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 book is about playing with mathematics, teaching: (1) How to multiply and divide large numbers mentally; (2) Making addition and subtraction easy; (3) Tricks for understanding fractions and decimals; and (4) How to quickly check answers for each calculation. Described as a foolproof way to do multiplication, division, factoring estimating,…

This book contributes to a growing body of research relevant to efforts to make algebra an integral part of early mathematics instruction, an area of studies that has come to be known as Early Algebra. It provides both a rationale for promoting algebraic reasoning in the elementary school curriculum and empirical data to support it. The authors…

This article explores how conceptualization of absolute value can start long before it is introduced. The manner in which absolute value is introduced to students in middle school has far-reaching consequences for their future mathematical understanding. It begins to lay the foundation for students' understanding of algebra, which can change…

Current neurocognitive theories of number processing [Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. "Cognitive Neuropsychology," 20, 487-506] state that mathematical performance is made possible by two functionally and anatomically distinct subsystems of number processing: a verbal system…