The Impact of Early Algebra on Later Algebra Learning

Principal Investigator: 
Project Overview
Background & Purpose: 

In a previous longitudinal intervention study ("Algebra in Early Mathematics" - NSF-ROLE #0310171), we have shown that introducing algebra as part of the early mathematics curriculum is highly feasible and that specific representational tools—tables, graphs, numerical and algebraic notation, and certain natural language structures—can be employed to help students express functional relations among numbers and quantities and solve algebra problems. In the current project, our major research question concerns the impact of students’ Early Algebra (EA) experiences on their performance in middle school mathematics. We are following up, from 6th to 8th grade, the students who had participated in the previous EA’s three hours per week intervention. We collect data on students who were in the EA intervention and their peers who serve as controls, through classroom and summer camp observations, written assessments, and interviews.


The study is carried out in middle schools in the Boston area as well as in a summer camp we convene and carry out ourselves.

Research Design: 

This is a longitudinal study designed to generate descriptive [case study, observational]; associative [quasi-experimental] and causal [quasi-experimental] evidence. Original data are collected through school records or policy documents; assessments of learning; observation [personal, video]; and survey research [informal interviews].

Quantitative data obtained through written assessments and interviews are used to compare the learning of algebra by students in the previous intervention group to that of students in the control group. In-depth qualitative analysis are developed to understand the strategies used by students in different groups.


Results from the 6th grade written assessment show a significantly higher performance for the intervention group, where students were particularly stronger in items involving algebra notation to represent and solve verbal problems.

Publications & Presentations: 

Brizuela, B. M., Martinez, M. V., & Cayton, G. A. (in preparation). A longitudinal analysis of children’s understanding of algebraic tools and representations in grades 3-8.

Some of the publications on results of the intervention in grades 3 to 5 are:

Brizuela, B. M., Martinez, M. V., & Cayton, G. A. (submitted). The impact of Early Algebra: Results from a longitudinal intervention.

Brizuela, B. M., & Earnest, D. (2008). Multiple notational systems and algebraic understandings: The case of the "best deal" problem. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the Early Grades (pp. 273-301). Mahwah, NJ: Lawrence Erlbaum and Associates.

Brizuela, B. M., & Schliemann, A.S. (2008). Alumnos de diez años de edad resolviendo ecuaciones lineales. Enseñar Matematica: Nivel Inicial y Primario, vol. 5, 7-24.

Carraher, D.W., Martinez, M., & Schliemann, A.D. (2008). Early algebra and mathematical generalization. ZDM – The International Journal on Mathematics Education (formerly Zentralblatt fur Didaktik der Mathematik), 40(1), 3-22.

Carraher, D. W., & Schliemann, A. D. (2007). Early Algebra and Algebraic Reasoning. In F. Lester (Ed.), Handbook of Research in Mathematics Education. Greenwich, CT: Information Age Publishing, pp. 669-705.

Carraher, D.W., Schliemann, A.D., & Schwartz, J. (2008). Early algebra is not the same as algebra early. In J. Kaput. D. Carraher, & M. Blanton (Eds.), Algebra in the Early Grades. Mahwah, NJ, Erlbaum, pp. 235-272.

Schliemann, A.D., Carraher, D.W., & Brizuela, B. (2007). Bringing Out the Algebraic Character of Arithmetic: From Children’s Ideas to Classroom Practice. Lawrence Erlbaum Associates.

Other Products: 

The project's website contains lesson plans and publications produced by the research team.