We are analyzing the intended algebra curriculum as represented in a variety of high-school mathematics textbooks – Core Plus Mathematics Project (CPMP), Discovering Mathematics (Key Curriculum Press), EDC's Center for Mathematics Education, Glencoe, Interactive Mathematics Program (IMP), and University of Chicago School Mathematics Project (UCSMP). The textbook analysis is based on two dimensions frequently used for curriculum analysis: a content dimension and a cognitive dimension.
Projects
This study can provide a basis for design research focused on developing effective materials and programs for flipped instruction in secondary mathematics, which is already occurring at an increasing rate, but it is not yet informed by empirical evidence. This project will result in a framework for flipped instruction robust enough to be useful at a variety of grade levels and contexts. The framework will provide a better understanding of the relationships among various implementations of flipped instruction and student learning.
This project develops images, extended examples, and principles that illustrate how the articulation, representation and justification of general claims about operations evolve in the elementary grades and how this work supports the transition from arithmetic to algebra in the middle grades. An online course uses the Sourcebook as a text to engage teachers in considering the underlying pedagogical and mathematical aspects of the work and implementing these ideas in their instruction.
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 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.
This project seeks to identify teaching practices that can be linked to students' early algebra learning in grades three, four and five. The goal of the project is to use assessment data and videos of classroom teaching in order to create a tool that can be used to document effective instructional practices. This observation tool can then be used to support teacher professional development in early algebra and research about how teachers' actions can be linked to students' learning.
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?
This project explores the mechanisms by which teachers translate what they learn from professional development into their teaching practice. The goal of this project is to study how the knowledge and skills teachers acquire during professional development (PD) translate into more conceptually oriented mathematics teaching and, in turn, into increased student learning.
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.
This project operationalizes research in number, operation, and early algebra. It builds on the paradigm of Dynamic Geometry (the interactive and continuous manipulation of geometric shapes and constructions) with a new technological paradigm, Dynamic Number, centered on the direct manipulation of numerical representations and constructions. Using The Geometer’s Sketchpad as a starting point, KCP Technologies is developing new software tools to deepen students’ conceptions of number and early algebra in grades 2–8.
In this project, the team will address questions about how collaborative problem solving, learning progressions, and facilitation interact in the development of students’ mathematical learning. The work affords an opportunity to advance equitable access to high-quality education for all students by enhancing the quality of instruction for students lacking opportunities to learn key concepts of mathematics because of the inequitable structures of education in the country.
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.
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.
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.
EDC is developing a high school capstone course in linear algebra. Student resources contain a core semester that develops two- and three-dimensional geometry using vectors and that treats matrix algebra and its applications to geometry; a semester of material that completes a typical undergraduate course (exploring bases, determinants and eigentheory); and 5 stand-alone modules that develop applications of this core to mathematics, engineering, science, and other STEM fields.
This project is using data from interviews with 160 K-12 students and 20 adults to describe common understandings and progressions of development for negative number concepts and operations. The project is motivated by the widely acknowledged finding that students have difficulty mastering key concepts and skills involved in work with integers.
This project will develop games to build conceptual understanding of key early algebra topics. The materials will be freely accessible on the web in both English and Spanish. The project will develop 4-5 games. Each game will include supporting materials for use by students in inquiry-based classroom lessons, and web-based professional development tools for teachers.
The project will develop modules for grades 9-12 that integrate mathematics, computing and science in sustainability contexts. The project materials also include information about STEM careers in sustainability to increase the relevancy of the content for students and broaden their understanding of STEM workforce opportunities. It uses summer workshops to pilot test materials and online support and field testing in four states.
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 will explore the learning of mathematics through architectural tasks in an online simulation game, E-Rebuild. In the game-based architectural simulation, students will be able to complete tasks such as building and constructing structures while using mathematics and problem solving. The project will examine how to collect data about students' learning from data generated as they play the game, how students learn mathematics using the simulation, and how the simulation can be included in middle school mathematics learning.
This project is developing, designing, and testing materials for professional development leaders (e.g., teacher educators, district mathematics specialists, secondary mathematic department chairs) to use in their work with secondary mathematics teachers. The aim is to help those teachers analyze the discourse patterns of their own classrooms and improve their skills in creating discourse patterns that emphasize high-level mathematical explanation, justification, and argumentation.
In this project, we examine middle-school students’ understandings of coordinate systems and frames of reference prior to examining their graph construction and interpretation. This focus allows us to design instructional materials that can support students’ graphing understandings in ways that avoid or mitigate how persistent challenges in students’ graphing understandings identified in the research literature.
This project will develop three replacement units for biology and refine them through classroom testing. The units will be models of STEM integration by using the important concepts of proportional reasoning and algebraic thinking and engineering re-design to address big ideas in science while also promoting the learning of 21st century skills. The materials will be educative for teachers, and the teacher materials and professional development methods will work at scale and distance.
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.
The purpose of this project is to create a research-based model of how students with learning disabilities (LDs) develop multiplicative reasoning via reform-oriented pedagogy; convert the model into a computer system that dynamically models every students’ evolving conceptions and recommends tasks to promote their advancement to higher level, standard-based multiplicative structures and operations; and study how this tool impacts student outcomes.