We share results from a one-year early algebra classroom intervention. One kindergarten, one first-grade, and one second-grade classroom participated in the intervention and three classrooms of the same grade levels served as control sites. The intervention addressed the structure of even and odd numbers, mathematical equivalence and equations,…

This research shares progressions in thinking about equations and the equal sign observed in ten students who took part in an early algebra classroom intervention across Kindergarten and first grade. We report on data from task-based interviews conducted prior to the intervention and at the conclusion of each school year that elicited students'…

This research focuses on the retention of students' algebraic understandings one year following a Grades 3-5 early algebra intervention. Participants included 1455 Grade 6 students who had participated in a cluster randomized trial. Approximately half of these students received an early algebra intervention as part of their regular instruction in…

In this paper, we analyze individual semi-clinical interviews conducted with one kindergarten and one first-grade student. We build on prior research to offer evidence, via excerpts from these interviews, that children as young as kindergarten have a powerful, intuitive sense of generality and indeed naturally draw upon it to reason through…

Mathematics educators have argued for some time that elementary school students are capable of engaging in algebraic thinking and should be provided with rich opportunities to do so. Recent initiatives like the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) have taken up this call by reiterating the place of early algebra in…

In this article, we analyze a first grade classroom episode and individual interviews with students who participated in that classroom event to provide evidence of the variety of understandings about variable and variable notation held by first grade children approximately six years of age. Our findings illustrate that given the opportunity,…

The study of functions has traditionally received the most attention at the secondary level, both in curricula and in standards documents--for example, the Common Core State Standards for Mathematics (CCSSI 2010) and "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics [NCTM] 2000). However, the…