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.)

Previous research has shown that--due to the extensive attention spent to proportional reasoning in mathematics education--many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the "illusion of linearity". For example, in…

The Center for Improved Engineering and Science Education (CIESE) at Stevens Institute of Technology helps mathematics teachers to integrate and implement engaging and innovative collaborative lessons into their curriculum for illustrating complex mathematics concepts. CIESE has developed online projects that incorporate complex mathematics…

In this article, the author discusses the combined artistry of third, fourth, and fifth graders as they illuminate a formerly dark corner of their school's entry plaza with a sparkling mosaic mural. The students worked in small groups to form the letters of the alphabet on 12" x 15" (30.5 x 38 cm) panels of cement board decorated with flat-backed…

According to the National Council of Teachers of Mathematics (2000), children need to learn how to create and use mathematical diagrams to represent and reason about phenomena in the world. The author proposes a model of diagram literacy that includes six types of knowledge required for diagrammatic competence--implicit, construction, similarity,…

The authors measure math skills with a broader set of explanatory variables than have been used in previous studies. To identify what math skills are important for student success in introductory microeconomics, they examine (1) the student's score on the mathematics portion of the ACT Assessment Test, (2) whether the student has taken calculus,…