The Impact of a Teacher-Led Early Algebra Intervention on Children's Algebra-Readiness for Middle School
Co-Principal Investigators: Despina Stylianou (City University of New York), Eric Knuth (University of Wisconsin, Madison), Ana Stephens (University of Wisconsin, Madison), and Lindsay Demers (TERC)
Purpose: Current reforms in mathematics education underscore the critical role of algebra in elementary, middle and high school. It is argued that the traditional "arithmetic-then-algebra" approach, where an arithmetic curriculum in the elementary grades is followed by a formal treatment of algebra in secondary grades, does not allow the time and space necessary for students to develop depth in their understanding of algebra. However, the premise that beginning algebra instruction in the elementary grades—rather than waiting until secondary grades—will more effectively prepare children for a formal study of algebra has not been tested. The primary purpose of this project is to evaluate whether students who receive longitudinal, early algebra instruction during the elementary grades are better prepared for algebra in middle school than children who receive only arithmetic-focused instruction.
Project Activities: The researchers will evaluate the efficacy of a fully developed intervention targeting students’ early algebraic learning in Grades 3 to 5. The project consists of an Early Algebra Learning Progression (EALP) intervention materials in Grades 3 to 5, accompanying assessments to measure students’ learning, and teacher professional development materials.
Products: The outcomes of the project include evidence of the efficacy of a fully developed early algebra intervention for elementary school students. Peer-reviewed publications will also be produced.
Setting: The study will be conducted in elementary schools in North Carolina representing ethnically and socio-economically diverse communities.
Sample: The sample will consist of approximately 4,900 students in Grades 3 to 5 and 200 elementary school teachers drawn from 49 schools.
Intervention: The intervention focuses on core algebraic thinking practices (generalizing, representing, justifying, and reasoning with mathematical relationships) across key mathematical content domains (e.g., functional thinking, generalized arithmetic). The intervention includes about 20 one-hour algebra lessons that are implemented throughout the school year in each of grades 3–5. The early algebra content embeds important mathematics concepts – particularly arithmetic – in rich algebraic tasks in ways that can deepen children’s understanding of these concepts. Teacher professional development includes a 1-day summer workshop and 4-hour sessions monthly, throughout the school year.
Research Design and Methods: A randomized control trial will be conducted with 49 elementary schools across three school districts in North Carolina. Schools will be stratified by district and then randomly assigned within each district to treatment or control conditions. Each school averages about 100 participating students in Grade 3 (25 students per class, 4 classes per grade), or about 4,900 total students. In addition, about 200 elementary teachers will participate in the study each year. The intervention will take place in all Grade 3 classrooms in Year 1, all Grade 4 classrooms in Year 2, and all Grade 5 classrooms in Year 3. All student participants (experimental and control) will be given a follow-up assessment at the end of Grade 6 in Year 4 of the study.
Control Condition: Students in schools assigned to the control condition will receive business-as-usual instruction in mathematics.
Key Measures: The measures of student performance include early algebra assessments developed by the researchers collected at baseline (beginning of Grade 3) and at the end of each year of the project for Grades 3 to 6 (5 time points total). The North Carolina End-of-Grade standardized state assessment will also be collected at the end of Grades 3 to 6 as a distal measure of student mathematical performance. Measures used to characterize teachers’ fidelity of implementation include surveys, interviews, document reviews, and classroom observations. In addition, in order to document the experiences of all treatment and control classrooms for comparison group practices, the researchers will collect general course syllabi produced at the school or district level, teachers’ brief lesson guides, a unit/chapter log from all participating teachers, and curricular materials used during regular instruction.
Data Analytic Strategy: HLM will be used to analyze yearly performance differences between students in treatment and control schools, and latent growth curve modeling will be used to assess longitudinal performance differences between students in treatment and control schools from Grades 3 to 6. Quantitative and qualitative analyses will also be conducted to assess teacher fidelity of implementation.
Blanton, M., Brizuela, B., Stephens, A., Knuth, E., Isler, I., Gardiner, A., Demers, L., and Fonger, N (2018). Implementing a Framework for Early Algebra. In C. Kieran (Ed.), Teaching and Learning Algebraic Thinking with 5–to 12–year-olds: The Global Evolution of an Emerging Field of Research and Practice (pp. 27–49).
Related Projects: Project LEAP: Extending a Grades 3–5 Early Algebra Learning Progression into Grades K-2 (R305A170378)