This longitudinal study examined how language ability relates to mathematical development in a linguistically and ethnically diverse sample of children from 6 to 9 years of age. Study participants were 75 native English speakers and 92 language minority learners followed from first to fourth grades. Autoregression in a structural equation modeling…

Background: Exposure to mathematical pattern tasks is often deemed important for developing children's algebraic thinking skills. Yet, there is a dearth of evidence on the cognitive underpinnings of pattern tasks and how early competencies on these tasks are related to later development. Aims: We examined the domain-specific and domain-general…

This study examined if solving arithmetic problems hinders undergraduates' accuracy on algebra problems. The hypothesis was that solving arithmetic problems would hinder accuracy because it activates an operational view of equations, even in educated adults who have years of experience with algebra. In three experiments, undergraduates (N = 184)…

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…

Proposed is a gradual transition from arithmetic to the idea of an equation with variables in the elementary grades. Vertical and horizontal formats of open sentences, the instructional sequence, vocabulary, and levels of understanding are discussed in this article. (KR)

Investigated the upper limits of (n=22) seventh-grade students' informal processes in solving first degree equations in one unknown prior to instruction. Results indicated the existence of a cognitive gap between arithmetic and algebra characterized as the students' inability to operate spontaneously with or on the unknown. (37 references)…

This is volume 6 of the series of translations of books from the Soviet literature on research in the psychology of mathematics instruction and on teaching methods influenced by the research. This book contains both a theoretical examination of the connection between instruction and the development of children, and experimental data on a definite…

This proceedings from the annual conference of the North American Chapter of the International Group for the Psychology of Mathematics Education includes the following topics and authors: area measurement (C. B. Beattys, C. A. Maher); error patterns (H. C. Bebout); formative evaluation (J. C. Bergeron, N. Herscovics, N. Nantais); interactive…

This study was an initial effort at Brenau College (Georgia) to analyze the relative effectiveness of a self-paced math lab approach to developmental pre-college algebra. Students enrolled in 1988-89 were taught under the lecture method; this applied to students needing both developmental arithmetic and developmental algebra. During the subsequent…

The Proceedings of PME-XVI has been published in three volumes because of the large number of papers presented at the conference. Volume 1 contains: (1) brief reports from each of the 11 standing Working Groups on their respective roles in organizing PME-XVI; (2) brief reports from 6 Discussion Groups; and (3) 35 research reports covering authors…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…