Many students in the United States, Canada, and around the world are required to take externally developed examinations. In many cases, these examinations are considered high stakes, and thus teachers spend time in class ensuring that their students are ready for the tests. After speaking with secondary math teachers about their experiences, the…

Shapedoku is a new type of puzzle that combines logic and spatial reasoning with understanding of basic geometric concepts such as slope, parallelism, perpendicularity, and properties of shapes. Shapedoku can be solved by individuals and, as demonstrated here, can form the basis of a review for geometry students as they create their own. In this…

Many mathematics teachers struggle to support their students' developing understanding of proof as an essential element in investigations of mathematics. The area of mathematics where the development of an understanding of proof is most challenging is algebra. In the case of algebraic proof, analysis of student written work on tasks that demand…

Lessons given to a group of mathematically talented eleventh and twelfth graders enrolled in a problem-solving course that provided practice in applying the heuristic strategy of working backward are detailed. Special attention was given to the process of formulating generalizations that represent large problem classes. (MP)

Features activities for advanced second-year algebra students in grades 11 and 12. Introduces three random variables and considers an empirical and theoretical probability for each. Uses coins, regular dice, decahedral dice, and calculators. (ASK)

Discusses the results of the 1996 National Assessment of Educational Progress (NAEP) of secondary school students on probability and statistics. The most recent results indicate that more attention is being given to data analysis, statistics, and probability, and that student performance on these items is gradually improving compared to the 1990…

Comparisons are given for data from the Second International Study for both eighth- and eleventh-grade students in the United States and Japan. U.S. students were closer to Japanese students at the eighth-grade level than at the twelfth-grade level; differences have increased since the First International Study. (MNS)

A representative sample of 237 twelfth-grade mathematics classrooms completed internationally developed achievement tests. What was taught, what teachers and teaching were like, students' attitudes and achievement, and comparisons with students in other countries are included. (MNS)