Mathematics

CAREER: Exploring Teacher Noticing of Students' Multimodal Algebraic Thinking

This project investigates and expands teachers' learning to notice in two important ways. First, the research expands beyond teachers' noticing of written and verbal thinking to attend to gesture and other aspects of embodied and multimodal thinking. Second, the project focuses on algebraic thinking and seeks specifically to understand how teacher noticing relates to the content of algebra. Bringing together multimodal thinking and the mathematical ideas in algebra has the potential to support teachers in providing broader access to algebraic thinking for more students.

Award Number: 
1942580
Funding Period: 
Mon, 06/01/2020 to Sat, 05/31/2025
Full Description: 

Effective teachers of mathematics attend to and respond to the substance of students' thinking in supporting classroom learning. Teacher professional development programs have supported teachers in learning to notice students' mathematical thinking and using that noticing to make instructional decisions in the classroom. This project investigates and expands teachers' learning to notice in two important ways. First, the research expands beyond teachers' noticing of written and verbal thinking to attend to gesture and other aspects of embodied and multimodal thinking. Second, the project focuses on algebraic thinking and seeks specifically to understand how teacher noticing relates to the content of algebra. Bringing together multimodal thinking and the mathematical ideas in algebra has the potential to support teachers in providing broader access to algebraic thinking for more students.

To study teacher noticing of multimodal algebraic thinking, this project will facilitate video club sessions in which teachers examine and annotate classroom video. The video will allow text-based and visual annotation of the videos to obtain rich portraits of the thinking that teachers notice as they examine algebra-related middle school practice. The research team will create a video library focused on three main algebraic thinking areas: equality, functional thinking, and proportional reasoning. Clips will be chosen that feature multimodal student thinking about these content areas, and provide moments that would be fruitful for advancing student thinking. Two cohorts of preservice teachers will engage in year-long video clubs using this video library, annotate videos using an advanced technological tool, and engage in reflective interviews about their noticing practices. Follow-up classroom observations will be conducted to see how teachers then notice multimodal algebraic thinking in their classrooms. Materials to conduct the video clubs in other contexts and the curated video library will be made available, along with analyses of the teacher learning that resulted from their implementation.

CAREER: Investigation of Beginning Teachers' Expertise to Teach Mathematics via Reasoning and Proof

This project aims to develop the knowledge to teach reasoning and proving with secondary teacher candidates, and to follow them into they first years of independent practice to better understand how they are using that knowledge.  The goals of the project are to better understand how beginning teachers' knowledge, dispositions, and proof-related practices evolve over time, and how the sociocultural context and support structures of the schools teachers are in influences their teaching of reasoning and proving.

Lead Organization(s): 
Award Number: 
1941720
Funding Period: 
Mon, 06/01/2020 to Sat, 05/31/2025
Full Description: 

Supporting teachers in integrating reasoning and proving as a mathematical practice into secondary math classes is a persistent challenge. These disciplinary practices are challenging to learn and to teach, and are frequently taught in a procedural way that is limited to the context of high school geometry courses. While much is known about the robust nature of reasoning and proving in mathematics and the content knowledge needed to teach it, less is known about how beginning teachers develop that knowledge and how that knowledge is translated into classroom practice. This project aims to develop the knowledge to teach reasoning and proving with secondary teacher candidates, and to follow them into they first years of independent practice to better understand how they are using that knowledge. The goals of the project are to better understand how beginning teachers' knowledge, dispositions, and proof-related practices evolve over time, and how the sociocultural context and support structures of the schools teachers are in influences their teaching of reasoning and proving.

This project consists of three stages: preservice teacher preparation, the teaching internship, and novice teaching (the first two years of independent practice). During the teacher preparation phase, preservice teachers will take part in a capstone course focused on reasoning and proving, including enacting lessons in related to reasoning and proving in local middle schools. Using the Mathematical Knowledge for Teaching Proof framework, teachers' knowledge and dispositions towards reasoning and proving will be assessed through pre- and post-course assessment and surveys. Their example lessons will be video recorded and analyzed with respect to proof content, and they will engage in post-course interviews. In the next phase, during year-long student teaching internships, they will be asked to integrate reasoning and proving into their classroom practice. A set of target lessons will be recorded and analyzed, with full unit artifacts being collected and analyzed and pre- and post-unit interviews with the teacher conducted. The third phase follows teachers into their first two years of teaching practice and asks them to identify two units related to reasoning and proving to serve as data sources. The research team will conduct start and end of year interviews with the teachers, collect video recordings of the units and associated artifacts, administer a dispositions towards proof survey, and conduct pre- and post-unit interviews. Teachers will also participate in a professional learning community designed to support their teaching related to reasoning and proving. Data will be analyzed across the three phases using case study methodology to characterize patterns of knowledge, dispositions, and practice related o reasoning and proving. The project will also make available educational materials related to the capstone course and the professional learning community that will further support the development of teachers' knowledge and capacity for teaching reasoning and proving.

CAREER: Supporting Model Based Inference as an Integrated Effort Between Mathematics and Science

This project will design opportunities for mathematics and science teachers to coordinate their instruction to support a more coherent approach to teaching statistical model-based inference in middle school. It will prepare teachers to help more students develop a deeper understanding of ideas and practices related to measurement, data, variability, and inference.

Award Number: 
1942770
Funding Period: 
Sat, 02/01/2020 to Fri, 01/31/2025
Full Description: 

This project will design opportunities for mathematics and science teachers to coordinate their instruction to support a more coherent approach to teaching statistical model-based inference in middle school. It will prepare teachers to help more students develop a deeper understanding of ideas and practices related to measurement, data, variability, and inference. Since there is little research to show how to productively coordinate learning experiences across disciplinary boundaries of mathematics and science education, this project will address this gap by: (1) creating design principles for integrating instruction about statistical model-based inference in middle grades that coordinates data modeling instruction in mathematics classes with ecology instruction in science classes; (2) generating longitudinal (2 years) evidence about how mathematical and scientific ideas co-develop as students make use of increasingly sophisticated modeling and inferential practices; and (3) designing four integrated units that coordinate instruction across mathematics and science classes in 6th and 7th grade to support statistical model-based inference.

This project will use a multi-phase design-based research approach that will begin by observing teachers' current practices related to statistical model-based inference. Information from this phase will help guide researchers, mathematics teachers, and science teachers in co-designing units that integrate data modeling instruction in mathematics classes with ecological investigations in science classes. This project will directly observe students? thinking and learning across 6th and 7th grades through sample classroom lessons, written assessment items, and interviews. Data from these aspects of the study will generate evidence about how students make use of mathematical ideas in science class and how their ecological investigations in science class provoke a need for new mathematical tools to make inferences. The resulting model will integrate mathematics and science learning in productive ways that are sensitive to both specific disciplinary learning goals and the ways that these ideas and practices can provide a better approximation for students to knowledge generating practices in STEM disciplines.

CAREER: Understanding Latinx Students' Stories of Doing and Learning Mathematics

This project characterizes and analyses the developing mathematical identities of Latinx students transitioning from elementary to middle grades mathematics. The central hypothesis of this project is that elementary Latino students' stories can identify how race and language are influential to their mathematical identities and how school and classroom practices may perpetuate inequities.

Lead Organization(s): 
Award Number: 
1941952
Funding Period: 
Mon, 06/01/2020 to Sat, 05/31/2025
Full Description: 

Although the Latino population throughout the United States continues to increase, various researchers have shown that Latino students are often not afforded high quality learning experiences in their mathematics classrooms. As a result, Latino students are underrepresented in higher level mathematics courses and careers involving mathematics. Having a better understanding of Latino students' perspectives and experiences is imperative to improving their opportunities to learn mathematics. Yet, little research has made central Latinos students' perspectives of learning and doing mathematics, especially over a critical period of time like the transition from elementary to middle school. The goal of this study will be to improve mathematics teaching and learning for Latino youth as they move from upper elementary to early middle school mathematics classrooms. The project involves three major parts: investigating the policy, media, and oral histories of Latino families/communities to understand the context for participating Latino students' mathematics education; exploring Latino students' stories about their experiences learning and doing mathematics to understand these students' perspectives; and creating documentary video portraitures (or composite cases) of participants' stories about learning and doing mathematics that can be used in teacher preparation and professional development. Finally, the project will look across the experiences over the duration of the project to develop a framework that can be used to improve Latino students' mathematics education experiences. This project will provide a window into how Latino students may experience inequities and can broaden mathematics educators' views on opportunities to engage Latino students in rigorous mathematics. The project will also broaden the field's understanding of how Latino students racial/ethnic and linguistic identities influence their experiences learning mathematics. It will also identify key factors that impact Latino students' experiences in learning mathematics to pinpoint specific areas where interventions and programs need to be designed and implemented. An underlying assumption of the project is that carefully capturing and understanding Latino students' stories can illuminate the strengths and resilience these students bring to their learning and doing of mathematics.

This research project characterizes and analyses the developing mathematical identities of Latinx students transitioning from elementary to middle grades mathematics. The overarching research question for this study is: What are the developing stories of learning and doing mathematics of Latino students as they transition from elementary to middle school mathematics? To answer this question, this study is divided into three phases: 1) understanding and documenting the historical context by examining policy documents, local newspaper articles, and doing focus group interviews with community members; 2) using ethnographic methods over two years to explore students' stories of learning and doing mathematics and clinical interviews to understand how they think about and construct arguments about mathematics (i.e., measurement, division, and algebraic patterning); and 3) creating video-cases that can be used in teacher education. Traditional ways of teaching mathematics perpetuate images of who can and cannot do mathematics by not acknowledging contributions of other cultures to the mathematical sciences (Gutiérrez, 2017) and the way mathematics has become a gatekeeper for social mobility (Martin, Gholson, & Leonard, 2010; Stinson, 2004). Focusing on Latino students' stories can illuminate teachers' construction of equitable learning spaces and how they define success for their Latino students. The central hypothesis of this project is that elementary Latino students' stories can identify how race and language are influential to their mathematical identities and how school and classroom practices may perpetuate inequities. Finally, the data and video-cases will then be used to develop a conceptual framework for understanding the development of the participating students' developing mathematical identities. This framework will provide an in-depth understanding of the developing racial/ethnic, linguistic, and mathematical identities of the participating Latino students. The educational material developed (e.g. video documentaries, discussion material) from this project will be made available to all interested parties freely through the project website. The distribution of these materials, along with further understanding of Latino students' experiences learning mathematics, will help in developing programs and interventions at the elementary and middle grade level to increase the representation of Latino students in STEM careers. Additionally, identifying the key factors impacting Latino students' experiences in learning mathematics can pinpoint specific areas where interventions and programs still need to be designed and implemented. Future projects could include the assessment of these programs. This project will also inform the development of professional learning experiences for prospective and practicing teachers working with Latino or other marginalized students.

Fourteenth International Congress on Mathematical Education (ICME14) Travel Grant

This project will support the participation of 53 US K-12 mathematics teachers, graduate students, community college/university mathematicians, mathematics teacher educators, and mathematics education researchers to attend the Fourteenth International Congress for Mathematical Education (ICME-14) in Shanghai, China.

Project Email: 
Lead Organization(s): 
Award Number: 
1908084
Funding Period: 
Sun, 09/01/2019 to Mon, 02/28/2022
Project Evaluator: 
Full Description: 

This project will support the participation of 53 US K-12 mathematics teachers, graduate students, community college/university mathematicians, mathematics teacher educators, and mathematics education researchers to attend the Fourteenth International Congress for Mathematical Education (ICME-14) to be held in Shanghai, China July 9-16, 2020. While mathematics education in the United States has its own culture and expectations, the work and conversations of mathematics educators across the world might contribute to our understanding of issues facing our community today such as curriculum development, the use of technology, strategies for reaching all students, teacher education and professional development. The questions we have as a nation about our own mathematics education might be informed and enlightened by international conversations with others confronting similar issues. A research team led by Sharon McCrone, University of New Hampshire, will prepare a 2020 Fact Book on US mathematics education, building on reports for prior ICMEs. The travel grant will increase the number and diversity of the US mathematics education community attending the international congress, which will enable a broader representation from the US to benefit from interaction with the world's leading mathematics educators.

Through a careful selection process, experts in the field will identify travel recipients most likely to benefit from attending ICME-14 and well-positioned to disseminate insights from their experience. Fostering understanding of international issues and practices among educators and researchers in the US may enhance their capacity to take an informed, global perspective in their work, which, in turn, may benefit their local communities. Digital media will allow educators and classrooms to make and maintain contact across the world, enabling ICME-14 grantees to maintain connections initiated at the meeting and have an impact on large numbers of school children and teachers, both preservice and practicing, in the US. At ICME-14 these educators will engage in learning about the "state of the art" with respect to research and practice in mathematics education from a wide variety of perspectives and will be able to discuss common challenges in teaching and learning mathematics.

Alternative video text
Alternative video text: 

PBS NewsHour Student Reporting Labs StoryMaker: STEM-Integrated Student Journalism

In this project, Student Reporting Labs will develop an online curriculum delivery platform called StoryMaker and a unique set of tools called Storymaker:STEM that will supply in-demand interdisciplinary, multi-modal, STEM-infused teaching and learning tools to classrooms across the country. The project aims to produce unique STEM stories from a teen perspective and partners with local public media stations to provide mentorship and amplify the voices of young people.

Project Email: 
Award Number: 
1908515
Funding Period: 
Sun, 09/01/2019 to Thu, 08/31/2023
Project Evaluator: 
Full Description: 

PBS NewsHour's Student Reporting Labs (SRL) is a youth journalism program that creates transformative educational experiences through video production and community engagement. The program aims to produce unique STEM stories from a teen perspective and partners with local public media stations to provide mentorship and amplify the voices of young people. In this project, Student Reporting Labs will develop an online curriculum delivery platform called StoryMaker and a unique set of tools called Storymaker:STEM that will supply in-demand interdisciplinary, multi-modal, STEM-infused teaching and learning tools to classrooms across the country. SRL StoryMaker:STEM will be a free, self-directed online curriculum delivery system designed to guide educators working with middle and high school-age students through videojournalism experiences that highlight and integrate STEM skills, concepts, issues, and potential solutions into the learning process. This program will also develop mentoring connections with 40 journalism professionals and STEM professionals to provide supports for participating teachers and students. The project will recruit and work with about 100 teachers and their students over the course of the project to inform, test, implement and provide feedback on the SRL StoryMaker:STEM platform and resources. The associated research will explore evidence-based strategies for structuring co-learning and mentorship connections for students and teachers with journalists and science content experts around SRL StoryMaker:STEM to best support student and teacher outcomes.

The four-year associated research study will contribute to understanding how teachers collaborate on teaching STEM across academic disciplines through a series of interviews, surveys, and site visits with the pilot teachers and their students using SRL StoryMaker:STEM. The analysis of the data will focus on identifying the benefits of developing a community of teachers who collaborate on teaching STEM across the academic discipline through journalism practice. Specifically, a combination of quantitative and qualitative methods will be used to examine the following research questions: What teacher affordances are necessary for using journalism practices to support STEM learning across academic disciplines? How do teacher perceptions of their school constraints influence their use of STEM-based learning activities? How do teachers from different disciplines teach numerical reasoning, communicating with data, and the other essential STEM thinking skills? How might an online support community be structured to encourage teacher-to-teacher scaffolding related to STEM content given variation in their pedagogical training? Meanwhile, front-end evaluation will identify barriers and opportunities specific to this project. Formative evaluation will focus on how each specific iteration is meeting teachers' needs and aspirations, and summative evaluation will examine teachers' STEM learning and teachers' perception of students' STEM outcomes.

Alternative video text
Alternative video text: 

Looking Back and Looking Forward: Increasing the Impact of Educational Research on Practice

The focus of this conference is to carefully examine past and current research with an eye toward improving its impact on practice and to create concrete steps that could shape the nature and impact of mathematics education research.

Lead Organization(s): 
Award Number: 
1941494
Funding Period: 
Sun, 09/01/2019 to Mon, 08/31/2020
Full Description: 

The focus of the proposed conference is to carefully examine past and current research with an eye toward improving its impact on practice. This conference is designed to create concrete steps that could shape the nature and impact of mathematics education research for years to come. A diverse group of 50 participants will be invited to participate. Participants include 10 experienced K-12 educators whose perspectives will be used to anchor the conference in problems of practice. Other participants represent senior through more junior scholars who have demonstrated a commitment to addressing the disconnect between research and practice, along with technology experts to advise participants on capabilities and innovative uses of modern technologies for instruction, assessment and data management.

The overarching goal for the conference is to help the field of mathematics education think deeply about the most productive ways to answer the following questions: [1] Why hasn't past research had a more direct impact on practice? What can be learned from this historical analysis for future research? [2] What is a possible vision for research that would have a more direct impact on practice? What questions should be asked? What methods should be used? What concrete steps can be taken to launch the new research programs? [3] What are the implications of adopting new kinds of research programs? If they gain traction, how will such changes affect the broader education community and infrastructure, including preservice teacher education, teacher professional development, and the training of future researchers? How should the roles of researchers and teachers change? What incentive structures might motivate these changes? How will new programs of research interact with existing programs?

Improving Evaluations of R&D in STEM Education

The primary goal of this set of workshops is to provide STEM education researchers with the framework, skills, and community they need to implement new developments in causal inference methods into their research.

Project Email: 
Lead Organization(s): 
Award Number: 
1937719
Funding Period: 
Sun, 09/01/2019 to Wed, 08/31/2022
Project Evaluator: 
Full Description: 

The primary goal of this set of workshops is to provide STEM education researchers with the framework, skills, and community they need to implement new developments in causal inference methods into their research. These methods will be immediately implementable in their current (or near future) studies and will result in stronger causal findings, providing higher-quality evidence regarding the potential of new innovations to improve STEM education broadly. Additionally, a secondary goal is to provide the graduate assistants at the workshop (students in statistics) with a strong foundation in the real-world problems facing researchers in STEM education today. By being immersed in this community, the goal is to improve their communication skills, while also providing them with opportunities to develop new methods that address problems facing the STEM education community today.

STEM education research and development studies often focus on the development and iterative refinement of interventions meant to increase STEM participation and skills. Since large-scale randomized experiments are not often possible, researchers typically use correlational methods instead to explore the effects of interventions. Over the past several years, however, statisticians have developed a broad array of methods for understanding causality that do not require these large-scale randomized trials. While these causal inference methods are now common in fields like medicine and education policy, they are much less commonly found in STEM education fields. The purpose of this set of workshops is to introduce STEM education researchers to these methods and how they relate to three research designs they already use: (1) matching on a single variable (e.g., age, gender), (2) pre-test post-test comparisons, and (3) lab experiments. In addition to introducing these new developments, broader discussions of confounding, validity types and trade-offs, design sensitivity, effect size reporting, and questionable research practices (e.g., p-hacking) will also be included.

Alternative video text
Alternative video text: 

The Developmental Emergence and Consequences of Spatial and Math Gender Stereotypes

This project will investigate the development and emergence of spatial gender stereotypes (and their relation to math gender stereotypes) in elementary school-aged children and their impact on parent-child interactions in the pre-school period.

Lead Organization(s): 
Award Number: 
1920732
Funding Period: 
Thu, 08/01/2019 to Sun, 07/31/2022
Full Description: 

There is currently a gender gap in STEM fields, such that females participate at lower rates and have lower career attainment than their male counterparts. While much research has focused on gender differences in math attitudes, little work has explored how attitudes in a closely related STEM domain, spatial reasoning, may also contribute to the observed gender gap. The proposed research will characterize the acquisition of gender stereotypes in childhood in two key domains critical to success and participation in STEM fields: math and spatial skills. Recent evidence suggests that children acquire math gender stereotypes (i.e., the belief that "math is for boys") as early as 1st - 2nd grades, but less is known about children's attitudes about spatial abilities. This project will be one of the first to investigate the development and emergence of spatial gender stereotypes (and their relation to math gender stereotypes) in elementary school-aged children, and their impact on parent-child interactions in the pre-school period.

Eight behavioral studies involving 1290 children (Pre-K - 4th graders), 240 caregivers, and 180 adults will participate in studies that evaluate an integrated theoretical model of the relations between gender, gender stereotypes, attitudes, and abilities in the domains of math and space. In Series 1, studies will characterize the emergence of and assumptions behind spatial- and math- gender stereotypes in 1st - 4th graders, while determining how they may be acquired. In Series 2, studies will explore the real-world impacts of spatial-gender stereotypes on STEM participation and achievement in childhood. Lastly, Series 3 studies will explore the malleability of these stereotypes in the hopes of identifying ways to ameliorate their impact early in development. The project will provide training for doctoral graduate and undergraduate students. Moreover, this project will support new and ongoing collaborations with local children's museums, which facilitate interactions and communication with families, educators, and the public about the research findings. By being some of the first work to uncover the developmental origins and consequences of math and spatial stereotypes, this work may inform possible future interventions to reduce and/or eliminate the perpetuation of these stereotypes in children, long before they can have greater lifelong impacts.

Early Emergence of Socioeconomic Disparities in Mathematical Understanding

This study will provide foundational knowledge about the activities and interactions in the home environment that drive the early emergence of math skills disparities related to SES.

Project Email: 
Lead Organization(s): 
Award Number: 
1920545
Funding Period: 
Sun, 09/01/2019 to Wed, 08/31/2022
Project Evaluator: 
Full Description: 

The math skills of children from high income families have grown faster than those of children from middle- or low-income families resulting in a significant and persistent gap. These disparities emerge in preschool and are larger by the start of kindergarten. As children progress through school, the gap in math skills persists or even widens. Importantly, SES-related disparities in math skills have implications for long-term academic achievement and educational attainment, as well as access to STEM education and professions in adulthood. As such, there is an urgent need to identify the factors shaping early math development before children start formal schooling. This investigation will provide foundational knowledge about the activities and interactions in the home environment that drive the early emergence of math skills disparities related to SES. In the long term, findings from this work could inform home visitation programs and early care and education curricula aimed at strengthening the early math skills of children living in low resourced communities. The knowledge generated by this study has the potential to enhance equity in access to STEM education and professions for all children.

Using a longitudinal sequential study of two cohorts of socioeconomically diverse 30-month-olds (N = 320) and their parents, the proposed study will strengthen knowledge of the etiology of SES disparities in math skills by addressing three aims. First, it will examine associations between the home learning environment (HLE) and early math skills. Second, it will describe SES disparities in HLE and their implications for math learning. Third, it will test family stress and family culture as pathways through which SES shapes HLE and early math skills. Children will complete assessments of early math skills and other general cognitive abilities at age 30 months and again around 42-47 months. In addition to the child assessments at 30 months, in-home structured observations with a parent, parent surveys, and time diaries will measure the quantity and quality of children's opportunities for math learning at home. To measure family stress, parents will complete questionnaires assessing general stress as well as stress specifically related to performing and teaching math. To measure family culture, parents will complete questionnaires assessing their general and math-specific parenting beliefs and observations of family interactions will be conducted. This study will test whether domain-general and math-specific family stress and culture mediate the relation between HLE and SES. In sum, this study will make contributions to understanding the early emergence of economic disparities in early math skills. Theoretically, it will delineate whether domain-general or math-specific differences in HLE explain disparities in early math skills related to socioeconomic status. It will advance research by concurrently considering the roles of stress and culture in shaping disparities in children's opportunity to learn math in their early home environments. This project is funded by the EHR Core Research program, which emphasizes STEM education research that will generate foundational knowledge in the field.

Alternative video text
Alternative video text: 

Pages

Subscribe to Mathematics