Effective assessment of mathematical problem solving requires more than an examination of student answers. Students tend to make calculations without explanations. Teachers need to analyze their processes and get students to communicate their thinking. This article suggests ways to understand students' thinking, their conceptions, their…

Many students in U.S. schools have trouble understanding fractions and Algebra II, the one difficultly occurring at the end of elementary school, the other in high school. One reason is that schools generally focus on one aspect of mathematics--calculation--and often fail to address the second aspect--interpretation. Also responsible is the…