We introduce the concept of the "sequence of the ratios of convex quadrilaterals," identify some properties of these sequences and use them to provide new characterizations for some classic quadrilateral families. The research involves aspects of geometry, arithmetic and mathematical analysis, which converge to produce the results.

Although the complexity of children's number learning is recognized, trade books about number have been treated as a simple, undifferentiated set. This analysis of 186 children's books, however, categorized a distinct subset of books about number as "counting books." These counting books were complex with regard to portrayal of counting…

This study examined the effects of two teaching treatments [multiple-representation instruction (MR) and traditional algorithmic instruction (TA)] on students' performance on mathematics problems that integrated fractions, decimals, and percent. Using a 2 × 2 crossover design, the effect of the teaching treatments and their sequences on student…

In this article, we obtain a genetic decomposition of students' progress in developing an understanding of the decimal 0.9 and its relation to 1. The genetic decomposition appears to be valid for a high percentage of the study participants and suggests the possibility of a new stage in APOS Theory that would be the first substantial change in…

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional…

Efforts to meet the needs of children's learning in arithmetic has led to an increased emphasis on the teaching of mental calculation strategies in England. This has included the adoption of didactical tools such as the empty number line (ENL) that was developed as part of the realistic mathematics movement in the Netherlands. It has been claimed…

FIFTH GRADE WORK SHOULD CONTINUE THE SEQUENTIAL DEVELOPMENT OF MATHEMATICAL UNDERSTANDINGS AND COMPUTATIONAL SKILLS. THE PROBLEMS APPROACH SHOULD BE USED SO CHILDREN MAY DISCOVER MATHEMATICAL TRUTHS AND ARRIVE AT GENERALIZATIONS. THE NUMBER SYSTEM UNIT SHOULD EMPHASIZE THE ABILITY TO READ AND WRITE NUMERALS TO SIX PLACES AND THE ABILITY TO READ…

THE 4TH YEAR SHOULD CONTINUE THE SEQUENTIAL PRESENTATION MATHEMATICAL UNDERSTANDINGS AND RELATIONSHIPS. NEW LEARNINGS SHOULD BE PRESENTED CONCRETELY IN SOCIAL SETTINGS WITHIN THE CHILDREN'S FRAMEWORK OF UNDERSTANDING. GRAPHIC MATERIALS MAY BE USED TO BRIDGE THE UNDERSTANDINGS FROM THE CONCRETE TO THE ABSTRACT LEVEL. THE NUMBER SYSTEM UNIT SHOULD…

This guide contains six sections which offer suggested sequential steps for teaching addition, subtraction, multiplication, division, fraction concepts and algorithms, and decimal fractions. Based on the manipulative approach, the guide offers activities and teaching methods which give students many opportunities to work with models. This approach…

This textbook aims to (1) train the pupil in that part of arithmetic used in everyday business which he can understand; (2) develop his skill in rapid calculation by short cuts and time tests; (3) show the necessity for checking, and develop the habit of checking; (4) develop the habit of thrift by planning budgets, keeping accounts, and becoming…