Projects

Most students learn about negative numbers long after they have learned about positive numbers, and they have little time or opportunity to build on their prior understanding by contrasting the two concepts. The purpose of this CAREER project is to identify language factors and instructional sequences that contribute to improving elementary students' understanding of addition and subtraction problems involving negative integers. 

This project examines student and teacher experiences with the de-tracking of math sequences in a public school district in Western Oregon. It examines how a district-wide cohort of middle school students, as individuals and in groups, identify with and define what it means to be good at math, and how these identities shift over time as they progress through math sequences. It also establishes a partnership between a mathematics education researcher and a school district (Research Practice Partnership) to study changes in pedagogy, define problems of teaching practice, and design solutions as the district transitions to de-tracked classes.

Realizing the potential of preschool to address historical inequities demands a deeper, more nuanced understanding of the varied ways opportunities to learn play out for individual children within and across classrooms. The goal of this project is to illuminate the variability in opportunities for mathematics learning in early childhood through capturing the experiences of individual children over time. The goal is to understand how these children navigate opportunities to participate in mathematical activity, their perspectives of what knowing and doing mathematics entails, and the resources they draw upon to engage in mathematical practices.

The proposed project initiates new research and an integrated education plan to address specific problems in middle school mathematics classrooms by investigating (1) how to effectively differentiate instruction for middle school students at different reasoning levels; and (2) how to foster middle school students' algebraic reasoning and rational number knowledge in mutually supportive ways.

This project explores "backward transfer", or the ways in which new learning impacts previously-established ways of reasoning. The PI will observe and evaluate algebra I students as they learn quadratic functions and examine how different kinds of instruction about the new concept of quadratic functions helps or hinders students' prior mathematical knowledge of the previous concept of linear functions. This award will contribute to the field of mathematics education by expanding the application of knowledge transfer, moving it from only a forward focused direction to include, also, a backward focused direction.

This project is documenting how students with learning disabilities (LD) access and advance their conceptual understanding of fractions.  Rather than focusing on the knowledge students do not have, this work is focused on uncovering students' informal knowledge that can bridge to fractions and how instruction can be used to promote conceptual change. 

This project will develop and study co-learning, community-engaged educational programs that center STEM education pipelines and pathways for gifted Black girls. The central aim is to bring about an actionable theory of change at the elementary level to foster a sense of belonging in STEM, early STEM exploration and development, and nurturing a STEM identity, through critical and culturally relevant experiential learning. The project will also develop curricular materials for gifted Black girls and their families (See Me in STEM) as well as professional development materials for teachers (Teachers as Talent Catalysts) as part of the educational integration plan.

Research increasingly provides insights into the magnitude of mathematics teacher turnover, but has identified only a limited number of factors that influence teachers' career decisions and often fails to capture the complexity of the teacher labor market. This project will address these issues, building evidence-based theories of ways to improve the quality and equity of the distribution of the mathematics teaching workforce. 

This project involves a longitudinal, ethnographic study of children's mathematical performances from preschool to first grade in both formal classroom settings and informal settings at school and home. The study seeks to identify opportunities for mathematical learning, to map varied performances of mathematical competence, to chart changes in mathematical performance over time, and to design and assess the impact of case studies for teacher education.

This project is investigating the learning that can take place when elementary school students are directly involved in the collection, sense-making, and analysis of real, personally-meaningful data sets. The hypotheses of this work are that by organizing elementary statistics instruction around the study of physical activities, students will have greater personal engagement in data analysis processes and that students will also develop more robust understandings of statistical ideas.

Elementary students need opportunities to see science as meaningful and relevant to their lives. One way to increase this relevance is with learning experiences that are grounded in community-based questions and inquiries that students identify and carry out themselves. An important contribution of this project is investigating how culturally relevant and community-based science curriculum helps to affirm and develop Black students’ science identities in an urban, elementary classroom. This project will partner with third, fourth and fifth-grade elementary teachers to create and to investigate such learning experiences.

This project will design and develop specialized instructional materials and guidelines for teaching secondary algebra in linguistically diverse classrooms. These materials will incorporate current research on student learning in mathematics and research on the role of language in students' mathematical thinking and learning. The work will connect research on mathematics learning generally with research on the mathematics learning of ELLs, and will contribute practical resources and guidance for mathematics teachers who teach ELLs.

This CAREER award aims to study the construct of "epistemic empathy" and examine how it can be cultivated in science and mathematics teacher education, how it functions to promote responsive teaching, and how it shapes learners' engagement in the classroom. In the context of this project, epistemic empathy is defined as the act of understanding and appreciating another's cognitive and emotional experience within an epistemic activity aimed at the construction, communication, and critique of knowledge.

There have been prominent and widespread calls for high school science students to work with data in more complex ways that better align with and support the work of professional scientists and engineers. However, high school students' analysis and interpretation of scientific data is often limited in scope, complexity, and authentic purpose. This project aims to support and advance students' work with ecological data in high school biology classrooms by embracing a new approach: Bayesian data analysis methods. Such methods involve expressing initial ideas or beliefs and updating them quantitatively with data that students access or record. This project will empower 20 high school teachers and their approximately 1,200 students to make sense of data within and beyond classroom contexts. It also will involve sharing research findings, an educational technology tool for Bayesian data analysis, and curricular resources in open and accessible ways.

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.

This project studies teaching practices in a year-long high school algebra course that integrates hand-held and other electronic devices. Of particular interest is how these technologies can support learners' capacity to efficiently and effectively draw on the distributed intelligences that technical and social networks make available. The investigation focuses on collaborative learning tasks centered on collective mathematical objects, such as functions, expressions, and coordinates that participants in a group must jointly manipulate through networked computers.

This study seeks to describe trajectories that describe the ways in which Black learners develop as particular kinds of mathematical learners. The study takes place in the context of an established, multi-year college bridge program that has as its goals to increase the representation of historically marginalized groups in the university community.

The goal of this CAREER program of research is to identify, from a cross-cultural perspective, essential Algebraic Knowledge for Teaching (AKT) that will enable elementary teachers to better develop students' algebraic thinking. This study explores AKT based on integrated insights of the U.S. and Chinese expert teachers' classroom performance.

This project will contribute new knowledge on two aspects of participation in mathematics education. First, this research aims to understand how perceptions of race influence how teachers, future teachers, and researchers assess how bilingual children use their languages and movement to participate in mathematical activity. Second, it will explore ways to counter deficit views that influence teachers’, preservice teachers’, and researchers’ perceptions of these multiple ways of participating as inferior to what is traditionally considered as meaningful participation.

This project seeks to investigate the possibilities and challenges of using a participatory approach to research and design, centering Black, Indigenous, Latinx, and Hmong students and their families in imagining and creating change. The project will generate new knowledge about the possibilities and limitations of participatory design research (PDR) as a method for advancing equity in mathematics education through PDR cycles at three middle schools over the five years of the project. This approach has the potential to disrupt inequitable practices of mathematics education as well as undemocratic processes for making decisions about mathematics education. Further, it will be a catalyst for developing racially just practices and processes in mathematics education.

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.

This project will investigate whether six urban middle schools are implementing highly effective science, technology, engineering and mathematics (STEM) programs based on factors identified through relevant research and national reports on what constitutes exemplary practices in 21st century-focused schools.

This project is developing an 8th-grade assessment for proportional reasoning from a cognitive diagnosis model (CDM) framework. CDMs are psychometric models developed specifically for diagnosing the presence or absence of fine-grained skills or processes required in solving problems on a test. Assessments based on CDMs can provide information deemed more diagnostic and descriptive, and therefore, more relevant in applied instructional settings.

Advancing Reasoning addresses the lack of materials for teacher education by investigating pre-service secondary mathematics teachers' quantitative reasoning in the context of secondary mathematics concepts including function and algebra. The project extends prior research in quantitative reasoning to develop differentiated instructional experiences and curriculum that support prospective teachers' quantitative reasoning and produce shifts in their knowledge.

STEM learning is a function of both student level and classroom level characteristics. Though research efforts often focus on the impacts of classrooms level features, much of the variation in student outcomes is at the student level. Hence it is critical to consider individual students and how their developmental systems (e.g., emotion, cognition, relational, attention, language) interact to influence learning in classroom settings. This is particularly important in developing effective models for personalized learning. To date, efforts to individualize curricula, differentiate instruction, or leverage formative assessment lack an evidence base to support innovation and impact. Tools are needed to describe individual-level learning processes and contexts that support them. The proposed network will incubate and pilot a laboratory classroom to produce real-time metrics on behavioral, neurological, physiological, cognitive, and physical data at individual student and teacher levels, reflecting the diverse dynamics of classroom experiences that co-regulate learning for all students.