Results of this study involving 120 kindergarten and first-grade boys and girls suggest that some understanding of the invariance of number appears to emerge earlier than the ability to pass the standard verbal test. (BH)

Two experiments were conducted to examine the input-order effect reported by Birnbaum (1975); he demonstrated that free recall of two-digit numbers presented in natural ascending order is superior to free recall of the same numbers presented in random order. (Author/RK)

This study investigates the use of infinities and limits during the first 12 years of schooling while a secondary study presents ideas and comments on the observations that were made during the primary study. (MVL)

Reviews and analyzes the number-line metaphor in textbooks. Presents examples to show a way to produce an internal critique of mathematical textbooks, a critique that targets the practices in which the notions are involved within the text. Presents the number-line metaphor as the horizon and the tiller of all the enlargements of the notion of…

Presents some known and lesser-known features of the number 11. (KHR)

Uses cryptography to demonstrate the importance of algebra and the use of technology as an effective real application of mathematics. Explains simple encoding and decoding of messages for student learning of modular arithmetic. This elementary encounter with cryptography along with its historical and modern background serves to motivate student…

Characterizes those numbers that are the sum of consecutive natural numbers and counts how many such representations a given number has. (Author/NB)

Employs statistical tools to determine whether the digits of Pi are pseudorandom. Discusses the difficulties in answering this question. (Author/NB)

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)