Takes the concept of using a geometrical or visual approach to teach algebraic concepts and extends it to connect with the section on binomial expansion by using three dimensional objects. (ASK)

Uses the average-monthly-temperature function as an application of the sine wave. Argues that the attractive aspect of gas bill graphs is that they clearly illustrate that sinusoidal curves are useful and meaningful in an everyday context. (ASK)

Presents an activity that uses square-foot tiles as a coordinate system on which human geometric models are constructed. (ASK)

Discusses the benefits of learning the history of mathematics and how it can be useful in teaching as well as interesting. Provides information on how to put mathematics in its historical context, show the interaction of mathematics with cultures, and shed light on the teaching and learning of mathematics. (Contains 25 references.) (ASK)

Presents activities that allow students to explore alternative voting methods and discover the advantages and disadvantages of each method. Features the statement and proof of Arrow's theorem which requires only basic arithmetic and allows students to engage in high-level mathematical thinking. (ASK)

The unique factor of the Japanese educational system is the use of entrance examinations. Presents examples and comments on questions from those examinations. (ASK)

Presents results from a study that examined students' understanding of connections between algebraic and graphical representations of functions. Discusses a possible reason for the inadequate and often absent connections that students made between them. (ASK)

Uses a particularly contentious newspaper report that makes a cause-and-effect claim as the basis for discussing the important aspects of statistical understanding. Suggests a hierarchy to help teachers plan for and assess student learning in this area, and closes with a plea for teachers to cooperate across subjects in order to achieve results.…

Diversity can be introduced in algebra without needing extra time. Explores three opportunities to encounter and engage diversity: (1) history; (2) multiple representations; and (3) object concept of function. (ASK)

Discusses representations in the context of solving a system of linear equations. Views representations (concrete, tables, graphs, algebraic, matrices) from perspectives of understanding, technology, generalization, exact versus approximate solution, and learning style. (KHR)

Reports on what actually happened with the role of the computer, the quality of math education, and curricular change in 2000. (KHR)

Describes how to use homemade tiles, sketches, and the box method to reach a broader group of students for successful algebra learning. Provides a list of concepts appropriate for such an approach. (KHR)

Describes the process of mathematical modeling, an extensive teacher's guide, and a student modeling activity to improve the efficiency of soft-drink packaging. (KHR)

Examines four areas of difficulty with graphing and modeling, identifies confusions and misconceptions, and shows how these areas interact in the presence of data-collection devices. (KHR)

Describes the angles-of-a-star problem designed to find the sums of the measures of the angles at the vertices of a five-pointed star. Shows that a good problem may have many correct solutions. (KHR)