The development of the idea that "The essence of mathematics lies in its freedom," a quotation from Cantor, is discussed. Several examples are given of relative truth, and the problem of consistency is discussed. Mathematics and its relationship to the physical world is also explored. (MNS)

A general solution to a problem in linear algebra is provided. (DT)

This paper explores the development of students' knowledge of mathematical procedures. Students' tendency to develop rote knowledge of procedures has been widely commented on. I postulate an alternative, more "intelligent" endpoint for the development of procedural knowledge, where students choose to deviate from solving patterns on…

This teacher guide helps build a solid foundation in algebra for students in grades 3-5 in which students gain essential understanding of properties of numbers, variables, functions, equations, and formulas. Throughout the problem solving activities, students use computational skills and gain a deeper understanding of the number system. Students…

This textbook is a teaching manual for arithmetic, algebra, and geometry. Historical sketches on the subjects are included. Each topic is discussed in detail, and the teacher is advised along what lines to work, and how the work may be successfully accomplished.

In the preparation of this textbook, no pains have been spared by the author to obtain from the best sources, such as the later treatises in highest repute, memoirs of scientific bodies, and mathematical journals in English, French, and German, the materials for a book suited to the present state of mathematical science and the wants of teachers…