Data Mining An Online Homework System

Abstract NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract Data-Mining an Online Homework System Abstract Online homework systems are becoming increasingly popular since (when they work) they are convenient for both faculty and students. Systems that rely on mechanical grading are naturally best adapted to more mechanical types of problems, raising issues of whether an increasing reliance on such systems will privilege the assessment of procedural knowledge over the assessment of conceptual knowledge. However, online systems naturally and efficiently capture large amounts of data about student work and data-mining techniques can be applied to evaluate conceptual understanding as well as procedural understanding, even though the prompts are all procedural. In this paper, we discuss how to use detailed analysis of procedural results captured by a locally designed online homework system (tuned for the purpose of assessing conceptual understanding) to recognize conceptual growth in classes in mathematics and the likelihood of successful transfer of this understanding to later engineering classes. Patterns that demonstrate students are wrestling with new concepts and techniques for disentangling correlations in different subjects caused by successful transfer from correlations caused by general skills are developed. While the analysis is based on our local system, the general approach and tools can be applied to other systems as long as they allow multiple attempts and retain information about unsuccessful attempts prior to the final submission. Introduction Online homework is becoming a common tool in college mathematics courses, as well as other science and engineering courses. One product, WebAssign, has a list of over 300 U.S. Colleges and Universities using their system1, and most publishers now offer online homework systems as an option with many of their texts. The popularity of online homework systems is easy to understand. For the faculty, an online homework system reduces the amount of effort spent on grading and can also reduce management issues relating to collecting, recording, and returning student papers. For the students, online homework systems allow them to work on their own schedule and receive immediate feedback on what they have done correctly and incorrectly. In addition, some systems allow students multiple attempts and extra practice compared to courses with traditional homework only. Given the practical advantages, the shift to online homework seems very likely to continue. Therefore, it is important to study how this shift may alter instruction and learning, and how teachers can best assess student learning in an online world. Using an online homework system can influence the types of assignments that are made. Online homework problems must be of a format that can be graded by machine. This can lead to more procedurally oriented problems that have well-defined answers and for which systems can be easily generate multiple variations by simply adjusting the numbers. More conceptual problems are more likely to require open-ended solutions and are usually much more difficult to implement with such systems. Thus the shift to more online homework raises the possibility that it will be accompanied by a shift toward more