Projects

Three-dimensional figures can now be represented as diagrams that appear to extend into space in ways that are free of material or physical constraints. They can be rendered at any size, in any orientation, and at any position in space, and can thereby realize a far more varied set of mathematical concepts than what is possible with physical models. The goal of this project is to investigate the transformative educational potential of these representations and to generate a knowledge base that teachers, teacher educators, and researchers can use to reimagine the learning and teaching of geometry.

The project is designing a web-based, district-led professional development implementation, focusing on improving mathematics discourse practices in K-2 classrooms, with particular attention to emergent multilingual learners. Building on two prior NSF-funded projects, the All Included in Mathematics K-2 New Extensions professional learning program will develop and research the impact of an augmented model for mathematics professional development on K-2 student learning through the addition of supports for coaches and leaders to the existing professional development model.

This project will explore how children in grades K-2 understand visual representations of algebraic concepts. For instance, children might create tables or graphs to organize information about the relationship between two quantities. They might use graphs and diagrams to explain their mathematical thinking and develop their understanding of relationships in numbers and operations. The project will use data gathered in K-2 classrooms and via interviews with children to describe their use of the visual representations. This exploratory project aims to develop learning trajectories as cognitive models of how children in grades K–2 understand visual representations for algebraic relationships.

This project focuses on developing the Adapted Measure of Math Engagement (AM-ME), a new evidence-based measure for math teachers to assess students’ engagement. This project develops a mathematics engagement measure that reflects the experiences of Black and Latino students, providing valuable insights into improving mathematics learning environments and fostering increased student engagement.

This project focuses on developing anti-racist mathematics teaching and learning practices that have led to inequitable school experiences for Black, Indigenous, and Latinx students. This study is a partnership with school and central office leaders from one district and educational researchers from three universities with expertise in both educational leadership and mathematics education. Partnership activities include documenting how leaders learn and develop anti-racist leadership practices and then measuring the impact on teachers’ instruction and students’ experiences.

This project focuses on developing the Adapted Measure of Math Engagement (AM-ME), a new evidence-based measure for math teachers to assess students’ engagement. This project develops a mathematics engagement measure that reflects the experiences of Black and Latino students, providing valuable insights into improving mathematics learning environments and fostering increased student engagement.

This project explores the effectiveness of two different versions of professional development (PD) designed to enhance middle school mathematics teachers’ understanding of fractions and proportions, and their teaching of these mathematical concepts to students. The PD uses an approach that engages teachers with web-based apps that allow them to test and experiment with their mathematical ideas. The apps, combined with guiding questions that challenge teachers’ thinking about fractions and proportions, serve both to promote critical thinking about the concepts and to further developing their understandings of the concepts. The researchers will use an innovative approach, topic modeling, to examine the effectiveness of each of version of the PD.

Teachers of mathematics engage in curricular reasoning as they design and interact with their students, choose curricular materials, and implement curriculum standards in the service of high-quality instruction. Currently, there is no shared measure of curricular reasoning of middle school teacher classroom decision making in mathematics. In this research project, the team develops and validates two measures of middle school teachers’ curricular reasoning in mathematics as practiced. The first measure looks at curriculum reasoning from the perspective of the teacher, the second measure attends to the perspectives of the mathematics education research community.

Teachers of mathematics engage in curricular reasoning as they design and interact with their students, choose curricular materials, and implement curriculum standards in the service of high-quality instruction. Currently, there is no shared measure of curricular reasoning of middle school teacher classroom decision making in mathematics. In this research project, the team develops and validates two measures of middle school teachers’ curricular reasoning in mathematics as practiced. The first measure looks at curriculum reasoning from the perspective of the teacher, the second measure attends to the perspectives of the mathematics education research community.

This project explores the effectiveness of two different versions of professional development (PD) designed to enhance middle school mathematics teachers’ understanding of fractions and proportions, and their teaching of these mathematical concepts to students. The PD uses an approach that engages teachers with web-based apps that allow them to test and experiment with their mathematical ideas. The apps, combined with guiding questions that challenge teachers’ thinking about fractions and proportions, serve both to promote critical thinking about the concepts and to further developing their understandings of the concepts. The researchers will use an innovative approach, topic modeling, to examine the effectiveness of each of version of the PD.

This project uses neural and behavioral measures of learning as a basis for making improvements to an immersive high school course that trains students in flexible spatial cognition and data analysis. Tracking students into college, the project measures long-term effects of improved spatial cognition resulting from the modified geospatial course curriculum.

Teachers of mathematics engage in curricular reasoning as they design and interact with their students, choose curricular materials, and implement curriculum standards in the service of high-quality instruction. Currently, there is no shared measure of curricular reasoning of middle school teacher classroom decision making in mathematics. In this research project, the team develops and validates two measures of middle school teachers’ curricular reasoning in mathematics as practiced. The first measure looks at curriculum reasoning from the perspective of the teacher, the second measure attends to the perspectives of the mathematics education research community.

This project aims to elaborate a structure for practice-oriented, collaborative professional development that increases the capacities for collaborative learning by facilitating teacher-to-teacher interactions within and across cultural contexts. By convening international groups of teachers to design lessons and provide and respond to commentaries on their lesson designs, the project introduces possibilities for surfacing and disrupting common experiences, assumptions, and norms in US mathematics teaching.

This project explores the effectiveness of two different versions of professional development (PD) designed to enhance middle school mathematics teachers’ understanding of fractions and proportions, and their teaching of these mathematical concepts to students. The PD uses an approach that engages teachers with web-based apps that allow them to test and experiment with their mathematical ideas. The apps, combined with guiding questions that challenge teachers’ thinking about fractions and proportions, serve both to promote critical thinking about the concepts and to further developing their understandings of the concepts. The researchers will use an innovative approach, topic modeling, to examine the effectiveness of each of version of the PD.

Teacher professional learning is a critical part of the mathematics education landscape. For decades, professional learning has been the primary strategy for developing the skills of the teaching workforce and changing how teachers interact with students in classrooms around academic content. Professional learning also can be expensive for districts, both financially and in terms of teacher time. Given these investments, most school leaders wish to spend their professional development dollars efficiently, making decisions about professional learning design that maximize teacher and student learning. However, despite more than two decades of rigorous research on professional learning programs, practitioners have little causal evidence on which professional learning design features work to accelerate teacher learning. This project seeks to identify features of teacher professional learning experiences that lead to better mathematics outcomes for both teachers and students.

Teachers of mathematics engage in curricular reasoning as they design and interact with their students, choose curricular materials, and implement curriculum standards in the service of high-quality instruction. Currently, there is no shared measure of curricular reasoning of middle school teacher classroom decision making in mathematics. In this research project, the team develops and validates two measures of middle school teachers’ curricular reasoning in mathematics as practiced. The first measure looks at curriculum reasoning from the perspective of the teacher, the second measure attends to the perspectives of the mathematics education research community.

Teachers of mathematics engage in curricular reasoning as they design and interact with their students, choose curricular materials, and implement curriculum standards in the service of high-quality instruction. Currently, there is no shared measure of curricular reasoning of middle school teacher classroom decision making in mathematics. In this research project, the team develops and validates two measures of middle school teachers’ curricular reasoning in mathematics as practiced. The first measure looks at curriculum reasoning from the perspective of the teacher, the second measure attends to the perspectives of the mathematics education research community.

This project will design and study an online, portable mentor teacher professional development (PD) program that target mentors’ teaching and feedback skills in elementary mathematics. The 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 addresses a major educational barrier, namely that rural students are less likely to choose a major in STEM and have far less access to advanced STEM courses taught by highly qualified teachers. The LogicDataScience (LogicDS) curriculum and virtual delivery are expected to relieve the resource constraints significantly and thus reach rural students. The strategy behind this curriculum development for data science explores the utility of emphasizing how the foundations of data science in computing, mathematics, and statistics are unified by mathematical logic. The project is studying the impacts of the new curriculum on students’ learning of computing, mathematics, and statistics.

Understanding probability is essential for daily life. Probabilistic reasoning is critical in decision making not only for people but also for artificial intelligence (AI). AI sets a modern context to connect probability concepts to real-life situations. It also provides unique opportunities for reciprocal learning that can advance student understanding of both AI systems and probabilistic reasoning. This project aims to improve the current practice of high school probability education and to design AI problem-solving to connect probability and AI concepts. Set in a game-based environment, students learn and practice applying probability theory while exploring the world of probability-based AI algorithms to solve problems that are meaningful and relevant to them.

Understanding probability is essential for daily life. Probabilistic reasoning is critical in decision making not only for people but also for artificial intelligence (AI). AI sets a modern context to connect probability concepts to real-life situations. It also provides unique opportunities for reciprocal learning that can advance student understanding of both AI systems and probabilistic reasoning. This project aims to improve the current practice of high school probability education and to design AI problem-solving to connect probability and AI concepts. Set in a game-based environment, students learn and practice applying probability theory while exploring the world of probability-based AI algorithms to solve problems that are meaningful and relevant to them.

This project addresses a major educational barrier, namely that rural students are less likely to choose a major in STEM and have far less access to advanced STEM courses taught by highly qualified teachers. The LogicDataScience (LogicDS) curriculum and virtual delivery are expected to relieve the resource constraints significantly and thus reach rural students. The strategy behind this curriculum development for data science explores the utility of emphasizing how the foundations of data science in computing, mathematics, and statistics are unified by mathematical logic. The project is studying the impacts of the new curriculum on students’ learning of computing, mathematics, and statistics.

Covariational reasoning, or the ability to reason about relationships as quantities change together, is one way of thinking that can provide a foundation for students to build their more abstract algebraic knowledge. This research builds a foundation for integrating education and research at the intersection of students’ developing algebraic knowledge, covariational reasoning, and new educational technologies to create a new path into algebra. This path can help remove barriers that have historically restricted access to mathematics and STEM coursework and careers.

Teachers’ beliefs influence their instructional decisions and these decisions shape the mathematical learning opportunities for all students. This is particularly important when considering the learning opportunities for groups that have historically been marginalized in mathematics, including girls and students of color. There are few validated, mathematics-specific instruments that measure teachers’ beliefs about mathematics learning related to race, ethnicity, and gender. This project seeks to investigate teachers’ beliefs related to how they explain the systemic racial and gender differences in mathematics education outcomes by developing and validating a survey instrument and to explore how those beliefs might impact their teaching.

This project connects interdisciplinary researchers and experts from four tribal nation partners to develop and implement an in-service teacher professional certificate program that integrates Indigenous Knowledge into STEM teaching. This multi-sited teacher professional development model will enroll K-12 teachers in four different Native-serving regions of the rural West into a 12-month certificate program that combines Indigenous science, Coupled Human and Natural Systems, and Land education concepts into an experiential learning cycle with local and broad study of learning with the Land. The project will add knowledge about the transferability of local epistemologies and practices and national science standards within four specific Indigenous contexts and expand space for tribal-lead professional development to transform teacher classroom practice.