# Learning Progression

## 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.

## A Learning Progression for Scientific Modeling

This project will provide an empirically-supported learning progression for a key scientific practice, scientific modeling. The specific instructional materials created as part of the project can serve as a model other developers can use to design materials supporting scientific modeling and other practices. The model for educative curriculum materials as a form of teacher support can be adapted to support teacher learning about modeling or other scientific practices in other curriculum materials.

## Mapping Developmental Trajectories of Students' Conceptions of Integers

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.

## Developing an Empirically-tested Learning Progression for the Transformation of Matter to Inform Curriculum, Instruction and Assessment Design

A principled framework is created for the development of learning progressions in science that can demonstrate how their use can transform the way researchers, educators and curriculum developers conceptualize important scientific constructs. Using the construct of transformation of matter, which requires understanding of both discrete learning goals and also the connections between them, a hypothetical learning progression is constructed for grades 5-12.

## Shifting Mindsets: A Study of a First-year Implementation of "New Technology High School"

This grant examines the changes teachers and students go through in their first year of implementing a New Technology High School project-based curriculum for ninth graders in two high schools. This first year of implementation is part of a phased-in implementation for subsequent grades. The NTHS approach calls for moving from more traditional approaches to mathematics and science education to project-based curricula that posits mathematics and science in the context of real-world issues and problems.

## Diagnostic E-learning Trajectories Approach (DELTA) Applied to Rational Number Reasoning for Grades 3-8

This project aims to develop a software diagnostic tool for integrating diagnostic interviews, group administered assessments, and student data in real-time so that teachers can enter and view student status information. This project would concentrate on rational number learning in grades 3-8. The design is based on a model of learning trajectories developed from existing research studies.