The Development of Children's Algebraic Thinking: The Impact of a Comprehensive Early Algebra Intervention in Third Grade

Abstract

This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to a written pre- and post-assessment that addressed their understanding of several big ideas in the area of early algebra, including mathematical equivalence and equations, generalizing arithmetic, and functional thinking. We found that the intervention group significantly outperformed the nonintervention group and was more apt by posttest to use algebraic strategies to solve problems. Given the multitude of studies among adolescents documenting students' difficulties with algebra and the serious consequences of these difficulties, an important contribution of this research is the finding that—provided the appropriate instruction—children are capable of engaging successfully with a broad and diverse set of big algebraic ideas.

Build an early foundation for algebra success

“…In our current work -Project LEAP (http:// algebra.wceruw.org) -we are addressing the aforementioned question and specifically whether children who experience comprehensive and sustained early algebra in grades 3-5 are better prepared for algebra in secondary school than children who have a traditional arithmetic-based experience in grades 3-5. To date, our findings indicate that elementary school children are capable of learning foundational algebraic concepts and skills and that a comprehensive and sustained early algebra experience significantly affects their algebra understanding (Blanton et al, 2015). For example, students in the early algebra classrooms demonstrated the ability to:…”

Second graders articulating ideas about linear functional relationships

“…Recent research challenges so-called limitations in children's capacities to work with algebraic topics (Brizuela & Martinez, 2012;Cai & Knuth, 2011;Molina & Ambrose, 2008). As summarized elsewhere (e.g., Blanton, Stephens, Knuth, Gardiner, Isler, & Kim, 2015), these capacities concern children's ability to develop relational thinking; use different representations to express generalizations; represent verbal statements as algebraic equations; and reason about and represent relationships between abstract quantities of physical measures.…”

An Analysis of Algebraic Thinking by Third Graders

“…The national elementary mathematics curriculum in Korea does not emphasize directly essential elements of algebraic thinking but indicates indirectly some of them. This study compared our students' performance related to algebraic thinking with results of Blanton et al (2015) which reported considerable progress of algebraic thinking by emphasizing it through a regular curriculum. The results of this study showed that Korean students solved many items correctly as compatible to Blanton et al (2015).…”

“…This study compared our students' performance related to algebraic thinking with results of Blanton et al (2015) which reported considerable progress of algebraic thinking by emphasizing it through a regular curriculum. The results of this study showed that Korean students solved many items correctly as compatible to Blanton et al (2015). However, our students tended to use 'computational' strategies rather than 'structural' ones in the process of solving items related to equation.…”