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The design of a curriculum that allows students talented in mathematics to develop their potential and explore new domains of knowledge is a high priority in many school systems. Such a curriculum should be based on the nature of mathematics itself and on the characteristics of students that are especially important in the learning of mathematics.

Vigorous debate is taking place on the relative emphasis to be given fractions and decimals. Pro and con arguments use the facts of poor performance on all state and national mathematics tests, the certain but slow introduction of the metric system in the United States, the widespread use of calculators, and the real-life uses of fractions and decimals

The book is a collection of articles, mainly research studies, edited after presentation and discussion at a seminar in Wisconsin in 1979. In an introductory chapter, Romberg states the aim: “To formulate precise models that describe children's addition and subtraction skills and how these skills change over time” (p. 4). He points to a growing consensus on the acute problems to be studied and the appropriate methodology for studying them.

The ancient Egyptian numerals used as far back as 3400 B.C. had groupings by ten but no place values. The use of these symbols will help students understand our base-ten system and the efficiency of our place-value notation. The basic rules for writing ancient Egyptian numerals (Egyptians now use Hindu-Arabic numerals, as we do) are relatively simple.

The use of manipulative materials and visual aids in teaching arithmetic is widely accepted by teachers and those concerned with the teaching of arithmetic. The Nationa Defense Education Act is an expression on the national level of a belief in the value of manipulative materials for instruction. While most modern arithmetic programs contain suggestions on the use of visual aids and manipulative materials, much remains to be done in evaluating the effectiveness of selected materials. Cost of materials varies considerably. One main concern of school systems is the cost of materials. Are inexpensive materials as effective as more expensive ones?

It is a continuing aim of mathematics instruction to develop an appreciation for and an understanding of our number system. Students come into junior high school mathematics with a correct but somewhat incomplete conception of place value, one feature of our system. They recognize that in the number 463, the 4 represents the number of hundreds, 6 the number of tens, and 3 the number of ones.

Enrichment should entail content and activities that require a high order of creative imagination; it should deepen and strengthen understanding.

With our certain, albeit slow, movement to the metric system and with the widespread use of calculators, there is general agreement that decimals wiU be introduced earlier in our elementary school mathematics curriculum. Decimals for tenths, for example, have been taught successfully in grade three. Nevertheless, there are major questions, substantial disagreements, and some sheer nonsensical statements being made about fraction concepts, fraction computation, and decimal computation.

Two major ways to view the numbers to 100 are counting by one and grouping by tens and ones.

There is still a need to teach factoring in algebra. Students must be able to factor trinomials for work on rational expressions and to solve quadratic equations. The purpose of this article is to explain a simple method of testing trinomials to see if they can be factored. The method described is designed with the average and below-average student in mind.

David Smith, a junior at Central High School, made C in algebra on his last report card; Jane Arnold made B, and Tom Jones made A. Seeing these grades, what did David, Jane, and Tom conclude about their progress in learning algebra? David said that he needs to do better on tests; Jane concluded that her homework is not too good; Tom decided that he is excelling in all phases of algebra. How accurately and how thoroughly have these students appraised their progress in mathematics? How closely did David and Jane locate their weaknesses in algebra? Was Tom right when he decided that his A meant that he is excelling in all aspects of the subject?

It is time for the formation of a National Commission on Elementary School Mathematics.