Examines the differences in preservice elementary school teachers' perceptions between divisibility by two, or evenness, and divisibility by another number. Concludes that the equivalence of the number properties of being even and being divisible by two is not taken for granted; rather, the parity is often perceived as a function of the last digit…

Compares sixth-grade American students to three samples of (Chinese, Japanese, and Taiwanese) sixth-grade Asian students to determine if the well-documented mathematical achievement of students from these Asian nations might be due in part to a greater understanding of mathematical representations. Indicates that all Asian samples scored…

Describes how the use of an area model manipulative can help students learn fractions and related concepts. Uses several illustrated examples. (MM)

Describes a lesson that connects geography and mathematics in which students develop an understanding of large numbers. Students listen to a story about the number one million, cut and paste faces on tagboard to estimate one million, and use blocks to represent the population of each state in the United States. (CMK)

The reliability and, to a lesser extent, the validity of the newly created Number Sense Test was evaluated with a group of 40 3- to 5-year-old children attending Head Start. Six number sense skills (e.g., counting, number identification, addition-subtraction) and children's feelings about school were assessed both before and after instruction…

Teachers who have Spanish-speaking students in their science class, will likely be interested in learning about the recent releases of Spanish trade books for children. From appealing paperback series about colors, opposites, shapes, and numbers to smooth Spanish renditions of Isaac Asimov's engaging overview of the universe, these books are just…

An analysis of the 1990 National Assessment of Educational Progress (NAEP) found that only 46 percent of all high school seniors demonstrated success with a grasp of decimals, percentages, fractions and simple algebra. This article investigates error patterns that emerge as students attempt to answer questions involving the ability to apply…

Triangular numbers are used to unravel a new sequence of natural numbers here-to-fore not appearing on the Encyclopedia of Integer Sequences website. Insight is provided on the construction of the sequence using "buildings" as a viewable model of the sequence entries. A step-by-step analysis of the sequence pattern reveals a method for generating…

This article focuses on the kinds of conceptual changes that occur when students have to deal with negative numbers in elementary algebraic operations. Interviews were carried out with twelve 8th-grade level students who were selected on the basis of their results in a test where they were required to reduce polynomials. The questions applied to…

Mathematics lecturers have long expressed concern about their students poor mathematical background and the effect this has on performance in first mathematics courses at university level. This article explores a similar concern about students' numeracy in a statistics course for psychologists.

Early childhood is a time of discovery when learning occurs at every turn. The task that early childhood teachers face is how to teach a class full of students who fall at each end of the learning spectrum (and every place in between). This article describes an easy and effective way to address widely diverse needs among young learners--to empower…

Recognizing that students shudder at revision and see it as a perfunctory task to satisfy only their teachers, the author offers an approach that motivates students to revise thoughtfully without increasing teachers' reading workload. Quite simply, good writing requires less time to read than poor writing. The Numbers Approach to grading can free…

Leaders in professional development have called for more learner-centered professional development opportunities for teachers. These approaches allow teachers to have some choice about the content and pedagogies on which they focus during professional development courses. This paper shares case studies of three participants from InterMath, a …

Charlotte, the author's 11-year-old daughter, was born with Down syndrome, and is currently attending the local middle school. In terms of her disability Charlotte is developing very well and has a reading age of 9+, however her maths skills age is approximately 4 years. It is not necessarily the case that if a child has good language and literacy…

In this article, the author presents a new maths aid for teaching place value, addition and subtraction up to 1 million. The need for a resource to help his wife understand place value motivated the author to create "Counting Cards". Here, he shares his invention, in the hope that it will help others. (Contains 4 figures.)