# Research Objectives

## Developing Algebra-Ready Students for Middle School: Exploring the Impact of Early Algebra (2009-2013)

Funded by National Science Foundation DRL #1207945

This first project was designed to build the preliminary components for investigating the impacts of early algebra education on students’ algebra readiness in middle grades through the construction of an Early Algebra Learning Progression [EALP]. In particular, the project goals were

- To coordinate research, curricular, and mathematical perspectives to design the EALP’s curricular framework and progression that identify core algebraic concepts and their progression in children’s thinking across upper elementary and middle grades (Grades 3-7). The curricular framework was based on the core algebraic concepts of (1) Variable, (2) Functional Thinking, (3) Equations, Expressions, Equality and Inequality, (3) Generalized Arithmetic and (5) Proportional Reasoning.
- Using the EALP’s curricular framework and progression, to design grade-based assessments of students’ algebra understanding for upper elementary and middle grades (Grades 3-7) and to validate these assessments through psychometric testing.
- To develop an instructional sequence based on the EALP’s curricular framework and progression and conduct a preliminary study concerning the intervention’s impact on students’ algebra learning as measured by the assessments developed in Project Goal 2.
- To use the EALP to identify appropriate tasks for content-based teacher professional development [TPD] and to refine this through implementation of the TPD.

## The Impact of Early Algebra on Students’ Algebra-Readiness (2012-2015)

Funded by National Science Foundation DRL #1219605/06

The goal of this second project was to use the EALP’s instructional sequence and grade-level assessments developed in the first project to examine the effectiveness of our early algebra intervention. We conducted a longitudinal study to measure the impact of our comprehensive, sustained Grades 3-5 early algebra intervention on students' algebra understanding in elementary grades and their algebra readiness in middle school. The project used a quasi-experimental design to compare the performance of students who received our early algebra intervention to students who receive more traditional elementary grades instruction. We additionally conducted yearly interviews with a small subset of students to gain further insight into their algebraic thinking.

## The Impact of a Teacher-Led Early Algebra Intervention on Children’s Algebra-Readiness for Middle School (2014-2018)

Funded by Institute for Education Sciences #R305A140092

This third project takes to scale the work of the first two projects and puts the early algebra instruction in the hands of regular classroom teachers. Approximately 50 elementary schools are taking part in a randomized longitudinal experiment in which experimental teachers are implementing a comprehensive, sustained early algebra intervention in Grades 3-5. Our goals include measuring the effectiveness of a teacher-led early algebra intervention on students’ algebra understanding and algebra-readiness for middle school as well as the fidelity with which teachers are able to implement the intervention with the support of our professional development.

## Project LEAP: Extending a Grades 3-5 Early Algebra Learning Progression into Grades K-2 (2017-2021)

Funded by Institute for Education Sciences #R305A170378

The goal of this project is to extend our Grades 3-5 work into the early grades by designing and testing a Grades K-2 early algebra learning progression. This work will include developing an instructional sequence and interview assessments and testing the impact of the instructional sequence on students’ learning. Two classrooms of students will be followed throughout Grades K-2 in a researcher-led intervention. In Year 4, a cross-sectional teacher-led effectiveness study will take place, with one experimental and one control classroom at each grade level.

## Building a Grades K-2 Early Algebra Learning Progression for Diverse Populations (2017-2020)

Funded by National Science Foundation DRL #1720129

The goal of this project is to extend our Grades 3-5 work into the early grades by designing and testing a Grades K-2 early algebra learning progression and paying particular attention to the needs and experiences of the diversity of learners, including those with math difficulties or disabilities. This work will include developing an instructional sequence and interview assessments, testing the impact of the instructional sequence on students’ learning, and proposing and testing strategies to help a diverse range of students. A cross-sectional researcher-led intervention will take place in one classroom in each of Grades K-2.

## Identifying Effective Instructional Practices that Foster the Development of

Algebraic Thinking in Elementary School (2017-2021)

Funded by National Science Foundation DRL #1721192

The goal of this project is to examine videos of classrooms collected in a previous project—The Impact of Teacher-Led Early Algebra Intervention on Children’s Algebra-Readiness for Middle School—to identify instructional practices that are associated with students’ early algebra learning and develop an early algebra classroom observational instrument.