Resources

Chapter 1 – Introduction
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…

Chapter 2 – Learning Theory, Curriculum, and Assessment
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…

Chapter 3 – Equity, Shame, and Anxiety in the Mathematics Classroom
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…

Chapter 4 – Planning
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…

Chapter 5 – Skills in Teaching Mathematics
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…

Chapter 6 – Technology
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…

Chapter 7 – ProblemSolving
Effective problemsolving requires openminded 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…

Chapter 8 – Discovery
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…

Chapter 9 – Proof
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…

Chapter 10 – Foundations of Mathematics
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…

Chapter 11 – Algebra I
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…

Chapter 12 – Geometry
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…

Chapter 13 – Algebra II – Advanced Algebra and Modeling
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…

Chapter 14 – PreCalculus and Calculus
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…

Chapter 15 – Probability and Statistics
Probability and statistics are crucial twentyfirstcentury 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.…