The principles of cognitive psychology as they relate to rational number learning and instruction are discussed. Issues of knowledge acquisition, organization, retrieval and transfer are reviewed as they affect this area of the elementary school curriculum. Specific problems in learning about rational numbers and systematic student errors are…

Ways of finding the sums of some interesting sequences of numbers are discussed. Finding the patterns creates a challenge, but the patterns are not too difficult for average pupils to discover. Mathematical induction can then be used to prove the formulas. (LS)

Suggests exercises to increase fluency with numbers for use primarily with children and teenagers learning English as a second language. (KM)

This is a supplementary unit to Mathematics for High School, Intermediate Mathematics, Part 1. In this publication, real numbers and rules for operating them are examined. The study begins by examining whole numbers and some of the properties of addition and multiplication of whole numbers. Most of the basic rules for algebra are developed from…

The factor-analytic history of the isolation and identification of the cognitive ability construct known as Number or Numerical Facility is described. Empirical documentation from the psychometric literature is discussed, and examples of items from a variety of tests which have defined and been associated with the Number factor are included to…

Worksheets for a short unit on magic squares, together with directions for their use and answer keys, are provided. They are suggested for use in grades seven through twelve. (SD)

Children were grouped according to ability to conserve number and then randomly assigned to training on arithmetic concepts or playing a game. The research hypothesis that there would be an interaction effect between conservation and effect of treatment was not confirmed. (SD)

The author presents two approaches she has used successfully as advance organizers for discussion of mathematical induction. These approaches provide examples which can be used in later discussion. (SD)

The author interprets several mathematical concepts as groupings using Piaget's definition. He also discusses (briefly) the implications for primary education. (SD)

This collection of jokes, riddles, and limericks is designed to be used to enliven the presentation of mathematical material by use in the classroom, on the bulletin board, or to add levity to test papers. Chapter topics include: (1) The Classics and Other Stories; (2) Jokes; (3) It Figures; (4) Quickies; (5) Riddles; and (6) In Verse. An index…

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the…

This study investigated the effect of initial instruction on the processes children use to solve basic addition and subtraction verbal problems. Prior to instruction and following a 2-month introductory unit on addition and subtraction, 43 first-grade children were individually tested on verbal problems representing different models of addition…