A Study of Multivariable Calculus Vector-Related Items in the WeBWorK Open Problem Library

WeBWorK is a free, online homework system that was developed in 1994. It has been supported by key organizations and is currently used by many in the postsecondary mathematics community. Its Open Problem Library (OPL) contains tens of thousands of items at the lower division undergraduate mathematics level. The goal of this study is to investigate multivariable calculus vector-related items in the WeBWorK OPL. We first consider the usage and nature of these items. Next, we consider the nature of the items by looking at each item’s cognitive complexity, the key vector ideas addressed in the item, and the vector representations used in the item by systematically adapting and employing previous coding schemes from documented mathematics education research. The findings in this study validate the critical features of vectors that were identified in earlier work. We conclude that the list of key vector ideas appears to be comprehensive since they addressed the topics in all multivariable calculus vector-related items studied. However, there are not many items of high or very high cognitive complexity. based on our findings, there appears to be a need for specific types of vector-related items available in the WeBWorK OPL. We conclude there is a need for additional items that involve contextual situations; graphical or geometrical interpretation; and reasoning, proof, and justification. We also provide detailed recommendations for the addition of vector-related items that address topics or use representations that are missing or in limited supply in the WeBWorK OPL.