This case study examines the ways in which a teacher education program develops prospective teachers who implement the principles of constructing mathematical knowledge via a learning discourse. The study presents and analyzes a mathematical discourse in a 4th grade class as well as the feedback conversation of prospective teachers with their…

Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively…

This book is intended for students who know the numbers from one to thirty thoroughly, who can count to one thousand, who know something of the multiplication tables of two, three, four, five, six, ten, and twelve, and who understand the simplest facts about ratio and fractions. The purpose of the textbook is to conform numbers in their facts and…

This textbook is for arithmetic students who can use numbers into the thousands in addition and subtraction, who know what ratio is and understand something about fractions, who know some facts of measures, and who have studied the multiplication tables. The book contains about a year's work, mostly in practice, partly in extension of knowledge.…

This textbook is a course in Euclidian geometry conic sections. It was translated by the original Latin, and was revised, corrected and enlarged.

This textbook aims to give a clear and concise exposition of the elements of algebra to be adapted to the present wants of common schools. It cannot be expected, at present, that Common Schools should pursue Algebra to the same extent as pursued in Colleges ; still they may, to good advantage, acquire the more elementary portions of this branch of…

This arithmetic textbook for common schools and academies presents lessons arranged from least complex to most complex to prepare students for algebra study. Lessons include practical business applications, and the book has been adapted to serve the business community's needs while respecting the science of numbers.

This textbook is intended for a course in mathematics and not as a reference book for the statistician. Although a knowledge of calculus is necessary for the proper appreciation of the various principles treated here, the applications are carefully restricted for the most part to those that do not require calculus except possibly for proper…

This textbook commences with a brief sketch of the history of Elementary Geometry. The definitions throughout have been somewhat amplified, and several notes have been added which it is hoped may be found useful and suggestive. The subject of Ratio has been expanded; a few new propositions have been added; and there is a considerable collection of…

This textbook covers the first six books of the elements of Euclid, the 11th and 12th books, and the book of Euclid's data. Elements of plane and spherical trigonometry are included.

This textbook is an analysis of the system of mathematical instruction which has been steadily pursued at the United States Military Academy over a quarter of a century and which has given to that institution its celebrity as a school of mathematical science. The book covers logic as science and art, mathematical science, and the utility of…

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…