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 study sought to examine the effects of Tier 2 intervention in a multitiered model on the performance of first- and second-grade students who were identified as having mathematics difficulties. A regression discontinuity design was utilized. Participants included 126 (Tier 2, n = 26) first graders and 140 (Tier 2, n = 25) second graders. Tier…

To date, few studies have investigated the evolution of problem solving and general numeracy abilities during adulthood: skills that have obvious social importance. In this research, evolutions in adults' mental arithmetic skills were investigated using data from the IVQ 2004 French national survey, which tested 9,185 adults aged between 18 and…

In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12 + 9 - 9 yields…

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…