Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

Many sets of state and national mathematics standards have come and gone in the past two decades. The Common Core State Mathematics Standards (CCSMS), which were released in June of 2010, have been adopted by almost all states and will be phased in across the nation in 2014. The main difference between these standards and most of the others is…

In this paper, we report on a comparison of the treatment of addition and subtraction of fractions in primary mathematics textbooks used in Cyprus, Ireland, and Taiwan. To this end, we use a framework specifically developed to investigate the learning opportunities afforded by the textbooks, particularly with respect to the…

This programed mathematics textbook is for student use in vocational education courses. It was developed as part of a programed series covering 21 mathematical competencies which were identified by university researchers through task analysis of several occupational clusters. The development of a sequential content structure was also based on…

This textbook is a course in elementary arithmetic. It stresses mental as well as written exercises. Addition and subtraction are first presented together, and later multiplication and division.

A BOOKLET DESIGNED FOR ELEMENTARY SCHOOL STUDENTS TO BE USED INDEPENDENTLY FROM AND IN ADDITION TO THE REGULAR CLASSROOM CURRICULUM IN MATHEMATICS IS PRESENTED. THE FIFTH- OR SIXTH-GRADE STUDENT IS GIVEN PRACTICE IN WORKING PROBLEMS IN SUBTRACTION AND DIVISION. SHORT CUTS AND HINTS ARE PRESENTED THROUGH EXAMPLES, SAMPLE PROBLEMS, AND ANSWERS. THE…

Cross-cultural studies on mathematical cognition and education have suggested that curriculum and teaching have contributed to U.S. versus Asian differences in student performance; however, previous discussions of curriculum and teaching practices have been very general and have not focused on a detailed analysis of how mathematics concepts are…

Surveys the format and contents of fifteenth- and sixteenth-century arithmetic textbooks. Discusses the types of problems that were most popular in these early texts and briefly analyzes problem contents. Notes the residual educational influence of this era's arithmetical and instructional practices. (Contains 29 references.) (Author/MDH)

This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration…