Findings on ratio and on fractions from a research project on strategies and errors in secondary mathematics are discussed, with typical errors described. Pupils seemed to learn rules without understanding. (MNS)

Properties of the harmonic number triangle are listed, and ways of generating the elements of harmonic triangles are described. (MNS)

This manipulative learning aid is featured as a tool that allows a teacher to build upon the recognition of number patterns to teach basic mathematical understanding. The activities provide a means to help children refine, develop, and extend their understanding of the number system. (MP)

The material is designed for pupil practice in: (1) associating numerals with sets of objects and finding sums of two or three numbers; (2) subtracting, one- and two-digit numbers with some regrouping; (3) mental computation using the basic operations; and (4) using combinations of basic operations with whole numbers and decimals. (MP)

Sorting activities for multiplication and division facts are suggested for developing concepts of prime factors. (MP)

Four activities and four manipulative materials for teaching place value are discussed. (MP)

A program designed in the BASIC programing language to provide drill and practice with positive and negative numbers is presented. (MP)

Calculators that have the constant arithmetic feature are promoted, and examples of ways this feature can be used in lessons are presented. (MP)

Students were encouraged to explore the concept of one million. A short pretest revealed many pupils could not easily comprehend a million. Research and practical investigations began to find "a million things." All students were reported to come through these experiences with a much better understanding. (MP)

In a three-year cumulative study, more than 1,000 children were observed either in randomly arranged preschool classrooms or in classrooms deliberately arranged to promote learning. Creativity, oral language use, and development of science and number concepts were significantly higher for children in the specially planned classrooms. (Author/SJL)

The author promotes an earlier introduction of decimals than is currently standard practice in most elementary mathematics programs. Suggested activities and related skills are reviewed. (MP)

Discussed is research which shows, in contrast to the dominant impression given by Piaget's work, that before the onset of schooling the young child possesses several kinds of fundamental "intuitions" concerning numbers. (Author/TG)

Three teaching ideas are discussed: the improvement of ditto reproduction, and exploration of congruent triangles, and an intuitive introduction to the concept of limit. (MP)

Two posters that can be used to provide experience in recognizing patterns in sequences of numbers are provided. Suggested number sequences for different grade levels are given. (MK)

Concludes that, of several reading readiness factors, knowledge of alphabet letter names is the best predictor of phonics skills other than vowel recognition and of reading abilities involving words in insolation, and that number knowledge is the best predictor of reading abilities involving words and syntax. (FL)