Project Activities
The researchers evaluated the efficacy of a fully developed intervention targeting students' early algebraic learning in grades 3 to 5. The project consisted of Early Algebra Learning Progression (EALP) intervention materials in grades 3 to 5, accompanying assessments to measure students' learning, and teacher professional development materials.
Structured Abstract
Setting
The study was conducted in elementary schools in North Carolina representing ethnically and socio-economically diverse communities in rural, urban, and suburban settings.
Sample
The sample consisted of 3,208 students in grades 3 to 5 and 464 elementary school teachers drawn from 46 schools. Each school provided the percent of students receiving free or reduced-cost lunch, which was used as a proxy for socio-economic status. The average was 63 percent students receiving free or reduced-cost lunch, with a range of 14 percent to 100 percent.
The intervention focused on core algebraic thinking practices (generalizing, representing, justifying, and reasoning with mathematical relationships) across key mathematical content domains (functional thinking; generalized arithmetic; equivalence, expressions, equations, and inequalities). Including this broad span of content and thinking practices over a 3-year period was critical to ensuring students received an intervention that was both comprehensive (as opposed to narrowly focused on one aspect of algebra) and sustained. This allowed students to develop their understanding of important concepts over time. The intervention included about twenty 1-hour algebra lessons in each of grades 3 through 5 that were implemented throughout the school year. Classroom teachers implemented at most one lesson per week during their regular mathematics instruction. The early algebra lessons emphasized writing and talking about mathematical ideas, including building strong mathematical arguments. The use of different representations—including natural language, variable notation, tables, and graphs—as well as understanding the meanings of these representations in different mathematical contexts, was emphasized. Lessons embedded important mathematics concepts—particularly, arithmetic concepts—in rich algebraic tasks in ways that deepened children's understanding of these concepts. Thus, it was not necessary to treat these lessons as an "add on" to an already full curriculum. Teacher professional development included a 1-day summer workshop and 4-hour sessions monthly throughout the period of implementation. Professional development focused on developing teachers' own understanding of early algebra content, students' algebraic thinking in response to LEAP tasks, and instructional strategies that could support students' algebraic thinking.
Research design and methods
Researchers conducted a randomized control trial with 46 elementary schools (23 intervention, 23 control) across 3 school districts in North Carolina. Schools were stratified by district and then randomly assigned within each district to treatment or control conditions. In total, 3,208 students and 464 teachers participated in the study over the 3 years. The intervention took place in all grade 3 classrooms in year 1, all grade 4 classrooms in year 2, and all grade 5 classrooms in year 3 in the 23 intervention schools. All student participants (experimental and control) were given a follow-up assessment at the end of grade 6 in year 4 of the study, 1 year after the conclusion of the 3-year intervention.
Control condition
Students in schools assigned to the control condition received business-as-usual instruction in mathematics.
Key measures
The measures of student performance included validated early algebra assessments developed by the researchers. These assessments were 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 scores were also 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 included surveys, interviews, and classroom observations. In addition, in order to document the experiences of all treatment and control classrooms for comparison group practices, researchers collected general course syllabi produced at the school or district level, curricular materials, and teachers' response to a monthly (years 1 to 2) or quarterly (year 3) log (survey) from all participating teachers regarding how early algebraic concepts were addressed in their regular instruction.
Data analytic strategy
Hierarchical linear modeling was used to analyze yearly performance differences and longitudinal performance differences between students in treatment and control schools from grades 3 to 6. Quantitative and qualitative analyses were conducted to assess teacher fidelity of implementation.
Key outcomes
The main findings of this efficacy study are as follows:
- Grades 3 to 5 students who received the EALP intervention significantly outperformed students who received only their regular arithmetic-focused instruction on assessments of algebra understanding (Blanton et al., 2019).
- Grades 3 to 5 students in underserved populations (e.g., low socio-economic status) who received the EALP intervention significantly outperformed students in comparable demographics who received only their regular arithmetic focused instruction on assessments of algebra understanding (Blanton et al., 2019).
- Teaching practices that were significantly positively related with students' performance on algebra assessments included (1) engaging students in the algebraic practices of generalizing, representing, and justifying mathematical structure and relationships; and (2) pursuing students' mathematical ideas (Stylianou et al., 2019).
- Students who experienced the EALP intervention in Grades 3–5 continued to outperform their control counterparts on measures of algebra understanding at the end of Grade 6, though their performance declined over the non-intervention year (Stephens et al., 2021).
People and institutions involved
IES program contact(s)
Project contributors
Products and publications
Project website:
WWC review:
Blanton, M., Stroud, R., Stephens, A., Gardiner, A. M., Stylianou, D. A., Knuth, E., ... & Strachota, S. (2019). Does early algebra matter? The effectiveness of an early algebra intervention in grades 3 to 5. American Educational Research Journal, 56(5), 1930-1972. [WWC Review].
Publications:
ERIC Citations: Find available citations in ERIC for this award here.
Select Publications:
Books
Blanton, M., Gardiner, A., Stephens, A., and Knuth, E. (in press). LEAP: Learning through an Early Algebra Progression - Grade 3. Didax Publishers.
Blanton, M., Gardiner, A., Stephens, A., and Knuth, E. (in press). LEAP: Learning through an Early Algebra Progression - Grade 4. Didax Publishers.
Blanton, M., Gardiner, A., Stephens, A., and Knuth, E. (in press). LEAP: Learning through an Early Algebra Progression - Grade 5. Didax Publishers.
Cañadas, M. C., Blanton, M., & Brizuela, B. (2019). (Eds.) Early aglebraic thinking. Special Journal Issue for Infancia y Aprendizaje/Journal for the Study of Education and Development.
Book chapters
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). Springer International Publishing.
Strachota, S., Knuth, E., and Blanton, M., (2018). Cycles of generalizing activities in classroom. 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. Hamburg, Germany: Springer International Publishing.
Stephens, A. C., Ellis, A. B., Blanton, M., & Brizuela, B. M. (2017). Algebraic thinking in the elementary and middle grades. In J. Cai (Ed.), Compendium for Research in Mathematics Education (pp. 386-420). Reston, VA: National Council of Teachers of Mathematics.
Journal articles
Blanton, M., Stroud, R., Stephens, A., Gardiner, A., Stylianou, D., Knuth, E., Isler, I., and Strachota, S. (2019). Does early algebra matter? The effectiveness of an early algebra intervention in grades 3-5. American Educational Research Journal, 56(5), 1930-1972.
Stephens, A., Stroud, R., Strachota, S., Stylianou, D., Blanton, M., Knuth, E., and Gardiner, A. M. (2021). What early algebra knowledge persists 1 year after an elementary grades intervention? Journal for Research in Mathematics Education, 52(3), 332-348.
Stylianou, D., Stroud, R., Cassidy, M., Gardiner, A., Stephens, A., Knuth, E., and Demers, L. (2019). Putting early algebra in the hands of elementary school teachers: Examining fidelity of implementation and its relation to student performance. Journal for the study of education and development/Infancia y Aprendizaje (Special Issue: Early Algebra), 42(3), 523-569.
Published proceedings
Cassidy, M., Stroud, R., Stylianou, D., Blanton, M., Gardiner, A., Knuth, E. and Stephens, A. (2017). Examining the fidelity of implementation of an early algebra intervention and student learning, In Galindo, E., and Newton, J., (Eds.), Proceedings of the thirty-ninth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 299-302). Hoosier Association of Mathematics Teacher Educators. ERIC ID:
Stephens, A., Stroud, R., Strachota, S., Blanton, M., Stylianou, D., Knuth, E., Veltri Torres, R., Murphy Gardiner, A., and Sung, Y. (2019). Sixth-grade students' retention of early algebra understandings after an elementary grades intervention. In Otten, S., Candela, A. G., de Araujo, Z., Haines, C., and Munter, C. (Eds.), Proceedings of the forty first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 147-156), University of Missouri.
Available data:
For access to anonymized data, please contact the PI at [email protected].
Additional project information
Additional online resources and information:
- Project Video: https://youtu.be/kNlX0qZffBI
Related projects
Supplemental information
Co-Principal Investigators: Stylianou, Despina; Knuth, Eric; Stephens, Ana; Stroud, Rena; Demers, Lindsay
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