Describes a study that explores secondary school students' conceptions of division by zero. Examines whether students identify expressions involving division by zero as undefined or tend to assign them numerical values. Studies students' justifications and analyzes the effects of age and level of achievement in mathematics on students' responses…

Pupils progress through a relatively small number of key stages called growth points in numeracy learning. Identifies growth points in developing numeracy and suggests that better support can be offered to children when teachers are aware of the growth points. (ASK)

Offers a matrix to assist mathematics-curriculum planners and teachers around the world in developing multicultural learning materials. Contains 22 references. (ASK)

Investigates possibilities for and manifestations of collaborative work with pairs of kindergarten students as they worked on tasks designed to promote early number development. Students generated four strategies, and three themes emerged from the analysis of the cooperative solutions. Contains 34 references. (Author/ASK)

Illustrates how the genesis and development of complex numbers can be explained by and supports a fallibilist model of trials and tests. Discusses the educational implications of this quasi-experimental approach. Contains 33 references. (DDR)

Uses an activity to assess students' understanding and use of the vocabulary of 'difference between' with four middle-ability children from years 1, 3, and 5. (Contains 14 references.) (ASK)

Shares experiences with using "The Wall", a number patterns spreadsheet idea developed by Dave Shiers, with children in a middle school. (ASK)

Used shift-rate recovery method in three experiments to examine extent to which 6-month-olds find perceptual cues such as density and length useful in discrimination of linearly arranged sets of large numbers of objects. Found that infants can discriminate between large number sets by relying on absolute cues such as density and on relative cues…

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…