The effective teacher of mathematics must be devoted to the profession. A teacher must create a stimulating atmosphere conducive to learning for all students. Whether in mathematics or in some other area, the teacher must…

Ed Begle said, “We have learned a lot about teaching better mathematics but not much about teaching mathematics better.” When perusing the history of teaching mathematics, it appears as if we constantly look for a…

Mathematics is still the most feared and disliked content area in the curriculum for children (and adults). It is socially acceptable to be terrible in mathematics and hate the subject, but it is not socially…

Knowing the mathematical content and more, including teaching from the overflow of knowledge implies careful planning and organization. Prior to teaching, it is imperative that the topics covered be carefully contemplated, studied, and organized. This…

How wonderful it would be if we knew everything about students, teaching, mathematics, and the teaching of mathematics. We could bottle it, sell it, become rich, and solve a lot of problems for everyone in…

We are living in a time when technology is changing almost faster than we can adapt to it or afford it. New products and upgrades are marketed at a rapid pace. The level of complexity…

Effective problem-solving requires open-minded approaches from teachers and students. This technique was demonstrated in another Egyptian problem, not found in the Rhind papyrus. Babylonians from 300 bce demonstrated a working knowledge of the Pythagorean theorem…

Discovery learning is a method of indirect instruction. The teacher structures a learning environment that allows students to develop conclusions. Normally, when doing a direct instruction lesson, students know the teacher will eventually “tell the…

Beginning with the Standards in 1989, the National Council of Teachers of Mathematics suggested a change in the role of proof in our mathematics curriculum. The call is for a decrease in attention given to…

Knowing where to begin this chapter and what to include is difficult. There are so many topics to be covered. What is the best order? What background information will students possess? Should topics be integrated…

Investigate some historical foundations of algebra Exercises Exercise 11.1 Compare and contrast your two positions. Exercise 11.2 Exercise 11.3 Exercise 11.4 Exercise 11.5 Exercise 11.6               34             ×21                 4 from 1…

For many students, geometry is the outside mathematical subject that you either love or hate. For many students, geometry has no connection to algebra or other mathematical concepts. Connecting geometry to algebraic concepts is important…

Should we continue with the emphasis on symbolic manipulation? How do we integrate technology into the picture? What is the impact of a more interdisciplinary and connected view of mathematics? Will the complexities of the…

Beginning with a conference at Tulane University in January 1986, there developed in the mathematics community a sense that calculus was not being taught in a way befitting a subject that was at once the…

Probability and statistics are crucial twenty-first-century mathematical tools! Selected topics have been incorporated and mandated into many state frameworks and mathematics curricula. The study of probability and statistics has been around for a long time.…