Using the ''between-grade levels'' regression discontinuity design, this study examined the hypothesized differential sensitivity of logico-mathematical (LM) and infralogical (IL) operational tasks to the effects of chronological age and first grade schooling in a sample of 580 1st and 2nd grade Israeli children. The results indicate that the…

The authors examined the impact of manipulative-based instruction on 2 independent cohorts of preservice elementary teachers. In Study 1, 50 participants engaged in problem solving with operations on whole numbers and fractions using concrete and representational manipulatives over 5 classes. Pre- to posttest performance on a mathematics survey…

The present research involved gauging preschoolers' learning potential for a key arithmetic concept, the addition-subtraction inverse principle (e.g., 2+1-1=2). Sixty 4- and 5-year-old Taiwanese children from two public preschools serving low- and middle-income families participated in the training experiment. Half were randomly assigned to an…

The principle of inversion--that a + b - b must equal a--requires a sensitivity to the relation between addition and subtraction that is critical for understanding arithmetic. Use of inversion, albeit inconsistent, has been observed in school-age children, but when use of a computational shortcut based on inversion emerges and how awareness of the…

In early years' (primary grade) classrooms in Australia repeated patterns are commonly explored as an early introductory activity to mathematics. Most young students have an extensive knowledge of and exhibit success in copying, continuing, creating and transferring patterns into other media. By contrast, research indicates one of the most…

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…

This textbook provides not only a mathematical basis, but also a scientific structure. Blackboard exercises are included, and great facility in comprehending the combinations and divisions of numbers will be acquired by this method.

This textbook is a second-grade course in arithmetic. While it contains a review of the work of Grade I, pupils who have not had the benefit of a kindergarten training or of Grade I drill will need to have certain principles and definitions more carefully explained. Starting with this knowledge, which is usually given in all Kindergartens, the…

This textbook is a third-grade course in arithmetic. It contains a review of the preceding book, a continuation and extension of the work in the fundamental processes and in fractions, and the introduction of several new principles in their simplest form, as percentage. The exercises are divided into lessons for convenience. Better results will…

This textbook is a fourth-grade course in arithmetic. It contains a review of the principles taught in Book III, with their extension to problems of greater difficulty. A few new principles are introduced from time to time, the aim being to introduce the new thought side by side with the review of those already taught. Realizing that the highest…

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…