Discusses the problem of how the stars on the American flag would be arranged were another state added to the Union. Presents solutions using linear equations based on conditions given in the problem. (MDH)

Discusses the contributions in each chapter of the book, highlighting the textbook analyses for each arithmetic topic presented. (MDH)

Presents student comments as they explain their mathematical reasoning and thinking about place value in addition and subtraction. (ASK)

Compares two groups of preschool children to assess the effect of children's counting ability on their ability to reason about numbers. Describes the research design and the set of expected possible outcomes. Reports results in light of these predictions, concluding that counting ability is not necessary for number-relevant operations. (DSK)

Twenty-nine children with learning disabilities (LD) in grades 2 and 4 through 7 were compared with children without LD for their development of proportional structures of thought. Significantly fewer children with LD had constructed second-order logical structures necessary to act on problems using multiplicative and preproportional reasoning.…

Describes collection-development strategies for use in the identification, evaluation, and selection of numeric-data resources. Addresses three primary issues: the delineation of collecting scope and organizational role; the identification of potentially relevant data resources; and the evaluation of those resources in accordance with objective,…

Provides activities adaptable for a range of learning contexts. The activities focus on Gardner's multiple intelligences, first aid, conversational language skills, mastering ordinal numbers, and detail in writing. (Author/VWL)

Describes some basic difficulties in early algebra and their causes and presents some strategies for overcoming them. Lists five areas as being essential foundations for learning algebra: (1) seeing the operation, not just the answer; (2) understanding the equals sign; (3) understanding the properties of numbers; (4) being able to use all numbers;…

This article argues that the reason the mathematics performance of students with mild disabilities is so limited is the mathematics. Using illustrations from subtraction, the article proposes number sense be a primary goal and that within the realm of number sense, big ideas be included among the dependent variables. (Contains references.)…

This article proposes a two-factor theory of mathematics disabilities based on the premise that weak cognitive representations lead to poorer retrieval of information from long term memory. Comparison of children with math disabilities alone (MD) and those with both math and reading disabilities (MD/RD) suggests that weak phonological processing…

Tested 3- to 7-year-olds' ability to calculate with whole numbers, fractions, and mixed-numbers, in a task in which an amount was displayed, then hidden. Subjects were to determine the hidden amount resulting when numbers were added or substracted. Found that, although fraction problems were more difficult than whole-number problems, competence on…

This study compared the "Digit Naming Speed Test" (DNS) performance of 20 children with Attention-Deficit/Hyperactivity Disorder (ADHD) to 20 carefully matched peers without ADHD. Matching variables included age, grade, gender, and word reading ability. Sample construction included procedures that allowed for the identification and removal from…

This article discusses three solutions to the "Tower of Hanoi" problem offered by students in a mathematics content course for prospective elementary school teachers. The course uses standards-based pedagogy and teaching via problem solving. Within this work, we consider the growth supported by collaboration at both the students' level…

This study contributes to the debate about the Flynn effect by proposing a long-term comparison (1921-2001) of the numerical knowledge of two cohorts of three- to five-and-a-half year-old children. In 1921, Beckmann (1923) assessed the numerical development of children using four tasks (Production, Distinction, Recognition, and Naming). In 2001,…

Computer operations involving complex numbers, essential in such applications as Fourier transforms or image processing, are normally performed in a "divide-and-conquer" approach dealing separately with real and imaginary parts. A number of proposals have treated complex numbers as a single unit but all have foundered on the problem of the…