Describes three labs designed to help students in a first course on ordinary differential equations with three of the most common numerical difficulties they might encounter when solving initial value problems with a numerical software package. The goal of these labs is to help students advance to independent work on common numerical anomalies.…

Two experiments examined the development of children's understanding of part-whole relations. Found that five- and six-year olds evidenced understanding of part-whole relations, but four-year olds did not. Results support the conclusion that an understanding of the relationship between a superordinate set and the basic-level sets that comprise it…

Discusses how experiments can offer students different points of view on the mathematical concepts presented in class and bring these concepts to life. Presents an experiment that demonstrates the interaction between mathematics and fluid dynamics. (Author/ASK)

A study found that among second-grade children with mathematics difficulties (n=49), children with both mathematics and reading difficulties were distinct from children with only mathematics difficulties, with the former being characterized by pervasive deficiencies in mathematical thinking and the latter by more specific deficits in problem…

Two studies of adolescents in England and Russia examined the effects of prolonged instruction on students' development of abstract deductive reasoning and understanding of logical necessity in algebraic and verbal reasoning. Results indicated that prolonged instruction emphasizing the metalevel of algebraic deduction contributed to enhanced…

Two experiments examined development of the ordinality concept in infants. Found that 11-month-olds successfully discriminated, whereas 9-month-olds failed to discriminate sequences that descended in numerical value from sequences increasing in numerical value. Nine-month-olds could discriminate the ordinal direction of sequences that varied in…

Examines one preschooler's conversation with author to determine what concepts educators consider "difficult" for this age group. Finds that concepts such as "infinity" and "negative numbers," typically avoided by primary educators, were brought into view in the task-based conversations. Argues that individual…

This paper describes a proportional reasoning problem set within a real-life context and a complete analysis of one small group discussion of this problem over the course of a 90-minute block. The seventh-grade students' discourse is described to provide insights into typical mathematical interpretations of this problem, as well as some…

The current research explored children's ability to recognize and explain different concepts both with and without reference to physical objects so as to provide insight into the development of children's addition and subtraction understanding. In Study 1, 72 7- to 9-year-olds judged and explained a puppet's activities involving three conceptual…

The National Research Center for Career and Technical Education at the University of Minnesota (NRCCTE) is continuing the national Math-in-CTE project into the 2004-05 school year. The Center is experimentally testing the idea that high school students who participate in a math-enhanced CTE curriculum will develop a deeper and more sustained…

The concepts of ratio and proportion are among the most important topics in school mathematics, especially at the middle school level. However, studies have repeatedly shown that most middle school students have difficulties with these concepts (National Council of Teachers of Mathematics 2000). This article includes ideas and examples used by…

This article, which originally appeared in the May 1998 issue of "Mathematics Teaching in the Middle School," explores the runway numbering system. The activity described in this paper furnishes an excellent setting for discussing rounding rules and, in particular, what to do if the digit to the right of the place to be rounded is equal to five. A…

This article describes a mathematical communication game that was used by the author to facilitate middle school students' understanding of algebraic expressions. (Contains 1 table and 2 figures.)

This article from the NCTM's 2003 Yearbook Learning and Teaching Measurement discusses various literary works containing measurement topics. (Contains 1 figure and 26 resources.)

This article describes the authors' experiences using clock arithmetic to help students understand key structural properties in algebra, such as identities and inverses. (Contains 10 figures.)