Discusses the importance of mental mathematics beyond the middle school. Presents sample objectives for different courses or strands, and teaching ideas to make mental mathematics an important, ongoing goal in secondary mathematics instruction and beyond. (KHR)

Describes a teaching experience through student-centered activities in a second year algebra class with gifted and talented students. Concludes that students learned more mathematics than the teacher originally planned to teach. (KHR)

Describes a low-tech, hands-on activity to improve student understanding of irrational numbers. Each student creates a number line from adding machine tapes and uses a square and a precisely folded triangle as the only measuring device. (KHR)

Discusses the historical and cultural background of magic squares. (KHR)

Describes an activity that allows students to investigate families of linear functions and families of quadratic functions. Offers an opportunity for students to conjecture, explain, and justify in an environment based on Euclidean geometry. Includes a teacher's guide, answers, and student worksheets. (KHR)

Presents two examples of using the limitations of calculators to help students understand important mathematical ideas. The first example shows how a simple algebraic calculation can make a recursive model work long enough to perform the job at hand while the second shows how the limitations of a calculator can be used to introduce the need for…

Describes a student's work on a word problem after which she was very comfortable with her answer but her work was not correct. Discusses symbol sense, goals for students, and how tasks can be used to help meet those goals. (KHR)

Describes experience using a new approach to teaching induction that was developed by the Mathematical Methods in High School Project. The basic idea behind the new approach is to use induction to prove that two formulas, one in recursive form and the other in a closed or explicit form, will always agree for whole numbers. (KHR)

Presents student solutions to real-world problems that allow students to develop and defend their mathematical models of the situations. Elicits proofs and offers recommendations for the potential of real-world problems as contexts for proof. (KHR)

Describes experience of teaching truth tables and problems that exercise students' critical reasoning. (KHR)

Describes a calculator exercise that can help students develop a better visual and numeric feel for Newton's method. (KHR)

Explores developing a concept image of functions. Includes assessment items, describes students' responses to these items, and interprets those responses. (KHR)

Presents five guided activities that use a graphing calculator to help students discover the fundamental theorem of algebra. Includes student worksheets and illustrates solutions. (KHR)

Examines several periods of world history including Greece, the middle ages, and the 17th century to gain a better understanding of the development of mathematics and share this information with students so that they can learn mathematics as a product of the people who lived their lives surrounded by the cultural influences and distractions of…

Points out the importance of incorporating minority life histories in education. Presents biographical information on Gloria Hewitt, a woman mathematician of color, to help encourage all potential mathematicians, especially those who belong to minority groups. Includes practical suggestions that teachers can use to encourage or inspire students to…