"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…

This third edition of the best-selling "Mathematics in Nursery Education" provides an accessible introduction to the teaching of mathematics in the early years. Covering all areas of mathematics learning--number and counting, calculation, pattern, shape, measures and data handling--it summarises the research findings and underlying key concepts…

The principle of the permanence of the rules of calculation is contrasted with the concretization permanence principle. Both apply to situations where some arithmetical operation known to children for numbers of a certain kind is to be extended to include further numbers. (MNS)

Describes various aids and activities to help in planning lessons that will encourage the development of sound place value knowledge. Also discusses various instructional strategies to help students avoid problems which may lead to an incomplete or faulty understanding of place value. (JN)

Two ideas to use as a bulletin board display as an activity center, or as worksheets emphasizing whole number concepts are described. (JT)

The concepts of number sense and numeration, operations, and whole-number computations and their importance are discussed. Activities cover developing concepts of operations, exploring patterns and relationships, and building an understanding of mathematical structure. (KR)

Provides methods of teaching negative number operations, including addition, subtraction, and multiplication. Presents examples and activities for the operations. (YP)

Argues that the type of calculator that is used in mathematics instruction is very important. Suggests that four-function calculators fail to give correct values of mathematical expressions far more often than do scientific calculators. (PK)

Argues that number concepts are not single-faceted ideas that children either have or do not have. Suggests that number concepts can be broadened by helping children develop a collection of relations. Examples of classroom activities are included. (PK)

"Chisanbop" is a Korean word which means finger calculation method. It is based on the Korean abacus, and its emphasis is on fives. By using Chisanbop techniques, one can add, subtract, multiply, and divide large numbers. Chisanbop can be taught most effectively to large groups in the second grade. (JN)

Discusses a number series made from the multiplication of numbers to digits. Presents a number series for diverse multiplication numbers. (YP)

Noitcarf numbers provide a simulation activity that allows teachers or education students to gain an understanding of the feelings of students who are taught mathematics by a "rules" method. They are actually an abstract presentation of operations with fractions. (MK)

Discusses mental computation and how and when it should be taught. Describes seven properties of mental algorithms. (YP)

Describes examples of rational representation as a guide for translating terminology and information encountered in manuals for computers. Discusses four limitations of the representation. (YP)

Discusses arithmetic during long-multiplications and long-division. Provides examples in decimal reciprocals for the numbers 1 through 20; connection with divisibility tests; repeating patterns; and a common fallacy on repeating decimals. (YP)