This textbook is a fifth-grade course in arithmetic. It contains a review of the work done in Book IV, the extension of the principles taught there to more difficult problems, and a few new topics. Notation and numeration receive more attention. The work in fractions is extended to include multiplication and division, using only small…

This textbook is a sixth-grade course in arithmetic. The topics in book V are reviewed in this book. Some topics, as fractions, are completed as special subjects; and others, like percentage, enlarged. Compound numbers are completed, and ratio introduced. The latter subject will be found helpful in much of the higher work in percentage, and it has…

This textbook is a seventh-grade course in arithmetic. The plan pursued in this series of arithmetics is that of giving constant practice in those principles already acquired at the same time that new topics are presented. Accordingly, many review examples in percentage are given as the subject is more fully developed. The form lessons, which have…

This textbook is an eighth-grade course in arithmetic. This book completes the ordinary grammar school course in arithmetic, and covers all the work not included in the preceding books of this series. It is suggested, however, that, in places where there are nine grades, some topics should be omitted from the eighth grade and presented in the…

Included in this document are tests used to assess achievement in mathematics (K-6) in an experimental study conducted in the Clark County School District in Nevada. Each test is designed to assess learning at a definite skill level. Included are directions for administering each test, behavioral objectives assessed by each test and each test…

Results of a study that measured rankings of achievement in arithmetic by self, peers, and teachers, and their relation to arithmetic achievement measured by standardized tests. (DR)

Procedures for using an abacus to teach addition to learning disabled children are described. Considerations in choosing, constructing, and doing basic problems with an abacus are discussed. (CL)

Cryptology, the science of secret writing, is a great way to introduce students to different areas of mathematics such as number theory, linear algebra, probability and statistics. Cryptology consists of two branches: cryptography and cryptanalysis. Cryptography is the science of designing techniques for encrypting and decrypting a message.…

Three experiments investigated the roles of resource-sharing and intrinsic memory demands in complex working memory span performance in 7- and 9-year-olds. In Experiment 1, the processing complexity of arithmetic operations was varied under conditions in which processing times were equivalent. Memory span did not differ as a function of processing…

The article describes the harmonic mean and explores situations for using it. Activities that involve hands-on practice for students are provided. Students learn to recognize which mean, harmonic or arithmetic, is appropriate.

This article shares investigation possibilities that lie within familiar concepts of greatest common factor and least common multiple.

This article summarizes research on how students who are bilingual or learning English use two languages and examines how this research is relevant to mathematics classrooms. It is easy to notice that bilingual students sometimes use two languages. It is more difficult to know whether this practice might be significant to learning mathematics.…

This study examines the communication between pre-service teachers and sixth grade students in a project in which email was used for communication as students learned about fractions and were supported by the pre-service teachers. Specifically, the study investigated how the pre-service teachers applied their mathematical knowledge to understand…

Two developments have contributed to the convergence of views about the benefits of real-life and inquiry-based pedagogies in mathematics learning. First, the mathematics teaching community is increasingly focused on the learning of mathematics that involves the transfer of prior knowledge to novel problem-solving situations, a key element in…