Research
Below is a listing of current research grants underway by Mathematics Education faculty. Click on an a faculty member to see all of their grant work.
Collaborative Research: Advancing Mentor Teachers’ Practices through Collaborative Pedagogical Reasoning
PI: Meghan Shaughnessy
National Science Foundation Award # 2300666
There is growing momentum to support teachers to engage in responsive mathematics teaching, which is critical to realizing more equitable instruction. In this approach, teachers recognize and attend to the diversity and substance of all students? ideas and leverage those ideas in instruction. Yet, learning to engage in responsive mathematics teaching is challenging as this work requires interpreting classroom activity in-the-moment and making decisions that are well reasoned and intentional. This decision-making process, known as pedagogical reasoning, is often invisible to observers, making it hard for novices to learn. Teacher education programs typically provide novice teachers with opportunities to work in classrooms, alongside seasoned professionals (mentor teachers), however, the activity of pedagogical reasoning is rarely a focus of such mentoring. Given the importance of mentor teachers for novice teachers? development of instructional practices and the amount of time novices spend in mentored classroom placements, the project researchers view the mentor-novice teacher relationship as a critical site for intervention. This project leverages the role of mentor teachers to support novices? development of pedagogical reasoning and increase the likelihood that they will be prepared to engage in responsive mathematics teaching. Mentor teachers in three differently structured teacher education programs will receive professional development aimed at making their pedagogical reasoning visible and supporting them in engaging collaboratively with novices in this type of teacher thinking. The researchers refer to this type of mentoring as collaborative pedagogical reasoning (Co-PR). They will study mentor teachers? development of Co-PR and its relationship to responsive teaching. They will also consider how different program structures and characteristics influence the development of Co-PR. Findings will produce usable practices for developing teachers? mentoring strategies across different teacher education programs, which will subsequently support mentor and novice teachers? learning of responsive mathematics teaching.
This project aims to enhance the quality of elementary mathematics teaching by supporting mentor teachers to better prepare the next generation of novice teachers to engage in responsive mathematics teaching. This design-based intervention study is based on several hypotheses about how mentor teachers might play a stronger role in supporting novices to develop these practices in K-8 classrooms. Specifically, the researchers hypothesize that if mentor teachers make their pedagogical reasoning visible to novices through engagement in collaborative pedagogical reasoning (Co-PR), then novice teachers will learn about the invisible decision-making that skilled teachers engage in as they carry out responsive mathematics teaching. Further, they hypothesize that mentor teachers can be supported to engage in Co-PR through the design of learning opportunities that afford joint inquiry with others and are mediated with shared tools, designed to guide both disciplinary and equitable aspects of responsive teaching. Using an inquiry group professional development structure at three strategic sites, the researchers aim to build mentoring tools and structured opportunities that support mentor teachers to make visible the layers of their decision making and to facilitate Co-PR with novices before, during, and after teaching. The project team will study the development of mentor and novice teachers? Co-PR, exploring growth in their pedagogical reasoning and factors that contribute to this development. They will also investigate how the enactment of Co-PR differs across teacher education types and programs. Findings will contribute to scholarly insights about mentor and novice teacher development and will generate a set of mentoring tools useful to the fields of mathematics education and teacher education.
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. 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.
Preparing Mathematics Teachers to Teach for Justice and Joy in High-Needs Schools
PI: Aaron Brakoniecki
Co-PI: Gregory Benoit, Debra Borkovitz, Eric Cordero-Siy, Alejandra Salinas
National Science Foundation Award # 2243465
This project aims to serve the national need for preparing high-quality secondary mathematics teachers in high-need school districts. Towards this end the project will focus particular attention on examples of how mathematical modeling and analysis can be used to reveal and investigate issues of social inequity that affect local communities where teachers may be placed. The investigators posit that such an approach will improve on more traditional mathematics instruction where students often leave class asking, ?Why do I need to know this??, and that it will illustrate how mathematics can be used to create a more socially just world. Additionally, instead of students leaving with a negative disposition toward the field of mathematics, this project will support teachers in creating joyful mathematical experiences that excite and engage students. Students who have a productive relationship with mathematics are more likely to pursue careers that require a mathematical background. Moreover, students who understand that mathematics has the power to describe the world can value mathematics beyond career choices; they can use mathematics to advocate for themselves and others when they see injustices in their community. By supporting preservice and beginning teachers in developing teaching philosophies and practices that highlight justice and joy in their lessons, more students are likely to engage with mathematics and see it as relevant to their lives.
This project at Boston University includes partnerships with the Boston Public Schools, Malden Public Schools, and Waltham Public Schools. Over a five-year period, the project intends to recruit a mix of 31 STEM professionals and highly talented post-baccalaureate students who possess a degree in a STEM discipline, most often mathematics, to teach secondary mathematics in a high-need school district. This project seeks to address the need for preparing and retaining highly effective secondary mathematics teachers in high-need-school districts who are properly trained in facilitating joyful mathematical experiences in the classroom while simultaneously increasing students? critical consciousness of how mathematics can illuminate issues of racism and other social injustices. This project will contribute to the improvement of mathematics education at the secondary level by pursuing the following two objectives. First is to generate an exemplary model for recruiting, training and retaining a diverse mathematics teacher community with a commitment to and facility with using examples of how mathematics can be applied to investigate issues of social justice. Second is to disseminate findings of this project through publications and conference presentations to teacher educators and researchers who study how teachers learn to implement and center justice-oriented mathematics. This Track 1: Scholarships and Stipends project is supported through the Robert Noyce Teacher Scholarship Program (Noyce). The Noyce program supports talented STEM undergraduate majors and professionals to become effective K-12 STEM teachers and experienced, exemplary K-12 teachers to become STEM master teachers in high-need school districts. It also supports research on the effectiveness and retention of K-12 STEM teachers in high-need school districts.
Preparing mentors to support novices in eliciting student thinking during mathematics discussions: Developing and testing a simulation-based PD program
PI: Julie Cohen
Co-PI: Matthew Ronfeldt, Meghan Shaughnessy, Nicole Garcia
National Science Foundation Award # 2200915
Nearly 200,000 candidates graduate from teacher preparation programs each year, and mentor teachers have a crucial role in the preparation of teacher candidates as they spend far more time engaging with candidates than any other teacher educator. Effective mentoring of teacher candidates can help to bridge the gap between the teacher-centered practices of today?s elementary mathematics classrooms and the student-centered practices that are needed to grow curious and competent STEM students. And yet, mentors receive little to no support about how support candidate development. This project aims to support mentor teachers in better modeling the effective mathematics teaching practices for candidates in their own teach and providing candidates with actionable feedback on those practices as they learn to teach elementary mathematics. The project supports mentors as both: (1) teacher learners who benefit from additional support in ambitious teaching in mathematics; and (2) teacher educators who need support in recognizing candidates? strengths and areas for growth, as well as in giving useful feedback. The project will design and study an online, portable mentor teacher professional development (PD) program that target mentors? teaching and feedback skills in elementary mathematics. Designing online modules will support large-scale work in ways that in-person PD cannot. Additionally, the project will identify factors that contribute to the differential uptake of the PD. More broadly, this project aims to (1) promote educator development by generating new knowledge about how to help mentors support teacher candidate learning; (2) broaden participation in mathematics by historically marginalized and minoritized youth, who are far more likely than their peers to be taught by a first year teacher; and (3) enhance infrastructure for research and education by generating PD materials and measures that can be used and studied at scale.
This project aims to enhance the quality of elementary mathematics teaching by developing mentors who can better support the next generation of teacher candidates. Teaching simulations are used as a cornerstone of the design of the professional learning, providing a low-stakes practice space for mentors to practice and model effective elementary mathematics teaching. The PD will focus on eliciting students? thinking, a teaching practice that is fundamental to leveraging students? mathematical resources and ideas. The professional learning also focused on mentors? skills in giving candidates actionable feedback on their elicitation of student thinking in mathematics. This study uses a mixed-methods, randomized control trial design in which 150 mentor-candidate pairs are randomly assigned to either PD or control (business-as-usual) conditions. Mentors and candidates are observed in both simulations and live classroom interactions to answer the following questions: (1) Does the mentor PD impact mentors? teaching and feedback skills, as well as candidates? teaching skills? (2) How are mentors? teaching and feedback skills similar in simulated and live classroom settings? And (3) What is the nature of the feedback that mentors give candidates? Are there differences between the feedback of PD and control groups across the year? Very few studies have used experimental designs to estimate credibly causal effects of teacher education reforms on candidate (or mentor) outcomes. This study will provide much-needed causal evidence for the effects of practice-based preparation on the development of both mentors? and candidates? teaching in elementary mathematics.
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. 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.
Facilitating Formative Feedback – Using Simulations to Impact the Capability of Novice Mathematics Teachers
PI: Meghan Shaughnessy
Co-PI: Daniel Heck, Tim Boerst, Evelyn Gordon, Nicole Garcia
National Science Foundation Award # 2101343
During their initial teacher preparation experiences, preservice teachers need meaningful formative assessment that can support them in developing their skills and practices as new teachers of mathematics. While field placements offer some such opportunities, too often preservice teachers are not able to see, experience, and enact a full range of research-based effective mathematics teaching practices. This Level II four-year Design and Development Study in the Assessment strand explores the ways in which thoughtfully designed simulations can provide preservice teachers with formative assessment opportunities that serve as a complement to, or alternative to as needed, feedback derived from field placement contexts. A set of simulations will be designed with a focus on eliciting and interpreting student thinking. These simulations will be used with preservice teachers in three elementary teacher preparation programs of varying size and demographics. Data will be collected to understand the ways in which the feedback from engaging in the simulations serves to strengthen preservice teachers' abilities to elicit and interpret student thinking through an analysis of performance in the simulations, interviews with preservice teachers, and feedback from teacher educators. An associated study will establish the reliability and validity of the simulations as assessment tools.
Simulations will be developed and tested in three cycles, with iterative improvements made between each cycle. The first cycle will involve 10 preservice teachers in a pilot study separate from participation in a course, in which preservice teachers engage in a simulation, receive formative feedback, and engage in a second similar simulation. This cycle will evaluate the extent to which feedback appears to influence subsequent performance. In the second cycle, the project will work with three teacher educators in diverse contexts to enact the simulations with all preservice teachers in one section of their elementary mathematics methods courses. In the final cycle, the use of the simulations will shift from a research team actor playing the role of the student to a site-based actor recruited by the teacher educators at each of the three institutions. To validate the tools, researcher reliability and teacher educator reliability studies will be conducted to asses the extent to which the four different simulation assessments provide consistent feedback on the targeted teaching practices and the extent to which the scoring of the assessments are reliable. A G study (generalizability study) will be conducted to evaluate the extent to which the teacher participant is the primary source of variation as compared to variations from student actors or the rater administering the assessment. Results will be disseminated in a variety of mathematics education settings and the simulation materials will be made available to practitioners and adapted for additional use in mixed-reality simulation platforms.
Teachers as learners of equitable discussion practices
PI: Deborah Ball
Co-PI: Leslie Herrenkohl, Meghan Shaughnessy, Nicole Garcia
National Science Foundation Award # 2000189
Growing evidence about the powerful effects of skillful teaching on students? learning creates a need for professional development that impacts teachers? actual practice. Teaching practices have been shown to play a crucial role in the reproduction or disruption of injustice. This project aims to create opportunities for teachers to notice and understand how normalized practice often reproduces inequity and learn ways to disrupt typical patterns of inequity in their classroom. The project will design and study professional development that works on practice centered on the disruption of patterns of injustice. This project focuses on classroom discussions because they can be a key site for either reproducing or disrupting inequities and they have been established as a powerful instructional practice. In addition to studying the impact of the professional development on teachers? teaching skill, the project also explores teachers? perceptions of their learning, influences on teachers? professional learning, and the impact of a mathematics-focused professional development versus a generalized focus on teaching practice and perception of learning. The project will generate new knowledge regarding ways in which elementary mathematics teachers can be supported to learn effective teaching practices.
Teachers benefit from professional development that addresses both the technical and contextual aspects of teaching practice, including the identities of their students and associated patterns of inequity in schools and society. This research will examine how elementary teachers? perceptions of professional learning and influences on such learning in combination with professional development on leading discussions, impact their skill with and willingness to take up teaching that disrupts patterns of inequity in classrooms. In terms of influences on teachers? professional learning, the project will address teachers? beliefs about students and learning, their understanding of the pervasiveness of inequity in normalized practice, contextual factors such as their relationship with administration or their status in the school community, and their readiness for, skill with, and implementation of the practice upon beginning the professional learning. The studies will examine: (1) What are teachers? perceptions of their own learning, discussion-leading practice, and attention to disrupting inequity? How well matched are these perceptions with external measures? What supports do teachers perceive as impacting their learning? How does principal selection criteria and communication with teachers about their selection impact teachers? perceptions and engagement? (2) In what ways does professional development on leading discussions combined with peer and coach support impact teachers? skill and willingness to engage in that teaching practice including disrupting patterns of inequity? (3) Does a mathematics focus produce different outcomes than a generalized focus for teaching practice or perception of learning? The project will collect and analyze several types of data, including measures of skill with leading mathematics and literacy discussions, teacher perceptions, and willingness and skill with disrupting patterns of inequity during discussions. This project will contribute foundational knowledge and theory related to (a) teachers? perceptions of and influences on their learning to lead discussions with attention to disrupting inequity, (b) components of professional development that impact teaching practice, and c) how subject matter specificity effects these first two areas.
Preparing Mathematics Teachers to Enact Engaging Discourse-based Teaching Strategies
PI: Alejandra Salinas
Co-PI: Aaron Brakoniecki, Steven Rosenberg
National Science Foundation Award # 1758218
This Track 1 Noyce project seeks to address the national need for more highly qualified mathematics teachers with strong backgrounds in both math content and effective pedagogical methods. It aims to prepare 33 new middle and high school mathematics teachers to teach in high-need schools. The project is a collaboration of mathematics education faculty in the School of Education and mathematics faculty in the College of Arts and Sciences at Boston University (BU), and four high-need school districts (Boston, Chelsea, Malden, and Waltham). Research on mathematics teaching and learning supports the benefits of engaging students in mathematical discussions in the K-12 math classroom. This project will teach preservice mathematics teachers to use productive classroom discussions about math to improve students' attitudes toward and understanding of math. These skills can help teachers motivate students from linguistically and racially diverse low-income communities, well as communities that have suffered significant teacher attrition. This project will provide a model for recruiting, training, and retaining highly qualified STEM majors and professionals into teaching.
This project has the following goals: (a)recruit 33 diverse and highly talented STEM majors and STEM professionals to teach secondary mathematics in high-need schools across the five years of the award; (b) prepare highly effective secondary mathematics teachers who are skilled in using discourse-based teaching strategies and implementing related curriculum materials; and (c) support the retention of highly talented secondary mathematics teachers who teach in high-need schools. Scholars will receive scholarships to enroll in a one-year graduate program that leads to a Master of Arts in Teaching (MAT) degree and initial licensure to teach secondary mathematics. As part of the MAT program, scholars will: (1) enroll in education courses that prepare them to teach in high-need districts; (2) enroll in mathematics courses that integrate content and pedagogy to develop teachers' use of high-leverage teaching practices; and (3) participate in field placements through existing partnerships with four high-need urban and suburban school districts that provide opportunities to connect their university learning to the classroom. As part of the Noyce Seminar Series, scholars will also participate in six professional development workshops that focus on developing their ability to enact rich mathematical lessons using discourse-based instructional strategies. Following the completion of the MAT program, scholars will begin their teaching careers with mentoring support from BU. During their two-year induction period, scholars will continue to attend the Noyce Seminar Series to further develop their discourse-based teaching practices and collaborate with other BU Noyce scholars. Data documenting the Scholars? career decisions and effectiveness as mathematics teachers in high-need schools will inform the NSF, researchers, teacher educators, and the public about the usefulness of focusing on mathematical discourse and curriculum during teacher preparation programs.
CAREER – Designing and Enacting Mathematically Captivating Learning Experiences for High School Mathematics
PI: Leslie Dietiker
National Science Foundation Award # 1652513
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. 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.
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.