Mathematics

Perceptual and Implementation Strategies for Knowledge Acquisition of Digital Tactile Graphics for Blind and Visually Impaired Students (Collaborative Research: Smith)

This project lays the foundation and framework for enabling digital, multimodal tactile graphics on touchscreens for individuals with visual impairments (VI). Given the low-cost, portability, and wide availability of touchscreens, this work promotes the use of vibrations and sounds on these readily available platforms for addressing the graphical access challenge for individuals with VI.

Award Number: 
1644476
Funding Period: 
Sun, 01/15/2017 to Tue, 12/31/2019
Full Description: 

Students with disabilities often have fewer opportunities for experiential learning, an important component of quality STEM education. With continued shifts toward the use of digital media to supplement instruction in STEM classrooms, much of the content remains inaccessible, particular for students with visual impairments. The promise of technology and use of tactile graphics is an effective, emerging innovation for providing more complete access to important information and materials. Tactile graphics are images that use raised surfaces to convey non-textual information such as maps, paintings, graphs and diagrams. Touchscreen-based smart devices allow visual information to be digitally and dynamically represented via tactile, auditory, visual, and kinesthetic feedback. Tactile graphic technology embedded in touchscreen devices can be leveraged to make STEM content more accessible to blind and visually impaired students.

This project will develop a learner-centered, perceptually-motivated framework addressing the requirements for students with blindness and visual impairments to access graphical content in STEM. Using TouchSense technology, the investigators will create instructional materials using tactile graphics and test them in a pilot classroom of both sighted and BVI students. The investigators will work with approximately 150 students with visual impairments to understand the kind of feedback that is most appropriate for specific content in algebra (coordinate plane), cell biology, and geography. Qualitative research methods will be used to analyze the video-based data set.

Perceptual and Implementation Strategies for Knowledge Acquisition of Digital Tactile Graphics for Blind and Visually Impaired Students (Collaborative Research: Giudice)

This project lays the foundation and framework for enabling digital, multimodal tactile graphics on touchscreens for individuals with visual impairments (VI). Given the low-cost, portability, and wide availability of touchscreens, this work promotes the use of vibrations and sounds on these readily available platforms for addressing the graphical access challenge for individuals with VI.

Lead Organization(s): 
Award Number: 
1644471
Funding Period: 
Sun, 01/15/2017 to Tue, 12/31/2019
Full Description: 

Students with disabilities often have fewer opportunities for experiential learning, an important component of quality STEM education. With continued shifts toward the use of digital media to supplement instruction in STEM classrooms, much of the content remains inaccessible, particular for students with visual impairments. The promise of technology and use of tactile graphics is an effective, emerging innovation for providing more complete access to important information and materials. Tactile graphics are images that use raised surfaces to convey non-textual information such as maps, paintings, graphs and diagrams. Touchscreen-based smart devices allow visual information to be digitally and dynamically represented via tactile, auditory, visual, and kinesthetic feedback. Tactile graphic technology embedded in touchscreen devices can be leveraged to make STEM content more accessible to blind and visually impaired students.

This project will develop a learner-centered, perceptually-motivated framework addressing the requirements for students with blindness and visual impairments to access graphical content in STEM. Using TouchSense technology, the investigators will create instructional materials using tactile graphics and test them in a pilot classroom of both sighted and BVI students. The investigators will work with approximately 150 students with visual impairments to understand the kind of feedback that is most appropriate for specific content in algebra (coordinate plane), cell biology, and geography. Qualitative research methods will be used to analyze the video-based data set.

CAREER: Designing and Enacting Mathematically Captivating Learning Experiences for High School Mathematics

This project explores how secondary mathematics teachers can plan and enact learning experiences that spur student curiosity, captivate students with complex mathematical content, and compel students to engage and persevere (referred to as "mathematically captivating learning experiences" or "MCLEs"). The study will examine how high school teachers can design lessons so that mathematical content itself is the source of student intrigue, pursuit, and passion.

Lead Organization(s): 
Award Number: 
1652513
Funding Period: 
Wed, 02/15/2017 to Mon, 01/31/2022
Full Description: 

This design and development project explores how secondary mathematics teachers can plan and enact learning experiences that spur student curiosity, captivate students with complex mathematical content, and compel students to engage and persevere (referred to as "mathematically captivating learning experiences" or "MCLEs"). This study is important because of persistent disinterest by secondary students in mathematics in the United States. This study will examine how high school teachers can design lessons so that mathematical content itself is the source of student intrigue, pursuit, and passion. To do this, the content within mathematical lessons (both planned and enacted) is framed as mathematical stories and the felt tension between how information is revealed and withheld from students as the mathematical story unfolds is framed as its mathematical plot. The Mathematical Story Framework (Dietiker, 2013, 2015) foregrounds both the coherence (does the story make sense?) and aesthetic (does it stimulate anticipation for what is to come, and if so, how?) dimensions of mathematics lessons. The project will generate principles for lesson design usable by teachers in other settings and exemplar lessons that can be shared.

Specifically, this project draws from prior curriculum research and design to (a) develop a theory of teacher MCLE design and enactment with the Mathematical Story Framework, (b) increase the understanding(s) of the aesthetic nature of mathematics curriculum by both researchers and teachers, and (c) generate detailed MCLE exemplars that demonstrate curricular coherence, cognitive demand, and aesthetic dimensions of mathematical lessons. The project is grounded in a design-based research framework for education research. A team of experienced high school teachers will design and test MCLEs (four per teacher) with researchers through three year-long cycles. Prior to the first cycle, data will be collected (interview, observations) to record initial teacher curricular strategies regarding student dispositions toward mathematics. Then, a professional development experience will introduce the Mathematical Story Framework, along with other curricular frameworks to support the planning and enacting of lessons (i.e., cognitive demand and coherence). During the design cycles, videotaped observations and student aesthetic measures (surveys and interviews) for both MCLEs and a non-MCLEs (randomly selected to be the lesson before or after the MCLE) will be collected to enable comparison. Also, student dispositional measures, collected at the beginning and end of each cycle, will be used to learn whether and how student attitudes in mathematics change over time. Of the MCLEs designed and tested, a sample will be selected (based on aesthetic and mathematical differences) and developed into models, complete with the rationale for and description of aesthetic dimensions.

CAREER: Investigating Changes in Students' Prior Mathematical Reasoning: An Exploration of Backward Transfer Effects in School Algebra

This project explores "backward transfer", or the ways in which new learning impacts previously-established ways of reasoning. The PI will observe and evaluate algebra I students as they learn quadratic functions and examine how different kinds of instruction about the new concept of quadratic functions helps or hinders students' prior mathematical knowledge of the previous concept of linear functions.

Lead Organization(s): 
Award Number: 
1651571
Funding Period: 
Sat, 07/01/2017 to Thu, 06/30/2022
Full Description: 

As students learn new mathematical concepts, teachers need to ensure that prior knowledge and prior ways understanding are not negatively affected. This award explores "backward transfer", or the ways in which new learning impacts previously-established ways of reasoning. The PI will observe and evaluate students in four Algebra I classrooms as they learn quadratic functions. The PI will examine how different kinds of instruction about the new concept of quadratic functions helps or hinders students' prior mathematical knowledge of the previous concept of linear functions. More generally, this award will contribute to the field of mathematics education by expanding the application of knowledge transfer, moving it from only a forward focused direction to include, also, a backward focused direction. An advisory board of scholars with expertise in mathematics education, assessment, social interactions, quantitative reasoning and measurement will support the project. The research will occur in diverse classrooms and result in presentations at the annual conferences of national organizations, peer-reviewed publications, as well as a website for teachers which will explain both the theoretical model and the findings from the project. An undergraduate university course and professional development workshops using video data from the project are also being developed for pre-service and in-service teachers. Ultimately, the research findings will generate new knowledge and offer guidance to elementary school teachers as they prepare their students for algebra.

The research involves three phases. The first phase includes observations and recordings of four Algebra I classrooms and will test students' understanding of linear functions before and after the lessons on quadratic functions. This phase will also include interviews with students to better understand their reasoning about linear function problems. The class sessions will be coded for the kind of reasoning that they promote. The second phase of the project will involve four cycles of design research to create quadratic and linear function activities that can be used as instructional interventions. In conjunction with this phase, pre-service teachers will observe teaching sessions through a course that will be offered concurrently with the design research. The final phase of the project will involve pilot-applied research which will test the effects of the instructional activities on students' linear function reasoning in classroom settings. This phase will include treatment and control groups and further test the hypotheses and instructional products developed in the first two phases.

STEM Videohall: Connecting Communities and Disseminating Cutting Edge Work through Video and Discourse

This project supports the expansion of an interactive, online STEM Videohall where hundreds of NSF-funded researchers share their work through brief video narratives and interactive discussion.

Lead Organization(s): 
Award Number: 
1642187
Funding Period: 
Sat, 10/01/2016 to Mon, 09/30/2019
Full Description: 

Video has become a key tool for scientific communication because it increases the outreach and impact of projects, furthers scientific research within and across fields of study, and offers an accessible medium to engage the public in the understanding of science. This project supports the expansion of an interactive, online STEM Videohall where hundreds of NSF-funded researchers share their work through brief video narratives and interactive discussion. While the Videohall is accessible year-round, periodic annual Showcase events are used to drive visitors to the site where they can engage with one another, the project investigators and trained facilitators. The Videohall is a multiplier of NSF's investments in individual projects because it allows STEM education researchers to become aware of, and learn from, related work that is funded across NSF programs and directorates, and other federal agencies. In 3-minute video narratives, investigators share ideas, resources, data, evidence of impact, strategies and challenges. The Videohall platform supports open access and is designed to foster communication in ways that scale beyond traditional formats such as academic conferences. Moreover, because the online STEM Videohall is open to the public, it allows STEM investigators to share their work with multiple stakeholder communities including K-12 educators and school leaders, informal educators and community organizations, the STEM industry, education policy makers and families. Finally, because each video narrative is accompanied by a facilitated online discussion thread, investigators have a unique and valuable mechanism for receiving feedback from these various stakeholder communities. The STEM Videohall project is funded by the Discovery Research K-12 program (DRK-12), which 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. 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 brings together seven NSF-funded resource centers who work with their respective communities to encourage Principal Investigators to share video narratives of their work through annual NSF STEM Showcase events. Each annual Showcase event presents videos created by 150-230 projects; many of the projects are affiliated with one of the seven resource centers, but others are from projects across NSF directorates and beyond. During a one-week period, Principal Investigators, their project staff, as well as the public at large, are invited to engage in interactive discourse, providing queries, comments, and feedback. Participants also vote for favorite presentations through "Presenters' Choice," "Public Choice," and "Facilitators' Choice," processes. This participant voting system serves to increase engagement and enhances outreach of the event through social media. After the one-week Showcase event concludes, all of the videos along with the related discourse remain available to the public online, who continue to access the Showcase throughout the year. Based on prior pilot work, it is estimated that over the course of a year, over 30,000 visitors, from over 150 countries, will engage with each annual Showcase. Videos from annual showcase events will be shared, reused, and repurposed to create new products with new constituencies. The project includes technical development efforts to iteratively improve its interactive platform, outreach efforts before each annual Showcase event, facilitation of the week-long event, and intensive dissemination efforts. A research component examines the extent of participation on various constituencies, the benefit of participation to projects, and the success of the events in terms of dissemination nationally and internationally.

Supporting English Learners in STEM Subjects

This project will conduct a study to identify instructional practices and professional development approaches for teachers and the policies needed to support ELLs' accomplishments in science and math. The study will synthesize research relevant to improving ELLs' STEM learning, offer insight into how to support both English language development and science and math learning, and provide a framework for future research to help identify the most relevant and pressing questions for the field.

Lead Organization(s): 
Award Number: 
1636544
Funding Period: 
Thu, 09/01/2016 to Thu, 02/28/2019
Full Description: 

The expectation that all students, including English language learners (ELLs), achieve high academic standards has become even more evident and complex to date as a result of several key factors. First, as the school-aged population continues to grow more racially, ethnically, and linguistically diverse, ELLs can now be found in virtually every school in the nation. Second, the science and mathematics education landscape has changed significantly resulting from the new visions in these fields, and the challenges posed by the new academic standards for all students. Third, the need to integrate new knowledge and perspectives from the language arts with knowledge from science and mathematics learning, instruction, and assessment has surfaced as a critical component of the potential strategies to be employed in addressing ELLs' current science, technology, engineering, and mathematics (STEM) education situation from pre-K-12 grades. The key challenges today include both enabling educators to better support this student subpopulation, as well as increasing the number and quality of research activities focused on how best to support ELLs' success in these subjects. In response to this challenge, the Board on Science Education (BOSE) of the National Academies of Sciences will conduct a consensus study focused on identifying instructional practices and professional development approaches for teachers, as well as the policies that are needed to support ELLs' accomplishments in science and mathematics education. The study will synthesize a wide range of research literatures relevant to improving ELLs' STEM learning, and provide a comprehensive understanding of how best to simultaneously support English language development and deep learning in the context of new and more challenging standards in science and mathematics. The study will also provide a framework for future research that can help to identify the most relevant and pressing questions for the field, as well as increase the number and quality of proposed research activities focused on ELLs in STEM.

To conduct the consensus study, BOSE will convene a multidisciplinary committee of experts who will synthesize the most relevant research on related subjects. The committee will include professionals in the fields of science and mathematics education, curriculum development, learning and instruction, linguistics, and assessment to address key sets of research questions: (1) Based on research-informed and field-tested models, strategies, and approaches, what are promising approaches to support ELLs (including ELLs with disabilities) in learning STEM? Given the diversity within the ELLs' population, what has worked, for whom, and under what conditions? What can be learned from these models and what additional research is needed to understand what makes them effective? What commonly used approaches may be less effective?; (2) What is the role of teachers in supporting the success of ELLs in STEM? What is known about the biases teachers may bring to their classrooms with ELLs and how these can be effectively addressed? What kinds of curriculum, professional development experiences, and assessment are needed in order for STEM teachers to improve their support for ELLs in STEM?; (3) How can assessments in STEM (both formative and summative) be designed to reflect the new content standards and to be appropriate for ELLs? What assessment accommodations might need to be considered?; (4) How do policies and practices at the national, state, and local level constrain or facilitate efforts to better support ELLs in STEM (including policies related to identification of students)? What kinds of changes in policy and practice are needed?; and (5) What are the gaps in the current research base and what are the key directions for research, both short-term and long-term? The committee will work over a 30-month period to synthesize relevant research literature and prepare a final consensus report, including results, conclusions, and recommendations. The study will address an issue of national importance and will inform future research on challenges directly related to ELLs, diversity, and equity in STEM education. This issue is particularly relevant to programs such as Discovery Research K-12 that supports efforts that reflect the needs of the increasingly diverse population, and Innovative Technology Experiences for Students and Teachers, which supports strategies for recruiting and selecting participants from identified groups currently underrepresented in STEM professions, careers, and education pathways. The report will target a broad audience of stakeholders, including teachers, school district administrators, researchers, congressional staff, and federal agencies that fund educational research and set policies related to ELLs.

Development of the Electronic Test of Early Numeracy

The project will develop and refine an electronic Test of Early Numeracy (e-TEN) in English and Spanish that will assess informal and formal knowledge of number and operations in domains including verbal counting, numbering, numerical relationships, and mental addition/subtraction. The overarching goal of the assessment design is to create a measure that is more accurate, more accessible to a wider range of children, and easier to administer than existing measures.

Partner Organization(s): 
Award Number: 
1621470
Funding Period: 
Thu, 09/15/2016 to Tue, 08/31/2021
Full Description: 

The project will develop and refine an electronic Test of Early Numeracy (e-TEN) in English and Spanish, focused on number and operations. The assessment will incorporate a learning trajectory that describes students' development of the understanding of number. The electronic assessment will allow for the test to adapt to students' responses and incorporate games to increase children's engagement with the tasks. These features take advantage of the electronic format. The achievement test will be designed to be efficient, user-friendly, affordable, and accessible for a variety of learning environments and a broad age range (3 to 8 years old). The overarching goal of the assessment design is to create a measure that is more accurate, more accessible to a wider range of children, and easier to administer than existing measures. This project is funded by the Discovery Research Pre-K-12 Program, which funds research and development of STEM innovations and approaches in assessment, teaching and learning.

The e-TEN will assess informal and formal knowledge of number and operations in domains including verbal counting, numbering, numerical relationships, and mental addition/subtraction. The items will be designed using domain-based learning trajectories that describe students' development of understanding of the topics. The test will be designed with some key characteristics. First, it will be semi-adaptive over six-month age spans. Second, it will have an electronic format that allows for uniform implementation and an efficient, user-friendly administration. The test will also be accessible to Spanish speakers using an inclusive assessment model. Finally, the game-based aspect should increase children's engagement and present more meaningful questions. The user-friendly aspect includes simplifying the assessment process compared to other tests of numeracy in early-childhood. The first phase of the development will test a preliminary version of the e-TEN to test its functionality and feasibility. The second phase will focus on norming of the items, reliability and validity. Reliability will be assessed using Item Response Theory methods and test-retest reliability measures. Validity will be examined using criterion-prediction validity and construct validity. The final phase of the work will include creating a Spanish version of the test including collecting data from bilingual children using both versions of the e-TEN.

Longitudinal Learning of Viable Argument in Mathematics for Adolescents

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.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1621438
Funding Period: 
Thu, 09/01/2016 to Mon, 08/31/2020
Full Description: 

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.

Algebra Project Mathematics Content and Pedagogy Initiative

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.

Award Number: 
1621416
Funding Period: 
Thu, 09/15/2016 to Mon, 08/31/2020
Full Description: 

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.

Strengthening Mathematics Intervention: Identifying and Addressing Challenges to Improve Instruction for Struggling Learners

This project's first goal is to study the national landscape of mathematics intervention classes, which are additional classes provided to struggling students, including learners with and without identified disabilities. We administered a survey to a nationally representative sample of 2,024 urban and suburban public schools with grades 6-8 to find out how these classes are being implemented and the types of challenges faced.

Award Number: 
1621294
Funding Period: 
Thu, 09/15/2016 to Mon, 08/31/2020
Full Description: 

Across the nation, schools face a pressing need to improve instruction for middle grades students who are not reaching proficiency on standardized assessments. One approach is to schedule additional mathematics classes to provide struggling learners with more time for instruction and support. For our study, we defined mathematics interventional classes as classes taken by struggling students during the regular school day in addition to their general education mathematics classes. These classes are for students who have difficulties learning mathematics, including learners who do not have identified disabilities and those with Individualized Education Programs (IEPs). 

While recommendations for intervention practices are present in the research literature, little is known about how schools are actually implementing intervention classes, including how often the classes meet, the number of students enrolled, who teaches them and the content focus. To address this gap in the knowledge base, we conducted an observational study and a national survey of current practices and challenges in mathematics intervention classes. The survey was administered to a nationally representative sample of 2,024 urban or suburban public schools with grades 6-8.  Approximately, 43% of schools (876 schools) responded; the findings revealed widespread implementation of mathematics intervention classes and variations in class structures and practices. 

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. We are developing and testing a blended professional development course to help teachers build the knowledge and practices needed to provide high-quality, targeted instruction to struggling learners in mathematics intervention classes.

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