| Beliefs about mathematics have been widely researched by mathematics educators, but few studies have been conducted among young children in reform mathematics classrooms, understood here as classrooms in which the curriculum is aligned with the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards (1989). This study investigates young children's beliefs about arithmetic and algebra, and their beliefs about the differences between them, among students who are taught a reform mathematics curriculum ("Investigations") plus a reform-minded algebra-arithmetic intervention ("TERC-Tufts Early Algebra Project"). The following questions were addressed: What are young children's beliefs about arithmetic and algebra, among students who are taught a reform mathematics curriculum plus a reform-minded algebra-arithmetic intervention? Can children who are exposed to algebra understand how algebra differs from arithmetic? Can these children choose appropriate tools to solve both kinds of problems? A semi-structured interview protocol was developed and a total of 39 third and fourth grade students were interviewed individually. Quantitative and qualitative analyses revealed that: first, children who are exposed to reform mathematics curricula are developing a set of beliefs that are different from those held by children in non-reform mathematics classrooms as documented in the literature; second, children who are exposed to algebra in elementary school are beginning to capture the essence of both arithmetic and algebra and are aware of some of the differences between these two fields of mathematics; and third, children who are exposed to algebra in elementary school can correctly represent arithmetic and algebraic problems, and do so by successfully applying representational tools that are specific to each area. These results and their implications are discussed, in relation to issues of curriculum, instruction, and educational policy. |
