Description:

Co-Principal Investigator: Rena Stroud; Angela Gardiner; Eric Knuth (University of Wisconsin); Ana Stephens (University of Wisconsin)

Purpose: The purpose of this project is to develop and test the promise of a Grades K–2 Early Algebra Learning Progression (EALP) to build young children's algebraic thinking. Algebra is a subject with which students still struggle. One recommendation for improving algebra instruction that has gained widespread acceptance has been to adopt a longitudinal, K–12 approach to teaching and learning algebra, rather than waiting until secondary grades to begin students' formal algebra education. This project builds off of a fully developed Grades 3–5 EALP project, which has been evaluated under an IES Efficacy and Replication grant. The current project will extend the EALP into Grades K–2 to align with the existing Grades 3–5 EALP, resulting in a complete and comprehensive model for algebra education across the elementary grades.

Project Activities: The researchers will design, develop, and test a Grades K–2 EALP that will include (1) a curricular framework that specifies learning goals around core algebraic concepts and practices; (2) an instructional sequence designed to achieve these goals; (3) assessments that measure student learning in response to the instructional sequence; and (4) descriptions of the increasingly sophisticated levels of thinking students exhibit around the core algebraic concepts and practices addressed in the instructional sequence.

Products: The resulting Grades K–2 EALP, when aligned with the existing Grades 3–5 EALP, will provide an innovative model with classroom-ready resources that can potentially be used at scale to support a K–12 algebra education. The team will also produce peer reviewed publications.

Structured Abstract

Setting: The study will take place in elementary schools in Rhode Island.

Sample: The sample consists of approximately 300 students and 6 elementary school teachers from a school district in Rhode Island. The district consists of approximately 10% minority (non-white) student population, with about 16% of the district's school population categorized as low SES.

Intervention: The intervention, Grades K–2 EALP, focuses on core algebraic thinking practices (i.e. generalizing, representing, justifying, and reasoning with mathematical relationships) across key content domains (e.g., functional thinking, generalized arithmetic). There are four components to the intervention: (1) a curricular framework that specifies learning goals around core algebraic concepts and practices; (2) an instructional sequence consisting of fifteen 45-minute lessons at each grade level; (3) assessments that measure student learning in response to the instructional sequence; and (4) descriptions of the increasingly sophisticated levels of thinking students exhibit around the core algebraic concepts and practices addressed in the instructional sequence.

Research Design and Methods: As part of the iterative development process, researchers will conduct classroom teaching experiments (CTEs) to implement and test the instructional sequence in Grades K–2. The CTEs allow the researchers to coordinate (1) instructional design and planning, (2) ongoing analysis of classroom events, and (3) retrospective analysis of data generated in the course of an experiment. Using CTEs, the researchers will implement the Grades K–2 instructional sequence beginning with the Grade K instructional sequence in Year 1, followed by the Grade 1 instructional sequence in Year 2, and the Grade 2 instructional sequence in Year 3. Data to be collected include field notes from lessons taught in the CTEs at each of Grades K–2, video recordings of these lessons, videotaped individual student interviews, and students' written work on tasks used in the CTEs and interviews.

To demonstrate the promise of the Grades K–2 EALP, the researchers will conduct a cross-sectional, quasi-experimental pilot study in Year 4. The sample will include two classrooms at each grade level, with one classroom at each grade serving as the treatment classroom and one as the comparison classroom. Data will be collected from participating students using the interview-based assessments designed and validated during the development process in Years 1–3. Fidelity of implementation will also be examined through teacher logs, interviews, and surveys.

Control Condition: The control condition is business-as-usual mathematics instruction.

Key Measures: Measures of student learning outcomes from the pilot study include the Grades K–2 EALP assessments designed and validated during the development process. Measures used to characterize teacher's fidelity of implementation include teacher logs, surveys, and interviews.

Data Analytic Strategy: The research team will use qualitative methods of analysis in the development process to identify themes and strategy use regarding children's algebraic thinking. Specifically, they will analyze data from students' written work, interviews, CTE lessons, and classroom field notes qualitatively using a grounded theory approach. Researchers will also use quantitative methods to measure growth in performance, with differences in post-test scores examined using analysis of covariance.

Related Projects: The Impact of a Teacher-Led Early Algebra Intervention on Children's Algebra-Readiness for Middle School (R305A140092)

Project Video: