A mnemonic clue sentence--"He thinks mice bite trees"--is suggested for helping students with learning disabilities or mild mental retardation successfully identify up to 15 digit numbers by relating the sentence to the sequence of hundreds, thousands, millions, billions, and trillions. (DB)

Discusses convergence between instructional practices suggested by research on achievement motivation and practices promoted in mathematics-instruction reform literature by focusing on fourth- through sixth-grade students (N=624) and their teachers (N=24). Concludes that the instructional practices suggested in the literature of both research…

Examined the impact of object boundaries on 3-, 4-, and 5-year-olds' quantitative reasoning. Asked subjects to choose between alternative collections that differed in number and size of cookies and in aggregate amount. Found that children were influenced by size of individual cookies at 3 years but were generally unsuccessful in aggregating size…

Presents a case study with an at-risk second grade student on counting and numbers. Discusses counting stages that the student went through. (ASK)

Presents an activity in which students build their flexibility in using numbers and explore the connections between numbers and their representations with base-10 materials using the TI-15 calculator. (ASK)

Describes how the card game Numero helps students improve their knowledge of basic number facts while having fun. Suggests ways in which Numero can best be used in the classroom. (ASK)

This study compared 6- to 7-year-olds' knowledge of numerical fractions prior to school instruction in Croatia, Korea, and United States. Results suggested that the Korean vocabulary of fractions may influence the meaning children ascribe to numerical fractions and that this results in children being able to associated numerical fractions with…

Describes a lesson in which second grade students learn about data management, number sense, and patterns as they analyze, classify, and describe their fathers' shoes. (ASK)

Novices and experts used the same metaphors to understand and solve problems with negative numbers. Results suggest that the metaphors used by both the children and the adults are central to understanding arithmetic. (Author/MM)

This study investigated the developmental paths of Japanese Grade 1 students' understanding of quantities through the examination of their addition solution methods over the school year period. The individual students exhibited a wide range of experiences with and knowledge of addition from the beginning to the end of the school year. Students…

This note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript…

This paper reports a study designed to examine the neuronal correlates for comprehending the signs of American Sign Language representing numerals in deaf signers who acquired Japanese Sign Language as their first language. The participants were scanned by functional magnetic resonance imaging (fMRI) twice on the day of the experiment. The results…

Clinical interviews administered to third- to sixth-graders explored children's conceptualizations of rational number and of certain extensive physical quantities. We found within child consistency in reasoning about diverse aspects of rational number. Children's spontaneous acknowledgement of the existence of numbers between 0 and 1 was strongly…

We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…

The authors provide activities for overcoming some fraction misconceptions using calculators specially designed for learners in primary years. The writers advocate use of the calculator as a way to engage children in thinking about mathematics. By engaging with a calculator as part of mathematics learning, children are learning about and using the…