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resource project Public Programs
In partnership with the Pasadena and Los Angeles Unified School Districts, the Armory Center for the Arts will develop and implement comprehensive visual art-math and visual art-science curricula for grades two through five at Title I elementary schools. The curricula will be developed in conjunction with Armory teaching artists and educators, and will align with the Common Core Standards for math and science, and with the National Core Visual Arts Standards. The museum will deliver the program in 48 classrooms over a three-year period. Professional development, paired with in-class program modeling, will enable participating teachers to implement arts integration strategies into their teaching practice, with an overall goal of creating a sustainable and long-term impact on student learning. An external evaluator will oversee program assessment in the schools. The museum will post sample lessons from each curriculum online to demonstrate the style and scope of the program for possible use by additional school districts.
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TEAM MEMBERS: Julienne Fusello
resource research Public Programs
We characterize the factors that determine who becomes an inventor in the United States, focusing on the role of inventive ability (“nature”) vs. environment (“nurture”). Using deidentified data on 1.2 million inventors from patent records linked to tax records, we first show that children’s chances of becoming inventors vary sharply with characteristics at birth, such as their race, gender, and parents’ socioeconomic class. For example, children from high-income (top 1%) families are ten times as likely to become inventors as those from below-median income families. These gaps persist even
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TEAM MEMBERS: Alex Bell Raj Chetty Xavier Jaravel Neviana Petkova John Van Reenen
resource evaluation Media and Technology
Peg + Cat is a popular broadcast television series, developed by The Fred Rogers Company and airing on PBS, in which a girl named Peg and her sidekick, Cat, solve everyday problems using mathematics, creativity, persistence, and humor. Peg + Cat: Developing Preschoolers’ Early Math Skills was a three-year project, funded by the National Science Foundation, that aimed to impact children’s interest and engagement with mathematics, as well as their development of positive social-emotional skills. The project supported early math learning via the creation of additional Peg + Cat episodes, online
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resource project Media and Technology
This Research Advanced by Interdisciplinary Science and Engineering (RAISE) project is supported by the Division of Research on Learning in the Education and Human Resources Directorate and by the Division of Computing and Communication Foundations in the Computer and Information Science and Engineering Directorate. This interdisciplinary project integrates historical insights from geometric design principles used to craft classical stringed instruments during the Renaissance era with modern insights drawn from computer science principles. The project applies abstract mathematical concepts toward the making and designing of furniture, buildings, paintings, and instruments through a specific example: the making and designing of classical stringed instruments. The research can help instrument makers employ customized software to facilitate a comparison of historical designs that draws on both geometrical proofs and evidence from art history. The project's impacts include the potential to shift in fundamental ways not only how makers think about design and the process of making but also how computer scientists use foundational concepts from programming languages to inform the representation of physical objects. Furthermore, this project develops an alternate teaching method to help students understand mathematics in creative ways and offers specific guidance to current luthiers in areas such as designing the physical structure of a stringed instrument to improve acoustical effect.

The project develops a domain-specific functional programming language based on straight-edge and compass constructions and applies it in three complementary directions. The first direction develops software tools (compilers) to inform the construction of classical stringed instruments based on geometric design principles applied during the Renaissance era. The second direction develops an analytical and computational understanding of the art history of these instruments and explores extensions to other maker domains. The third direction uses this domain-specific language to design an educational software tool. The tool uses a calculative and constructive method to teach Euclidean geometry at the pre-college level and complements the traditional algebraic, proof-based teaching method. The representation of instrument forms by high-level programming abstractions also facilitates their manufacture, with particular focus on the arching of the front and back carved plates --- of considerable acoustic significance --- through the use of computer numerically controlled (CNC) methods. The project's novelties include the domain-specific language itself, which is a programmable form of synthetic geometry, largely without numbers; its application within the contemporary process of violin making and in other maker domains; its use as a foundation for a computational art history, providing analytical insights into the evolution of classical stringed instrument design and its related material culture; and as a constructional, computational approach to teaching geometry.

This project is funded by the National Science Foundation's (NSF's) Advancing Informal STEM Learning (AISL) program, which supports innovative research, approaches, and resources for use in a variety of learning settings.
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TEAM MEMBERS: Harry Mairson
resource project Informal/Formal Connections
As part of its overall strategy to enhance learning in informal environments, the Advancing Informal STEM Learning (AISL) program seeks to advance new approaches to, and evidence-based understanding of, the design and development of STEM learning in informal environments. This includes providing multiple pathways for broadening access to and engagement in STEM learning experiences, advancing innovative research on and assessment of STEM learning in informal environments, and developing understandings of deeper learning by participants. The three-year project, Montana Models: Connecting Local and Disciplinary Practices through University-Community Partnerships, focuses on creating, implementing, and studying several learning outcomes associated with youth engagement in mathematical modeling contexts. The project builds on existing partnerships between the state's two research universities and Montana 4-H to target outreach to rural youth and bring them into a network of people who can inspire, support, and sustain STEM learning. Middle school and high school students from rural communities will be invited to a university campus for a residential modeling-based summer program l focused on mathematics and mathematical modeling. Activities at the summer program are designed to engage them in problems relevant to their own backgrounds and experiences and to honor their local funds of knowledge. The primary goal of Montana Models is to use mathematical modeling as a mechanism for bringing everyday mathematical practices already present in rural communities into contact with disciplinary practices. The project focuses on the following research questions: (1) What are the everyday mathematical practices in Montana communities? (2) How can everyday mathematical practices be leveraged and brought into contact with disciplinary practices in service of mathematizing meaningful questions within the community? (3) How do youth identify and get identified with respect to mathematics and with respect to their role in the world? (4) How does participation in project activities affect participants' knowledge of mathematical practices and content? The project uses social design experimentation, a hybrid research methodology which combines the traditions of design-based research with forms of inquiry that involve collaboration among participants, researchers, and other stakeholders, such as critical ethnography. Data sources include field notes from ethnographic observations, interviews, videos of students engaging in modeling activities, artifacts that show their mathematical work, and results from the Attitudes Towards Mathematics Inventory. Through its collaboration with 4-H, Montana Models targets outreach to rural youth across the state, especially those from groups that are typically underrepresented in STEM fields. The project is poised to impact ways in which formal and informal educators understand the knowledge bases that are already present in rural communities and how those bases may inform, support, and sustain STEM learning. Findings and deliverables will be disseminated through a public-facing website and through the 4-H infrastructure. This infrastructure includes Montana 4-H's Clover Communication Contest that will allow participating youth to showcase their projects. Research findings will be shared through local and national conferences and peer-reviewed publications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
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TEAM MEMBERS: Mary Carlson Elizabeth Burroughs Frederick Peck Katharine Banner david thomas
resource project Public Programs
This award was provided as part of NSF's Social, Behavioral and Economic Sciences Postdoctoral Research Fellowships (SPRF) program and is supported by SBE's Developmental Sciences program and the Directorate for Education and Human Resources' (EHR) Advancing Informal STEM Learning program. The goal of the SPRF program is to prepare promising, early career doctoral-level scientists for scientific careers in academia, industry or private sector, and government. SPRF awards involve two years of training under the sponsorship of established scientists and encourage Postdoctoral Fellows to perform independent research. NSF seeks to promote the participation of scientists from all segments of the scientific community, including those from underrepresented groups, in its research programs and activities; the postdoctoral period is considered to be an important level of professional development in attaining this goal. Each Postdoctoral Fellow must address important scientific questions that advance their respective disciplinary fields. Under the sponsorship of Dr. Sandra D. Simpkins at the University of California, Irvine, this postdoctoral fellowship award supports an early career scientist exploring high-quality and culturally responsive, math afterschool program (ASP) practices for under-represented minority (URM) youth. Mathematical proficiency is the foundation of youth's STEM pursuits. Yet today, far too many youth do not pursue STEM based on a perception that they are "not good at math". Students need to engage in contexts that spark their interest and their continued mastery and growth. ASPs are settings for such dynamic opportunities, particularly for URM students such as Latinos who attend lower quality schools and do not feel supported. In college, URM students often struggle with uninspiring and culturally incongruent STEM learning environments. The intergenerational nature of university-based STEM ASPs, whereby younger students are paired with undergraduate (UG) mentors, are opportunities to support both K-12 and UG students' motivational beliefs in math and STEM more broadly. This project will examine these intergenerational developmental processes in the context of a math enrichment ASP located at a Hispanic-Serving Institution. By studying how ASPs can serve as an important lever for promoting URM students' access and success in STEM, this project seeks to meaningfully inform efforts to broaden the participation of underrepresented groups in these fields.

This project seeks to understand how participating in a math enrichment ASP supports both youth participants' and UG mentors' motivational beliefs in math; to describe high-quality and culturally responsive practices; and to understand how to support the effectiveness of youth-staff relationships. To accomplish these research objectives, data will be collected from both youth participants and UG mentors through multiple methods including surveys, in-depth interviews, participant-observations, and video observations of youth-staff interactions. This project will add to our understanding of university-ASP partnerships. Further, the knowledge gained from this study will impact the larger landscape of practice and research on STEM ASPs by 1) addressing critical gaps in the current literature on high-quality and culturally responsive STEM ASP practices and 2) informing ASP staff development training. Overall, this mixed methods project will provide critical and rich information on the ways that ASPs can effectively deliver on its promise of promoting positive development for all youth, especially URM youth who may need and benefit from these spaces the most. The invaluable insight garnered from this study will be disseminated to traditional academic audiences to advance knowledge, as well as to local, state, and national organizations to inform the larger landscape of practice in STEM ASPs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
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TEAM MEMBERS: Mark Vincent Yu Sandra Simpkins
resource project Informal/Formal Connections
Parents exert a strong influence on the development of foundational science, technology, engineering, and mathematical (STEM) skills in early childhood. This influence occurs, in large part, through playful parent-child interactions and conversations that expose children to mathematical and spatial concepts in interesting and useful ways. For example, parents of preschool children are often encouraged to use puzzles, board games, and construction activities to foster children's spatial thinking and early math skills. However, mastery-oriented toys like these typically elicit highly structured interactions, with parents directing children to follow explicit step-by-step instructions and game rules. Although this kind of parent-directed play can build content knowledge in STEM, it does little to encourage the kind of intrinsically-motivated discovery, generative collaboration, and creative problem-solving skills that support STEM education and attainment. This research in service to practice project seeks to understand how parents can play with their preschool children in ways that build children's STEM skills while also supporting children's social-emotional skills. As such, this research has the potential for advancing knowledge on effective strategies for enriching informal learning opportunities in under-resourced and sparsely populated communities where access to children's museums and other informal learning institutions is limited. Over a period of three years, approximately 135 children and parents from a rural Appalachian community are expected to participate in this research, which is organized into three phases. During Phase 1, human-centered design processes will be used to develop and refine play guides and parent scaffolds that promote productive pretend play, which is characterized by joyful and creative problem-solving and rich parent/child conversations featuring mathematical and spatial concepts and reasoning. In Phase 2, measures will be developed and validated to operationalize and code this kind of productive parent-child play and play guides will be tested and refined in a local children's museum. In the final phase, a formal field test will investigate the feasibility and acceptability of outreach programming involving the use of play guides over time. Pre-, mid-, and post-intervention measures will estimate program impact on child STEM and social-emotional skill acquisition, relative to a comparison group. An expected outcome of the project will be research-based educational materials that illustrate and support pretend play in ways that generate spatial and mathematical thinking and parent/child conversations. These materials will will be made available to families and informal learning practitioners. This project is funded by the Advancing Informal STEM Learning (AISL) program, which seeks to advance new approaches to, and evidence-based understanding of, the design and development of STEM learning in informal environments. This includes providing multiple pathways for broadening access to and engagement in STEM learning experiences, advancing innovative research on and assessment of STEM learning in informal environments, and developing understandings of deeper learning by participants. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
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TEAM MEMBERS: Karen Bierman Lynn Liben Meg Small Jessica Menold
resource research Informal/Formal Connections
Data are the workhorses of the scientific endeavor and their use is rapidly evolving (Haendel, Vasilevsky, and Wirz 2012). Ask almost any scientist about their work, and the conversation will involve the data they collect and analyze. The use of data in science is often captured in science classrooms as an ill-defined link between math and science that may not reflect authentic data practices (Tanis Ozcelik and McDonald 2013). Students often find themselves collecting data to confirm obvious conclusions within highly structured labs, and data become a way for students to demonstrate the
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TEAM MEMBERS: Michael Giamellaro Kari O'Connell
resource project Community Outreach Programs
This NSF INCLUDES Design and Development Launch Pilot will improve math achievement among elementary school students of color in public schools in Albuquerque, New Mexico. Recognizing the need to coordinate efforts related to students' math and science achievement, key stakeholders formed the NM STEM Ecosystem, a dynamic network of cross-sector partners committed to making real impact on STEM education and degree attainment in Albuquerque. The NM STEM Ecosystem identified the math achievement gap between low-income students of color and their more economically-advantaged peers as the Broadening Participation (BP) Challenge it would address first. While math achievement gaps between students of color and Caucasian students appear nationally, the situation is particularly dire in New Mexico. In order to keep doors open to future STEM careers, it is crucial that learning pathways for math are articulated early and that these pathways honor families' cultural ways of knowing. The innovative strategy of Math Families & Communities Empowering Student Success (Math FACESS) is to use a collective impact approach to close the math achievement gap by connecting formal and informal STEM educators around a coherent, multi-faceted program of early mathematics teaching and learning that empowers parents and teachers to support children's mathematical development. Implementation of Math FACESS includes four major components: 1) Teachers at two pilot schools will participate in professional development related to Math Talk and Listening; 2) Parents at the pilot schools will participate in parent workshops and community-based activities focused on supporting their children's math achievement; 3) Project partners will implement community-based family activities organized around a theme of Twelve Months of Math; and 4) Ecosystem partners will study what worked and what didn't, in order to identify best practices that can be shared with system leaders to scale effective practices and increase impact.

The near-term objectives for Math FACESS are: 1) improve students' attitudes, practices, and achievement in math; 2) improve parents' attitudes, practices, and confidence in math and increase their utilization of family math resources; 3) improve data-sharing among partners related to math participation and achievement; and 4) create pathways within the Ecosystem for family math learning. The effectiveness of the collective impact model and impacts on partner organizations also will be assessed. Through the math FACESS Launch Pilot, the NM STEM Ecosystem plans to: 1) demonstrate the power of a collective impact social innovation framework to address a systemic community condition -- in this case, the math achievement gap; 2) contribute to theory-of-change research that demonstrates student achievement can be affected by working with parents and teachers; and 3) provide a model that values different ways of knowing and uses cultural context in the design of STEM learning opportunities for students, families, and schools.
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TEAM MEMBERS: Joe Hastings Armelle Casau Obenshain Koren Kersti Tyson Angelo Gonzales
resource project Resource Centers and Networks
In this NSF INCLUDES Design and Development Launch Pilot the institutions of "Building on Strengths" propose to build and pilot the infrastructure, induction process, and early implementation of the Mathematician Affiliates of Color network. This network will consist of mathematicians of color from across academia and industry who want to invest time in, share their expertise with, and learn from students of color and their teachers. Building on Strengths will draw on basic needs cognitive theory to support these interactions and will focus narrowly on short and moderate term collaborations (from one month to a semester) between visiting mathematicians, students, and collaborating teachers that will involve three specific types of interactions: doing mathematics together as a habits-of-mind practice, talking about the discipline of mathematics and the experiences of mathematicians of color in that discipline, and relationship-building activities. The foundational infrastructure developed in the project will include systems for recruitment, selection and induction, a process for pairing affiliate mathematicians with classrooms, and support structures for the collaborations. To support the goals of the network a prototype virtual space will be developed in which real-time artifacts can be collected and shared from the classroom interactions. While Building on Strengths will pilot this program in the secondary context, once a viable model is established, scaling to K-16, as well as to other STEM fields, will be possible.

The research study in the project uses an exploratory sequential mixed-methods design and will be conducted in two phases. In the first, quantitative, phase of the study the following questions will be addressed: (1) Is the teacher-mathematician collaboration associated with a change for students in perception of basic human needs being met, mathematical or racial identities, or beliefs about mathematics or who can do mathematics? (2) Is the teacher-mathematician collaboration associated with a change for adults in perceptions of the role of basic needs or in adults' identities or beliefs about mathematics or who can do mathematics? In the second, qualitative, phase of the study, two types of interactions will be selected for in-depth qualitative study, identifying cases where groups of students experienced changes in their needs, identity, and beliefs. In this qualitative case-centered phase, the following questions will be explored: (1) What is the nature of the mentor-student interaction? (2) What aspects of the intervention do students feel are most relevant to them? (3) How did the implementation of the intervention differ from the anticipated intervention? The results of the study will help improve the infrastructure for, and better support the interactions between, mathematicians of color, students of color and their mathematics teachers; the outcomes will also shed light on how students experience their interactions.
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TEAM MEMBERS: Michael Young Maisha Moses Albert Cuoco Eden Badertscher
resource project Informal/Formal Connections
As part of its overall strategy to enhance learning in informal environments, the Advancing Informal STEM Learning (AISL) program funds innovative research, approaches and resources for use in a variety of settings. This Research in Service to Practice project will address the issues around Informal Education of rural middle school students who have high potential regarding academic success in efforts to promote computer and IT knowledge, advanced quantitative knowledge, and STEM skills. Ten school districts in rural Iowa will be chosen for this study. It is anticipated that new knowledge on rural informal education will be generated to benefit the Nation's workforce. The specific objectives are to understand how informal STEM learning shapes the academic and psychosocial outcomes of rural, high-potential students, and to identify key characteristics of successful informal STEM learning environments for rural, high-potential students and their teachers. The results of this project will provide new tools for educators to increase the flow of underserved students into STEM from economically-disadvantaged rural settings.

The President's Council of Advisors on Science and Technology predicts a rapid rise in the number of STEM jobs available in the next decade, describing an urgent need for students' educational opportunities to prepare them for this workforce. In 2014, 62% of CEOs of major US corporations reported challenges filling positions requiring advanced computer and information technology knowledge. The project team will use a mixed methods approach, integrating comparative case study and mixed effects longitudinal methods, to study the Excellence program. Data sources include teacher interviews, classroom observations, and student assessments of academic aptitude and psychosocial outcomes. The analysis and evaluation of the program will be grounded in understanding the local efforts of school districts to build curriculum responsive to the demands of their high-potential student body. The project design, and subsequent analysis plan, utilizes a mixed methods approach, incorporating case study and longitudinal quantitative methods to analyze naturalistic data and build robust evidence for the implementation and impact of this program. This project will provide significant insights in how best to design, implement, and support informal out-of-school learning environments to broaden participation in the highest levels of STEM education and careers for under-resourced rural students.
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TEAM MEMBERS: Susan Assouline
resource project Informal/Formal Connections
This proposal was submitted in response to EHR Core Research (ECR) program announcement NSF 15-509. The ECR program of fundamental research in STEM education provides funding in critical research areas that are essential, broad and enduring. EHR seeks proposals that will help synthesize, build and/or expand research foundations in the following focal areas: STEM learning, STEM learning environments, STEM workforce development, and broadening participation in STEM. The ECR program is distinguished by its emphasis on the accumulation of robust evidence to inform efforts to (a) understand, (b) build theory to explain, and (c) suggest interventions (and innovations) to address persistent challenges in STEM interest, education, learning, and participation.

The study will investigate the processes that connect gestures and mathematics learning. Gestures are an important yet under-investigated aspect of mathematics teaching. They can influence students' memory and understanding of mathematical representations. The series of studies will examine students' learning of the concept of mathematical equivalence by testing instruction that incorporates commonly used verbal explanations and gestures. Mathematical equivalence includes understanding the meaning of the equal sign and determining if two expressions are equal. Second and third grade children will be participants. Of particular interest in the studies is the influence of gestures on preexisting knowledge of procedures, how gestures support learning beyond emphasizing information and direct learners' attention, and the creation of procedural knowledge.

The series of experimental studies will examine the mechanisms that connect gestures and procedural understanding of mathematical equivalence. The studies begin in the first phase with examining how gesture is connected to procedural knowledge of mathematical equivalence. Subsequent studies investigate how gesture functions as a mechanism for learning beyond emphasizing or directing attention to relevant information. Data collected will students' responses to equivalence problems and eye tracking data to follow whether students are looking from one side of the equal sign to the other. In the second phase of the work, the studies will examine how gesture has beneficial effects on learning more generally in mathematics. Working memory will be assessed in order to examine the role of gesture across different individuals. Fraction tasks will be used to examine the generalization of the previous results regarding gestures to other mathematics concepts.
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TEAM MEMBERS: Kimberly Fenn Susan Cook