Uses a counting book to discuss how primary-age students can begin to think about a meaning for the equals sign. Mathematical representations emerge from discussions between teacher and student. (Author/NB)

A strategy is presented for teaching arithmetic to students with mental retardation, based on subitizing, skill of recognizing number of objects in a set without actually counting, and pattern recognition. The strategy helps children understand concept of addition by representing number configurations on 5-frames and 10-frames, and reduces need…

Inservice (n=36) and preservice (n=67) mathematics teachers were asked for a commutative, nonassociative binary operation. Responses were analyzed for correctness, productiveness, mathematical content, and underlying difficulties. Both groups exhibited a weak concept by failing to produce an example and using a limited content search space.…

Relationship between stimulus type (numeric or verbal) and type of precocity (mathematical and verbal) was studied in 104 gifted young adolescents through tasks measuring working memory. The relationship between type of stimulus and type of precocity suggests underlying differences between verbally and mathematically precocious youth in memory…

Presents a situation in which differential calculus is used with inverse trigonometric tangent functions to maximize an angle measure. A negative distance measure ultimately results, requiring a reconsideration of assumptions inherent in the initial figure. (Author/MKR)

Comparison of 15 English children (mean age 7.5 years) with specific language difficulties and 12 similar children with mathematical difficulties found few differences in their ability to process 2- and 3-digit numbers. Results suggest that a language difficulty may underlie delayed performance in mathematics. (DB)

Describes four word-and-picture problems through which students can hone their math skills, all of which involve shopping for goods and calculating prices of items that they would buy. Notes that shopping creates real-life problem-solving situations. (MDM)

Specific suggestions for teaching young children (ages 5-7) mathematical principles are offered, covering such concepts as addition, subtraction, multiplication, division, arithmetical laws, and utilizing a story to teach various mathematical concepts and skills. (DB)

Describes four easy-to-construct board games and puzzles that teachers can use to strengthen their students' mathematical problem-solving skills in both the classroom and the real world. (MDM)

Discusses the role of conjectures in learning mathematics, how conjectures demonstrate mathematical power, and how conjectures build understanding and encourage connections. (ASK)

Provides an overview of the conceptual analysis of the unit fraction that provided the framework for developing a comprehensive array of fraction activities for fourth-grade students. Reveals the students' difficulties in learning the unit-fraction concept and discusses the didactical implications of these difficulties. Contains 15 references.…

Dependence on algorithms is as insidious as dependence on technology. States that many children and adults lack the facility to recognize and work with relationships in and between numbers and number operations. (ASK)

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…

Interviews with 12 adults in General Educational Development classes, four adults in basic math, and 22 preservice teachers assessed their understanding of the part-whole concept, a key element in math success. Gaps in understanding were found in all three groups. (SK)

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)