# Learning Progression

## Systemic Formative Assessment to Promote Mathematics Learning in Urban Elementary Schools

This project builds on the study of the Ongoing Assessment Project's (OGAP) math assessment intervention on elementary teachers and students and combines the intervention with research-based understandings of systemic reform. This project will produce concrete tools, routines, and practices that can be applied to strengthen programs' implementation by ensuring the strategic support of school and district leaders.

## Building a Next Generation Diagnostic Assessment and Reporting System within a Learning Trajectory-Based Mathematics Learning Map for Grades 6-8

This project will build on prior funding to design a next generation diagnostic assessment using learning progressions and other learning sciences research to support middle grades mathematics teaching and learning. The project will contribute to the nationally supported move to create, use, and apply research based open educational resources at scale.

## Development and Empirical Recovery for a Learning Progression-Based Assessment of the Function Concept

The project will design an assessment based on learning progressions for the concept of function - a critical concept for algebra learning and understanding. The goal of the assessment and learning progression design is to specifically incorporate findings about the learning of students traditionally under-served and under-performing in algebra courses.

## Using Cognitive Science Principles to Help Children Learn Place Value (Collaborative Research: Smith)

This project will test new instructional approaches designed to help K-1 students comprehend place value. The project will emphasize the underlying relational structure of place value symbols, and target this structure with instructional materials and techniques drawn from the structure mapping literature. Its theory of action is that instruction which scaffolds structure mapping for place value will better prepare children to face the challenges of advanced operations, such as multi-digit calculation.

## Using Cognitive Science Principles to Help Children Learn Place Value (Collaborative Research: Mix)

This project will test new instructional approaches designed to help K-1 students comprehend place value. The project will emphasize the underlying relational structure of place value symbols, and target this structure with instructional materials and techniques drawn from the structure mapping literature. Its theory of action is that instruction which scaffolds structure mapping for place value will better prepare children to face the challenges of advanced operations, such as multi-digit calculation.

## CAREER: Designing Learning Environments to Foster Productive and Powerful Discussions Among Linguistically Diverse Students in Secondary Mathematics

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.

## Improving Formative Assessment Practices: Using Learning Trajectories to Develop Resources That Support Teacher Instructional Practice and Student Learning in CMP2

The overarching goal of this project is to develop innovative instructional resources and professional development to support middle grades teachers in meeting the challenges set by college- and career-ready standards for students' learning of algebra.

## Learning Algebra and Methods for Proving (LAMP)

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.

## CAREER: Fraction Activities and Assessments for Conceptual Teaching (FAACT) for Students with Learning Disabilities

The goal of this project is to study and support the development of conceptual understanding of fractions by students with learning disabilities (LD). The researcher proposes that rather than focusing on whether LD students can or cannot develop conceptual understanding of fractions, research should attempt to uncover the understanding LD students have and examine how growth of conceptual knowledge occurs in these students.

## Spatial Mathematics, Engineering, and Science: Toward an Integrated STEM Education

The goal of this project is to develop a provisional learning progression spanning grades K-5 that articulates and tests the potential of experiencing, describing, and representing space as the core of an integrated STEM education. The science of space has an extensive scope within and across disciplinary boundaries of science, mathematics and engineering; the project will create a coherent approach to elementary instruction in which mathematical reasoning about space is systematically cultivated.