Dicusses teachers' beliefs and perceptions of children's knowledge and learning about place value, addition, subtraction, multiplication, and division and how to teach those subjects. (ASK)

"Number sense" is "an intuition about numbers that is drawn from all varied meanings of number" (NCTM, 1989, p. 39). Students with number sense understand that numbers are representative of objects, magnitudes, relationships, and other attributes; that numbers can be operated on, compared, and used for communication. It is fundamental knowledge…

Preschool children are often good at counting things but seem slow to learn that there is more to counting than simply finding out how many are in a single set. Counting is useful when comparing sets and when creating new sets to match existing ones. This is part of the numerical understanding that educators wish to foster in schools. In two…

During the twentieth century, major changes occurred in conception of arithmetic as a school subject. These changes resulted from both the study of arithmetic itself and from influences from movements and developments outside the subject matter; and they have affected both the content of arithmetic and the methodology of presenting that content to…

"Transition Mathematics" aims to increase 7th- through 12th-grade students' skills in applied arithmetic, pre-algebra, and pre-geometry. This one-year curriculum also addresses general application to different wordings of problems, types of numbers, and contexts for problems and aims to promote mathematical reading skills. The curriculum…

Multiplication, division and fractions are "hotspots" for students in the middle years with many students experiencing difficulty with these concepts. Arrays effectively model multiplication and help children develop multiplicative thinking and learn multiplication facts. In this article the authors show how an open-ended array problem…

There are numerous teaching suggestions to offer in guiding pupils to greater achievement in mathematics. This paper suggests that the instructor should begin where the pupil is presently and observe what interests the pupil in learning. Different methods for teaching mathematics such as using blocks, beads, films, filmstrips or slides, a…

This book is for boys and girls who know the numbers from one to thirty thoroughly, who can count to one thousand, who know something of the multiplication tables of two, three, four, five, six, ten, and twelve, and who understand the simplest facts about fractions. This book is both to be read and to be studied. It calls for oral recitation and…

THE 4TH YEAR SHOULD CONTINUE THE SEQUENTIAL PRESENTATION MATHEMATICAL UNDERSTANDINGS AND RELATIONSHIPS. NEW LEARNINGS SHOULD BE PRESENTED CONCRETELY IN SOCIAL SETTINGS WITHIN THE CHILDREN'S FRAMEWORK OF UNDERSTANDING. GRAPHIC MATERIALS MAY BE USED TO BRIDGE THE UNDERSTANDINGS FROM THE CONCRETE TO THE ABSTRACT LEVEL. THE NUMBER SYSTEM UNIT SHOULD…

These syllabuses for K-6 were written, evaluated, and revised by a team of writers from the Orange County Science Education Improvement Project (OCSEIP). OCSEIP is a cooperative enterprise undertaken by the University of California (Irvine), California State College at Fullerton, the Orange County Schools Office, and local districts throughout…

As part of continuing research aimed at identifying optimal methods for training Navy personnel who have achieved marginal scores on military selection tests, flash card instruction methods were adapted for application to a comprehensive range of basic mathematical operations involved in a previously developed course in fundamental mathematics.…

The effects of the combined use of a nonsimulation game and student teams in mathematics on student achievement were investigated. Ninety-six seventh grade students in two low- and two average-ability mathematics classes participated in the study. One low- and one average-ability class played the nonsimulation game Equations twice a week for nine…