The author wonders if the headlines over stories about international comparisons of student achievement are projections of how the participating nations feel about their schools. In this article Gerald Bracey offers examples of headlines and offers his opinions on how they represent specific nations. (Contains 1 note.)

This study had two aims. The first was to test the postulate of analogical equivalents in number processing using a stimulus set based on the differences between pairs of numbers, and second, to look for IQ-dependent differences in this processing. Participants were asked to make judgments concerning the differences between pairs of numbers--each…

The mathematical depth that is potentially present, even in simple problems is illustrated. An extended analysis of a problem that is an analysis from a mature mathematical perspective with careful attention paid to mathematical reasoning and to using good mathematical habits of mind is used.

Six curriculum-based measures of math performance were developed for use with 4-year old preschool children. Measures included counting objects, selecting numbers, naming numbers, selecting shapes, counting, and visual discrimination. Technical properties of probe scores were assessed in two rural public preschool programs. Alternate forms,…

This article focuses on how young children build math skills in everyday play and activities. Children focus on six categories of mathematical content including classifying, exploring magnitude, enumerating, investigating dynamics, studying patterns, and exploring spatial relations. The article gives advice to both teachers and parents on how they…

This article describes the Adaptive Control of Thought-Rational (ACT-R) cognitive architecture (Anderson et al., 2004; Anderson & Lebiere, 1998) and its detailed application to the learning of algebraic symbol manipulation. The theory is applied to modeling the data from a study by Qin, Anderson, Silk, Stenger, & Carter (2004) in which children…

The open-ended assessment item supports students in achieving mathematical understanding that the National Council of Teachers of Mathematics (NCTM) advocates. The items encourage students to demonstrate their understanding in creative and informative ways.

Students in the classroom should be provided with engaging activities for improving their computational fluency, making effective use of time, and as a medium of self-motivation. Games such as Contig, the 24 Game, and Number Jumbler are useful for practicing basic facts and computational fluency of mathematics.

This longitudinal study assessed the emergence of gender differences in over 300 children's academic competency beliefs from kindergarten or first grade through fifth grade. Children, their parents and their teachers rated the children's competencies in math and literacy and their math and literacy skills were also assessed directly. Beginning in…

A growing shortage of technical and science graduates means that the question of determinants of differences in performance and choices in that field based, among other things, on social background characteristics (gender, socioeconomic status, ethnic origin, family composition) remains a topical one. In this study, a rational choice model is…

Recent publications in Australia focus on "number sense" as an important component of mathematics instruction. The current study attempted to tap into local expert knowledge in the area of early mathematics in an effort to establish a consensus on which skills reflect the number sense typically acquired by school entry. A modified Delphi…

In this study, we use children's prior knowledge to support their development of cardinality understanding, based on Bermejo's (1996) model of cardinality understanding and on the distinction between cardinality (the number of items in a set is represented by a number-word) and the cardinality principle (the last number-word used in counting…

Answers to mathematical problems come in all forms and most come with a variety of questions. Students often forget to ask questions once they have found an answer. This paper suggests that students would always benefit by questioning answers.

In this article, the author relates how she designed a math activity she called Beads to use in conjunction with their school's 100th day celebration. Beads has provided her kindergarten class with many opportunities to practice a variety of math skills - counting, patterning, sorting, comparing, making sets, predicting, identifying numerals,…

In this paper we describe an ontological and semiotic model for mathematical knowledge, using elementary combinatorics as an example. We then apply this model to analyze the solving process of some combinatorial problems by students with high mathematical training, and show its utility in providing a semiotic explanation for the difficulty of…