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…

Two samples of preschool children's representation and understanding of written number symbols was examined in two time points in one academic year. About 40% of Chinese four year olds (mean=4:7) were able to use conventional number symbols to represent the quantity of ten, on average. The majority of these children (85%) could represent written…

Although increasingly seen as critically important for pedagogy, young children's perceptions of number and of learning about number have not received much attention from researchers. This study uses a phenomenographic approach in that it seeks to map the range of possible conceptions about number and numerically-related learning amongst a group…

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…

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.)

This article describes a lesson study project that explored the impact of using storybooks to teach mathematics in three kindergarten classrooms. The study involved three kindergarten teachers and three university educators, who collaborated to plan, design, implement revise, and reflect on a unit of mathematics that focused on the concept of…

In this study, we investigated patients with focal neurodegenerative diseases to examine a formal linguistic distinction between classes of generalized quantifiers, like "some X" and "less than half of X." Our model of quantifier comprehension proposes that number knowledge is required to understand both first-order and higher-order quantifiers.…

This paper reports the results of an exploratory study of the perceptions of and approaches to mathematical proof of undergraduates enrolled in lecture-based and problem-based "transition to proof" courses. While the students in the lecture-based course demonstrated conceptions of proof that reflect those reported in the research literature as…

In math classes, teachers often focus instruction on the formulas and processes needed to solve different types of problems, but neglect to teach the concepts on which these tools are based. In this article, the author argues that before they can do this, teachers themselves need to understand "understanding math." Teaching mathematics with…

Seriation refers to the process of ordering objects along single or multiple magnitude dimensions such as length, weight, and color. The ability to order objects in terms of some attribute is essential for the child's understanding of the properties of numbers. This study investigated the effect on seriation performance of increasing both the…

Many have argued for the importance of numeracy, yet little is known about the opportunities for numeracy available to people in their daily lives. In this study, characteristics of rational numbers in magazines written for children, teenagers, and adults were analyzed and compared. Analysis indicated that difficult mathematical concepts that…

The Colorado Model Content Standards for Mathematics were designed to serve as a guide for school districts as they define standards that will enable every Colorado student to develop the mathematical literacy needed for citizenship and employment in the 21st century. A new vision is provided of the content students should study in order to…

Thirty-six studies on individualizing instruction in arithmetic are reviewed, and the general findings emerging from the combined research are discussed. (SD)

Using arrays of dots and grids many numerical concepts can be illustrated for students. (SD)