Illustrates how many key algebraic concepts can be informally developed within the number and operations strand taught in the primary grades. Discusses expressions and equations, properties and conventions, relationships between operations, and variables from this perspective. (ASK)

Presents a model of what it means to understand mathematics followed by examples of exercises designed to develop understanding in specific ways. Presumes that understanding is more likely to develop if it is the direct focus of exercises. (AIM)

Describes an episode involving conditional statements and the notion of logical equivalence that occurred in a 10th-grade college-preparatory geometry class. Illustrates some of the confusion that can arise in connection with this topic, for both students and teachers. (ASK)

Focuses on culture examined in the unique context of South Africa. Makes visible both conceptual difficulties in its formulation and also difficulties with respect to its interpretation into educational practice. Also explores a critique of ethnomathematics using the South African situation and conceptual tools of a critical mathematics education.…

Explores the relationship between learners' actions, visualizations, and the means by which these are articulated. Describes a microworld called Mathsticks which is designed to help students construct mathematical meanings by forging links between the visual and symbolic representations they develop and their actions. Presents a case study of two…

Describes an activity presented in sports fishing magazines on developing a formula that predicts the weight in pounds of a game fish given its length in inches by using a TI-83 graphing calculator. Highlights the importance of using real-life problems and mathematical explorations. (ASK)

Compares effects of two models of vocabulary instruction--an integrated graphic organizer/discussion model and a definition-only model--on the mathematical vocabulary use of fourth grade students. Finds, after two weeks of instruction, a larger number of mathematical concepts recorded by the group using the integrated model than the group using…

Interviewed 70 children learning multidigit addition and subtraction in 2 different learning environments. Found that understanding and skill were closely related for tasks in which students had received no instruction and on more difficult tasks even after instruction. The alternative instruction, which encouraged students to develop their own…

Examined effects of problem size in mental addition among elementary children in China (n=104) and Missouri (n=105) and among undergraduates in China (n=26) and Missouri (n=35). For all Missouri subjects and Chinese through first grade, larger-valued numbers took longer and induced more errors. (Author/NBI)

Presents an activity that explores the derivation of Pi. Involves students taking a constructivist role by collecting data, making conjectures, and using the data to construct graphs and tables and discourse about appropriate algebraic representations. Uses the computer as an instructional aid to enable students to view the data in a variety of…

Considers the effects of an Integrated Learning System (ILS) on the mathematics test scores of elementary school children. Results indicate that ILS software had its greatest effect on mathematics concepts scores, which is contrary to the commonly held opinion that mathematics software is effective primarily in drill and practice of computational…

Reports on part of a study that was conducted with individual students (n=5) and five groups of students who worked together in the first course of experimental calculus classes. The goal of the study was to discover how the concept of inverse function can be learned. (26 references) (DDR)

Presents an investigation, applicable for grades 3-6, that focuses on the concept of randomness and encourages children to conjecture and to conduct experiments which verify or contradict their intuitions. Involves using hands-on explorations, collecting data, and drawing conclusions on the basis of the information. (JRH)

Explains spreadsheets and presents activities that elementary school teachers can use to teach themselves and their students about spreadsheets for complex math concepts. Spreadsheet templates are then placed in electronic "posters" to create interactive activities to help students visualize and communicate mathematical concepts. (Author/LRW)

Recounts experiences of a university professor who returned to the elementary classroom and attempted to implement the National Council of Teachers of Mathematics Standards and appropriate assessment methods, including nontraditional paper-and-pencil tasks, journal-like writing assignments, focused observations, and performance-based assessments…