This textbook is designed to teach the principles of Arithmetical Science as far as they are involved in the elementary processes, and to secure a reasonable degree of accuracy and rapidity in expressing numbers and computing results. This work presents at first the idea of numbers connected with visual representations of objects; afterward, when…

The purpose of this study was to ascertain whether children in grade 3 who differ in cognitive processing capacity add and subtract differently. The researchers drew upon information from three sources: individual results from a battery of 14 tests, an objective-referenced achievement test measuring a variety of arithmetic skills related to…

Presented are twenty essays related to applications in school mathematics and aimed at the classroom teacher. The essays use numerous examples and illustrations that provide the teacher with something tangible for immediate use. Four thematic areas are addressed: (1) What are applications?; (2) Why include applications in school mathematics?; (3)…

An activity for secondary schools is presented and discussed which may be explored with a programmable calculator. The activity is non-standard and could not be easily explored without the use of a programmable calculator. Related activities are also discussed. Flow charts and programs for different programmable calculators are presented. (MP)

Progress that has been made in teaching estimation is reviewed. The paper shows that although little has been done in research and development, there is a great deal of interest in developing estimation as a primary skill in school mathematics. It suggests that it is feasible to design instruction sequences in computation, measurement, and problem…

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 focuses on the mental processes used during estimation. This research: (1) developed an operational definition of estimation; (2) created an instrument to identify exceptionally good estimators; (3) collected performance level data on 1187 subjects; (4) constructed interview problems and developed protocols to identify the thinking…

Refinements of work with calculator algorithms previously conducted by the author are reported. Work with "chaining" and the doing/undoing property in addition and subtraction was tested with 24 third-grade students. Results indicated the need for further instruction with both ideas. Students were able to manipulate the calculator keyboard, but…

This booklet contains a brief introduction to the use of the metric system. Topics covered include: (1) what is the metric system; (2) how to think metric; (3) some advantages of the metric system; (4) basics of the metric system; (5) how to measure length, area, volume, mass and temperature the metric way; (6) some simple calculations using…

THE READABILITY OF ANY BOOK IS DETERMINED BY WORDS AND SENTENCES WHICH ARE USED AND WHICH VARY IN DIFFICULTY FROM EASY TO HARD. PRESENTED HERE IS A PROCEDURE BY WHICH TEACHERS CAN DETERMINE THE READABILITY INDEX OF ANY BOOK AND TRANSLATE THE INDEX TO GRADE LEVELS. THE METHODS EMPLOYED IN THE DEVELOPMENT OF READABILITY FORMULAS AND WORD LISTS ARE…

This report presents the results of a teaching experiment which investigated (1) the role of mathematical experiences on the development of counting, addition, subtraction, mental arithmetic, classification, and other arithmetical topics and (2) the role of quantitative comparisons and class inclusion as readiness variables for learning the…

The purpose of this study was to compare the effects of a fourth-grade arithmetic sequence based on calculator flow-charting with those of traditional textbook instruction. Both achievement and attitude were compared. Students were matched on the basis of intelligence (Otis Quick-Scoring Mental Ability Beta Test Form EM) and sex, and then randomly…

Designed for the student who has acquired basic computational skills with non-negative rational numbers, this guidebook delineates minimum course content to further develop students' computational skills with whole numbers. Place value and estimation are also covered. General goals, performance objectives, a course outline, suggested teaching…

A teacher describes a banking unit used in a sixth-grade mathematics class. Students learned the value of money by receiving a pretend paycheck for their chosen occupation and paying weekly, monthly, and annual bills. (MP)