curriculum modules. The partner schools have student bodies drawn from a diverse student population in New York City.

Teaching STEM with Robotics: Design, Development, and Testing of a Research-based Professional Development Program for Teachers

Community for Advancing Discovery Research in Education 2 (CADRE 2)

This award will continue and enhance the resource center (titled the Community for Advancing Discovery Research in Education, or CADRE) for the Discovery Research K-12 program. The project builds on the experience and expertise that evolved over six years in the development and implementation of CADRE. 

Partner Organization(s): 
Award Number: 
1449550
Funding Period: 
Mon, 09/01/2014 - Wed, 08/31/2016
Full Description: 

This award will continue and enhance the resource center (titled the Community for Advancing Discovery Research in Education, or CADRE) for the Discovery Research K-12 program. The project builds on the experience and expertise that evolved over six years in the development and implementation of CADRE. With this award, CADRE2 will maximize the individual and collective potential of DR K-12 awards by fostering collaboration and cross-sharing, and promoting the generation of new knowledge and products. CADRE2 will provide technical support to the awardees through communities of practice, a strong virtual presence, and an annual PI meeting; professional growth opportunities targeted particularly to early career researchers and developers; and aggressive outreach and dissemination to the DR K-12 community and beyond. CADRE2 will establish connections with other networks to leverage each other's strengths and services. The evaluation will focus on components that have promise for adaptation by future endeavors and by other networks.

This award will focus on support for early career researchers and developers, looking at interests and needs for professional growth. The network will also contribute to the knowledge base on capacity building, and provide a lens on dissemination of DR K-12 resources, materials, and tools within and external to the research and development community. The DR K-12 portfolio includes an estimated 300 projects that are driven by the field yet respond to parameters established by the National Science Foundation. Understanding the scope of the portfolio is important because collectively, the awards produce resources, models, and technologies that can influence the field. Convening the awardees in virtual and person-to-person venues, and promoting collaboration and interaction among the projects, maximizes the collective potential of the projects. With an emphasis on early career researchers and developers, CADRE2's impact extends into the building of the next generation of scholars. With an emphasis on communication and dissemination of the project findings and experiences, the knowledge related to STEM research will create a more evidence-based understanding of STEM education.

Community for Advancing Discovery Research in Education 2 (CADRE 2)

CodeR4STATS - Code R for AP Statistics

This project builds on prior efforts to create teaching resources for high-school Advanced Placement Statistics teachers to use an open source statistics programming language called "R" in their classrooms. The project brings together datasets from a variety of STEM domains, and will develop exercises and assessments to teach students how to program in R and learn the underlying statistics concepts.

Lead Organization(s): 
Award Number: 
1418163
Funding Period: 
Mon, 09/01/2014 - Thu, 08/31/2017
Full Description: 

The Discovery Research K-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. Increasingly, all STEM fields rely on being able to understand data and use statistics. This project builds on prior efforts to create teaching resources for high-school Advanced Placement Statistics teachers to use an open source statistics programming language called "R" in their classrooms. The project brings together datasets from a variety of STEM domains, and will develop exercises and assessments to teach students how to program in R and learn the underlying statistics concepts. Thus, this project attempts to help students learn coding, statistics, and STEM simultaneously in the context of AP Stats. In addition, researchers will examine the extent to which students learn statistical concepts, computational fluency, and critical reasoning skills better with the online tools.

The resources developed by the project aim to enhance statistics learning through an integrated application of strategies previously documented to be effective: a focus on data visualization and representation, engaging students in meaningful investigations with complex real-world data sets, utilizing computational tools and techniques to analyze data, and better preparing educators for the needs of a more complex and technologically-rich mathematical landscape. This project will unite these lines of work into one streamlined pedagogical environment called CodeR4STATS with three kinds of resources: computing resources, datasets, and assessment resources. Computing resources will include freely available access to an instance of the cloud-based R-studio with custom help pages. Data resources will include over 800 scientific datasets from Woods Hole Oceanographic Institute, Harvard University's Institute for Quantitative Social Science, Hubbard Brook Experimental Forest, Boston University, and Tufts University with several highlighted in case studies for students; these will be searchable within the online environment. Assessment and tutoring resources will be provided using the tutoring platform ASSISTments which uses example tracing to provide assessment, feedback, and tailored instruction. Teacher training and a teacher online discussion board will also be provided. Bringing these resources together will be programming lab activities, five real-world case studies, and sixteen statistics assignments linked to common core math standards. Researchers will use classroom observational case studies from three classrooms over two years, including cross-case comparison of lessons in the computational environment versus offline lessons; student and teacher interviews; and an analysis of learner data from the online system, especially the ASSISTments-based assessment data. This research will examine learning outcomes and help refine design principles for statistics learning environments.

CodeR4STATS - Code R for AP Statistics
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