Describes three educational efforts in Kentucky that address the issue of access to mathematics for all children: (1) Learning Algebra through Technology, Investigation, and Cooperative Experiences (LATTICE) (high schools); (2) the Kentucky K-4 Mathematics Specialist Project; and (3) Partnerships for Reform in Science and Mathematics (PRISM)…

Presents a problem introducing pupils to the ideas of consecutive and integer while practicing addition. Investigates the overall pattern of results with regard to formulating some general results, considers the algebra of the problem, and suggests proofs of why some numbers can and others cannot be formulated in this way. (ASK)

The Georgia Preschool-Postsecondary Initiative was started in 1995 to bolster student achievement and classroom teacher preparation. Program success will be measured by increasing numbers of high-school students successfully completing algebra and geometry, raising postsecondary admission requirements, and having a qualified teacher in every…

The SouthEastern Regional Vision for Education (SERVE) is a coalition of educators, business leaders, governors, and policymakers seeking comprehensive and lasting improvement in education in Alabama, Florida, Georgia, Mississippi, North Carolina, and South Carolina. SERVE'S Consortium for Mathematics and Science Education provides support to…

The papers collected in this volume are intended both to present a summary 'history' and description of the International Association for the Evaluation of Educational Achievement (IEA) Second International Mathematics Study (SIMS) and to illustrate a variety of approaches to the analysis of the data that emerged from SIMS. The papers are intended…

Effects of graphic representations of algebraic functions on performance of tasks involving expression transformations were studied for 28 teachers debugging transformed expressions through syntactic manipulations (SYMs) or semantic interpretation (SEI). Those using SEI improved performance using graphs. Some positive effects of graphic feedback…

This resource book for algebra contains games, tricks, and quick activities for the classroom. Categories of activities include puzzlers, patterns, manipulatives, measurement, graphing, and a section that contains reproducible statement and value cards. Twenty one puzzle problems, four pattern activities, and 11 quick activities that engage…

Investigates whether the use of computer algebra systems could provide a significant advantage to students taking standard university entrance calculus examinations. Indicates that supercalculators would probably provide a significant advantage, particularly for lower-achieving students. Demonstrates that it is possible to write questions in which…

The author and many illustrious co-signers sent an open letter to the U.S. Department of Education protesting a report designating 10 "exemplary" or "promising" math programs. The programs over-emphasize data analysis and statistics, de-emphasize arithmetic and algebra, and advocate early calculator use, which can undermine…

Low achievement of state mathematics standards caused a rural Illinois school district to realize that repeated coverage of lower-level material blocked student progress. Subsequently, elementary teachers learned new ways to teach math, and secondary teachers replaced practical math with algebra courses. Students achieved new levels of math…

This paper presents a developmental model of students' acquisition of competence in quantitative and algebraic problem solving. A key notion underlying the developmental model is a distinction between grounded and abstract representations. Grounded representations, like story problems, are more concrete and familiar, closer to physical objects and…

Examines students' understanding of the quantitative relationships, operations, and properties of relationships and operations that are introduced in arithmetic and beginning algebra courses. Develops alternative approaches to the teaching of structure such as the structural-to-computational model and the procedural-to-structural model. Concludes…

Focuses on the implications of key findings and theoretical positions from social and cognitive developmental psychology of the use of information technology (IT) tools to support learning in algebra. Presents evidence from a small-scale study of graphics calculators in Hong Kong that supports the feasibility of the UK Cognitive Acceleration…

Two studies examined methods for arriving at cutscores in school districts, including the Angoff (W. Angoff, 1971), borderline, and contrasting groups methods and two new methods, one based on course enrollment and the other based on expert expectations. Results from a 10th grade algebra test and a test of third grade reading show the viability of…

Reports on an experiment in which Algebra I students (N=181) learned to translate word problems with two unknowns from the prose representation to symbolic representation using two variables when first solving word problems with two unknowns. Concludes that students who had learned to solve equations with the new method scored higher than those…