# Learning Progression

## 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.

## Student Mathematics Learning Through Self-Explanation, Peer Tutoring and Digital Media Production

This project engages high-school students as student-tutors who create screen-capture videos that demonstrate step-by-step solutions to mathematical problems and explicate the use of interactive applets. The project tests whether the mathematical and communication skills of student-tutors improve in the process of making the video materials. It also tests whether teachers and student users benefit from the videos. The project will examine whether the process of creating and disseminating the videos is replicable and scalable.

## Supporting Scientific Practices in Elementary and Middle School Classrooms

This project will develop a learning progression that characterizes how learners integrate and interrelate scientific argumentation, explanation and scientific modeling, building ever more sophisticated versions of practice over time using the three common elements of sense-making, persuading peers and developing consensus. The learning progression is constructed through students’ understanding of scientific practice as measured by their attention to generality of explanation, clarity of communication, audience understanding, evidentiary support, and mechanistic versus descriptive accounts.

## Reasoning Tools for Understanding Water Systems

This project builds on current learning progression research to study the effects of teaching Tools for Reasoning on development of middle school students' capacities to understand the Earth's hydrologic systems. The project applies a design-based research approach using iterative cycles of Tool design/revision, teacher workshops, and small-scale pilot tests of Tools through classroom experiments with teachers and students in Montana and Arizona.

## Rethinking How to Teach Energy: Laying The Foundations in Elementary School (Collaborative Research: Lacy)

This project is a collaborative effort that aims to develop a grade 3-5 Learning Progression that will provide a coherent approach to teaching energy in elementary school and lay a strong foundation for further learning in middle school. The project will identify a network of core concepts and principles about energy that are fundamental and general enough to be compatible with scientific ideas about energy, yet within reach of 5th graders.

## CAREER: Supporting Students' Proof Practices Through Quantitative Reasoning in Algebra

The aim of this project is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra.