Projects

This project is studying how young children in grades K-2 understand mathematical concepts that are foundational for developing algebraic thinking. Researchers are contributing to an ongoing effort to develop a learning trajectory that describes how algebraic concepts are developed. The project uses teaching experiments, with researchers talking directly to students as they explore algebraic ideas. They explore how students think about and develop concepts related to covariation, representations of functions, relationships among variable, and generalization.

This project is designing digital games for middle school students that will help them prepare for success in Algebra. The games are intended to help students gain a deep understanding of measurement and fraction concepts that are critical as they begin to learn algebra. The project studies students' development of fraction concepts, their engagement in the tasks, and the use of hand-held devices as a useful platform for games.

The aim of this project is to examine opportunity structures provided to students by inclusive STEM-focused high schools, with an emphasis on studying schools that serve students from underrepresented groups. The project is studying inclusive STEM-focused high schools across the United States to determine what defines them. The research team initially identified ten candidate critical components that define STEM-focused high schools and is refining and further clarifying the critical components through the research study.

This project is developing and testing a curricular learning progression of early algebra objectives and activities for students in grades 3 - 5. The goal of the work is to provide teachers with curricular guidance and instructional resources that are useful in preparing students for success in study of algebra at the middle grade level. The project is also developing and validating assessment tools for evaluating student progress toward essential pre-algebra mathematical understandings.

This five-year project investigates how to provide continuous assessment and feedback to guide students' understanding during science inquiry-learning experiences, as well as detailed guidance to teachers and administrators through a technology-enhanced system. The assessment system integrates validated automated scorings for students' written responses to open-ended assessment items into the "Web-based Inquiry Science Environment" (WISE) program.

This exploratory project is working in collaboration with teachers to increase their knowledge of mathematics for teaching in middle school. In addition to geometry and algebra, the research component of the project is providing insights into how teachers use their mathematical knowledge to increase argumentation in the classroom and to help students build skills in mathematical argumentation.

This project is developing Core Math Tools, a suite of Java-based software including a computer algebra system (CAS), interactive geometry, statistics, and simulation tools together with custom apps for exploring specific mathematical or statistical topics. Core Math Tools is freely available to all learners, teachers, and teacher educators through a dedicated portal at the National Council of Teachers of Mathematics (NCTM) web site.

This project is researching the efficacy of a learning and assessment system that emphasizes students' attaining proficiency or better on a limited set of high value learning objectives in Algebra.

Research has shown that engaging students, including students from underrepresented groups, in appropriately structured reasoning activities, including argumentation, may lead to enhanced learning. This project will provide information about how teachers learn to support collective argumentation and will allow for the development of professional development materials for prospective and practicing teachers that will enhance their support for productive collective argumentation.

This project is studying measurement practices from pre-K to Grade 8, as a coordination of the STEM disciplines of mathematics and science. This research project tests, revises and extends learning trajectories for children's knowledge of geometric measurement across a ten-year span of human development. The goal will be to validate all components of each learning trajectory, goal, developmental progression, and instruction tasks, as well as revising each LT to reflect the outcomes of the experiments.

This collaborative project is developing instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement.

This collaborative project is developing instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement.

In this project researchers are implementing and studying a research-based curriculum that was designed to help children in grades 3-5 prepare for learning algebra at the middle school level. Researchers are investigating the impact of a long-term, comprehensive early algebra experience on students as they proceed from third grade to sixth grade. Researchers are working to build a learning progression that describes how algebraic concepts develop and mature from early grades through high school.

In this project researchers are implementing and studying a research-based curriculum that was designed to help children in grades 3-5 prepare for learning algebra at the middle school level. Researchers are investigating the impact of a long-term, comprehensive early algebra experience on students as they proceed from third grade to sixth grade. Researchers are working to build a learning progression that describes how algebraic concepts develop and mature from early grades through high school.

This project uses learning analytics and educational data mining methods to examine how elementary students learn in an online game designed to teach fractions using the splitting model. The project uses data to examine the following questions: 1) Is splitting an effective way to learn fractions?; 2) How do students learn by splitting?; 3) Are there common pathways students follow as they learn by splitting?; and 4) Are there optimal pathways for diverse learners?

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 research and development project is premised on the notion that recent technological developments have made it feasible to represent classroom work in new ways. In addition to watching recorded videos of classroom interactions or reading written cases, teacher educators and teachers can now watch animations and image sequences, realized with cartoon characters, and made to depict activities that happened, or could have happened, in a mathematics classroom.

This project that creates a set of materials for middle grades students and teacher professional development that would support the learning of early algebra. Building on their prior work with an elementary version, the efficacy study focuses on the implementation of the principals underlying the materials, fidelity of use of the materials, and impact on students' learning.

This project tests and refines a hypothetical learning trajectory and corresponding assessments, based on the collective work of 50 years of research in mathematics education and psychology, for improving students' ability to reason, prove, and argue mathematically in the context of algebra. The study produces an evidence-based learning trajectory and appropriate instruments for assessing it.

The objective of this project is to develop a toolkit of resources and practices that will help inservice middle grades mathematics teachers support mathematical argumentation throughout the school year. A coherent, portable, two-year-long professional development program on mathematical argumentation has the potential to increase access to mathematical argumentation for students nationwide and, in particular, to address the needs of teachers and students in urban areas.

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.

This project will use classroom-based research to teach children about important algebraic concepts and to carefully explore how children come to understand these concepts. The primary goal is to identify levels of sophistication in children's thinking as it develops through instruction. Understanding how children's thinking develops will provide a critical foundation for designing curricula, developing content standards, and informing educational policies.

Students who fail algebra in the ninth grade are significantly less likely than their peers to graduate from high school on time. This project intends to test a common support strategy for at-risk students that provides an extra period of algebra, commonly known as a "double dose" condition. The Intensified Algebra (IA) is an intervention that addresses both the academic and non-academic needs of students.

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.

The Graphing Research on Inquiry with Data in Science (GRIDS) project will investigate strategies to improve middle school students' science learning by focusing on student ability to interpret and use graphs. GRIDS will undertake a comprehensive program to address the need for improved graph comprehension. The project will create, study, and disseminate technology-based assessments, technologies that aid graph interpretation, instructional designs, professional development, and learning materials.