The nature of the development of arithmetic performance has long been intensively studied, and available scientific evidence can be evaluated and synthesized in light of Nelson and Narens' model of metacognition. According to the Nelson-Narens model, human cognition can be split into two or more interrelated levels. Obviously, in the case of more…

Examines arithmetic and algebra knowledge from a cognitive perspective in an effort to determine what constitutes a pre-algebraic level of understanding. Presents results of a longitudinal study designed to investigate students' readiness for algebra. Proposes a model for the transition from arithmetic to pre-algebra to algebra. Contains 29…

This study showed that Oksapmin children not only spontaneously use the indigenous numerical system of their nontechnical culture but also have created new forms of numerical symbolization and calculation to deal with schooling arithmetic problems. Novel conceptual developments, factors mediating the schools effect, and the influence of prior…

A longitudinal study of students' developing understanding of decimal notation has been conducted by testing over 3000 students in Grades 4 to 10 up to 7 times. A pencil-and-paper test based on a carefully designed set of decimal comparison items enabled students' responses to be classified into 11 codes and tracked over time. The paper reports on…

This study investigated a theoretical structure which attempts to explain the problem-solving strategies used by first-grade students who are successful in solving simple arithmetic story problems. The structure used describes the problem-solving procedure as consisting of a three-stage model building process: (1) comprehending the story, (2)…

Learning activities and questioning skills that teachers in Tasmania can use to determine a child's mathematics understanding are presented. Covered topics include division, multiplication, subtraction, addition, sorting and classification, one-to-one correspondence, patterns, ordering, and counting. Included for each topic are the aim, needed…

Background: Arithmetical skills are essential to the effective exercise of citizenship in a numerate society. How these skills are acquired, or fail to be acquired, is of great importance not only to individual children but to the organisation of formal education and its role in society. Method: The evidence on the normal and abnormal…