A well-known optimization problem is the Popcorn Box investigation, which involves a movie theater snack container. The problem has been tailored for classroom investigations by the Ontario Association for Mathematics Education. The exploration was designed for students in grades 9 through 12. A common strategy proposed for algebra students is to…

Mathematics educators are intensely interested in how mathematics is taught and learned in other countries. In Korea, for instance, the college entrance examination has played a major role in shaping Korean mathematics education (Kwon 2006). All high school students who want to pursue a college degree are required to take a college entrance…

Most high school mathematics teachers completed a mathematics history course in college, and many of them likely found it intriguing. Unfortunately, very few of them find the time to allow much, if any, mathematics history to trickle into their instruction. However, if mathematics history is taught effectively, students can see the connections…

This article describes two instructional activities carried out in a ninth-grade Romanian classroom and suggests a number of reading and writing strategies that can be used to assist students in understanding and solving mathematics problems. (Contains 1 figure and 1 table.)

The Chinese used the idea of generating equivalent expressions for solving problems where the problems from a historical Chinese text are studied to understand the ways in which the ideas can lead into algebraic calculations and help students to learn algebra. The texts unify algebraic problem solving through complex algebraic thought and afford…

Describes the use of an extended problem-solving assessment task with a Japanese secondary class. Argues that extended problem-solving tasks have the potential to illuminate a much wider range of student performance and to offer learning opportunities almost never realized with more traditional--albeit often quicker--forms of assessment. (ASK)

Discusses the implications of a research study of more than 2000 students aged 11 to 15 that explored why the students interpret algebra in certain ways. Recommends strategies that can help teachers deal with prior knowledge that students may bring to their study of algebra. (DDR)

In the fall of 2003, the author conducted research on the student teaching process in Japan. The basis for most of the lessons observed was rich mathematics problems. Upon returning to the US, the author used one such problem while teaching an algebra 2 class. This article introduces that problem, which gives rise to both linear and quadratic…

Presents an approach to explaining a relation, a - b = -(b - a), that is difficult for algebra students to understand. The approach came about as a result of discussions with students in which they provided many novel explanations. (DDR)

Discusses a program in New Zealand to assist high school students who have an aptitude for mathematics. Uses the philosophy of extension and enrichment rather than acceleration and has a teaching emphasis of problem solving and the methodology of the research mathematician. (MKR)