Teaching for Understanding: The Importance of the Central Conceptual Structures in the Elementary Mathematics Curriculum
Giving students knowledge that is useful outside of the specific context in which learning occurs has been a central goal of education for as long as classrooms have existed. However, in spite of the efforts that have been devoted to this subject for much of the previous century, in the 1990s one has only to listen to any representative of the workplace to realize that this objective has not yet been met in the field of mathematics education. In the public press, there is mounting evidence that the mathematical knowledge U.S. students acquire in school does not prepare them to meet the demands of an increasingly sophisticated workplace or to compete successfully in a global economy. In a less public but equally concerned quarter, university faculty have also expressed dismay that U.S. students who demonstrate mathematical knowledge on standardized tests in high school are unable to use this knowledge to acquire the advanced mathematical understandings expected in college-level courses. Although both of these concerns suggest a problem in knowledge transfer, another body of evidence has accumulated over the past decade that points to a deeper problem: one that involves knowledge acquisition itself and one that may be centrally related to the issue of transfer. These findings are described here.