In this paper, a contextual approach to teaching Mathematics at the pre-university level is recommended, and an example is illustrated. A "context" in the form of a real common mathematical problem is presented to the students. Different approaches to tackle the problem (from topics within and outside the syllabus) can be elicited from students.…

Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…

Mathematics is an "artificial" deliberately constructed language, supported crucially by: (1) special alpha-numeric characters and usages; (2) extra-special non-alphanumeric symbols; (3) special written formats within a single line, such as superscripts and subscripts; (4) grouping along a line, including bracketing using round brackets,…

The inertial balance is one device that can help students to quantify the quality of inertia--a body's resistance to a change in movement--in more generally understood terms of mass. In this hands-on activity, students use the inertial balance to develop a more quantitative idea of what mass means in an inertial sense. The activity also helps…

In this article, the author offers two well-known mathematical images--that of a dot moving around a circle; and that of the tens chart--and considers their power for developing mathematical thinking. In his opinion, these images each contain the essence of a particular topic of mathematics. They are contrasting images in the sense that they deal…

There is offered in this book a year's work in numbers for those boys and girls who know one to ten thoroughly. The book is designed for the children themselves. The practical use of this text in various schools for several years gives evidence by its success that as soon as children can read they should have arithmetics in their hands. [Cover…

This textbook provides the foundation for a course in mathematics covering arithmetic, algebra, geometry, conic sections, and arithmetic of infinites. An appendix on practical gauging is included, as well as a supplement containing the history of logarithms. [This edition was corrected and improved by Samuel Clark.]

This textbook is an introductory mathematics course. It is a treatise of arithmetic, containing all the practical parts thereof; both in whole numbers, vulgar fractions, and decimals; likewise the theory of numbers, and their principal properties, demonstrated in a plain and easy manner.

This arithmetic textbook uses small concrete numbers to lead pupils to understanding numbers' properties and relations. This work is intended as a connecting link between the Primary and Written Arithmetics of the Author. It presents a mental analysis of Arithmetic adapted to the younger pupils by its easy gradations, and to advanced pupils by its…