"Improving Mathematics in the Early Years and Key Stage 1" reviews the best available evidence to offer five recommendations for developing the maths skills of 3-7-year olds. Recommendations include integrating maths into different activities throughout the day -- for example, at registration and snack time -- to familiarise children…

The article identifies five incorrect beliefs about mathematics often held by students who have difficulty with mathematics. They include: the relative size of numbers is more important than the relationships between quantities; computation problems must be solved by using a step-by-step algorithm; mathematics problems have only one correct…

Thinking strategies that are related to counting are discussed and activities that are necessary for the understanding of number and counting are suggested. (Author/MP)

This method of teaching the division of fractions emphasizes the use of concrete materials and helps students understand what division of fractions means. (MP)

Describes a method of teaching the order of mathematical operations based upon the psychological theory of conceptual generalization. (MDH)

Examples from almanacs are used to provide real-life problems that involve estimating, computing, and thinking. (MP)

Points out aspects of counting books that may impede learning, notes general and specific criteria for evaluating counting books, and offers an annotated bibliography illustrating the application of criteria. (RH)

Counting books offer children the time and the tools to develop the understanding needed to solve problems. Stimulated by these books, children may use mathematic language and talk about mathematics as they get involved with materials to move and manipulate, as they use supportive aids found in illustrations, and as they interact with materials to…

Describes a research project designed to monitor the transition from work based on concrete materials to the more formalized aspect of mathematics found in secondary schools. The topic of subtraction was chosen by three teachers who were involved in the investigation. (PK)

Establishing and maintaining the desirable kind of balance between meaning and computational competence is the subject of this reprint from a 1956 issue of the journal. Sources of the dilemma and suggestions for solution are discussed. (MNS)

Discusses mathematics education research on multiplication and division which implies that instruction should emphasize development of a sound conceptual basis for multiplication and division rather than memorization of tables and rules. Presents action research ideas. (10 references) (MKR)

This essay clarifies what it means to know mathematics by examining ways of knowing multiplication and explores what those ways of knowing imply for the teaching and learning of mathematics in schools. It reviews the perennial argument about whether computational skill or conceptual understanding should guide the school curriculum. A mathematical…

Describes a finger pattern method for teaching subtraction. It is suggested that the method has several advantages over the usual methods children adopt. (PK)

Activities to develop counting skills are given. (MK)

Discusses the use of middle-school students' natural understanding of large numbers to introduce the concept of infinity. Presents activities that investigate infinite sets by demonstrating a one-to-one correspondence between the counting numbers and the given set. Examples include prime numbers, Fibonacci numbers, fractions, even and odd numbers,…