Developing a Comprehensive Approach to Early Algebra

• In Event: 43.064 - Exploring Diversity and Synergy Across Research Programs Within Early Algebra

Abstract

Over the course of the past decade, our research team has sought to address the fundamental (yet, largely untested) assumption of early algebra education, that elementary school students who experience early algebra are better prepared for algebra in secondary school than students who experience a more traditional arithmetic curriculum. Briefly, our research efforts, to date, have included the development and "proof of concept" testing of a Grades 3-5 early algebra learning progression (EALP); the implementation of a small scale, quasi-experimental, longitudinal study of an EALP-based intervention in researcher-led elementary classrooms; and a large scale, randomized control, longitudinal study of the EALP-based intervention in teacher-led elementary classrooms. More recently, our research is seeking to extend our Grades 3-5 EALP to Grades K-2, including an emphasis on supporting the early algebra learning of diverse student populations (e.g., culturally and linguistically diverse students, struggling learners), and identifying instructional practices that are associated with students' early algebra learning.

Objectives: The presentation will highlight some of the challenges involved in developing and implementing a comprehensive approach to early algebra. In particular, challenges discussed will include those related to (i) developing an early algebra intervention that can be relatively seamlessly integrated into elementary school mathematics curricula, (ii) developing an early algebra intervention that is responsive to diverse student populations as well as to students’ prior school experiences, and (iii) implementing the intervention with fidelity (including aspects of measuring fidelity).

Perspective: Our EALP-based intervention was informed by an early algebra framework that consisted of a set of core algebraic concepts (e.g., mathematical equivalence) and practices (e.g., generalizing mathematical relationships), and was designed to be curricula independent. In particular, Kaput’s (2008) content analysis of algebra guided the development of the early algebra framework, and learning progressions research (e.g., Clements & Sarama, 2004; Shin, Stevens, Short, & Krajcik, 2009) guided the development of the EALP.

Data Sources: Data sources include two sets of longitudinal student assessment data (from the aforementioned quasi-experimental and randomized control studies) and fidelity of implementation data (observational data from a subset of teachers in the randomized control study).

Results: Overall, student assessment results from both studies showed statistically significant performance differences between students who experienced the EALP-based intervention and students who experienced a more traditional arithmetic curriculum. In addition, performance differences were greater among students in the researcher-led intervention compared to students in the teacher-led intervention. There was a range of implementation fidelity, with students in higher fidelity classrooms generally outperforming students in lower fidelity classrooms. Moreover, particular aspects of teachers’ instructional practices were found to be positively correlated with students’ early algebra learning.

Significance: Mathematics education scholars and reform initiatives alike continue to advocate for the integration of early algebra into elementary school mathematics as well as for the professional development of teachers aimed at the development of effective early algebra instructional practices. Thus, it is critical to better understand the challenges associated with the development and implementation of a comprehensive approach to early algebra.

Authors

• Eric J. Knuth, The University of Texas at Austin

• Ana C. Stephens, University of Wisconsin - Madison

• Maria Blanton, TERC

• Angela Gardiner, Tahoe Environmental Research Center

• Despina A. Stylianou, City College of New York - CUNY

• Rena Stroud, Merrimack College