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Article Excerpt
Of 19 college algebra classes, 12 used WeBWorK and 7 used traditional paper and pencil homework (PPH). Given the earlier quantitative result that no significant difference in performance between WeBWorK and PPH classes was found, a qualitative analysis of 358 student and instructor surveys revealed 3 primary categories of student perceptions related to WeBWorK: views about its usefulness, intentionality in engaging with mathematics, and challenges to student beliefs about mathematics. Student and instructor comments are reported within the context of self-regulated learning. Results support the conjecture that even a narrow use of WeBWorK, as a substitute for handwritten homework, is at least as effective as traditionally graded paper and pencil homework for students learning college algebra.
INTRODUCTION
Almost all new college students in the United States have used a personal computer by age 18 and approximately half of entering freshmen have used the Internet; the other half will be introduced to the Internet when they get to college (Pew, 2002). Opportunities to learn at a distance through online courses and modules have grown explosively in the last decade and Internet-based enhancements to traditional courses have proliferated in science, technology, engineering, and mathematics (STEM) disciplines (NSF, 1998; WebNet, 2001).
One Internet-based accessory to STEM learning gaining popularity in the U.S. is web-based homework (WBH). One of the reasons for the growth in popularity of WBH systems may be the fact that the average undergraduate teaching load for a mathematics instructor at a publicly funded U.S. college was approximately 100 students per term in 1998 (NCES, 1998). Reduced funding and concomitant assignment changes in the early years of the 21st century have increased that number by one class, or by about 35 students, to an average of 135 students per faculty member. Providing detailed, individual feedback to each student on a typical 10- to 20-problem homework assignment several times a week is problematic for college instructors within the current U.S. university culture. That culture also includes expectations that faculty do research and perform service for college and community in addition to preparing for, teaching, and evaluating their classes. Nonetheless, effective teaching practices necessitate feedback to students on their out-of-class attempts at learning.
The importance of homework, especially for the advanced cognitive development expected in high school and college mathematics, has already been established by many individual and meta-analytic studies (Cooper, 1989; Cooper, Lindsay, Nye, & Greathouse, 1998; Keith & Cool, 1992; Warton, 2001). Homework is an activity related to motivation, mastery of material, and to achievement (Keith & Benson, 1992). It is also clear from the research that homework may be necessary but not sufficient for achievement on exams (Peters, Kethley & Bullington, 2002; Porter & Riley, 1996). However, the role of homework in student achievement is only partly understood and there has been a call for both large-scale quantitative studies using multiple data collection methods as well as for smaller studies, like the present one, that investigate the self-regulatory aspects of homework (Trautwein & Koller, 2003).
Within the liberal arts tradition at U.S. colleges, the primary purpose of homework in college algebra is to foster development of a robust collection of knowledge structures for later use in calculus. The method for achieving this goal has traditionally been through separate practice with facts and concepts. Exercise sets in most college algebra textbooks offer drill practice with facts followed by practice with application and assimilation of concepts. Many texts end an exercise set with mildly non-routine problems aimed at generating disequlibrium and encouraging deeper reflection on concepts and their relationships. For a variety of reasons, from pressure to "cover" a proscribed collection of chapters in such textbooks to the personal epistemologies of students and instructors, the practice in college algebra teaching is to assign problems mostly from the first two categories (drill and application). Though there are efforts to rewrite college algebra textbooks along the lines of the reform of calculus in the U.S. (e.g., Connally, Hughes-Hallett, Gleason, Chiefetz, Flath, Lock, et al., 2004; Kime & Clark, 2001), this study was situated in a traditional setting and investigated perceptions of a technology-based perturbation to that traditional setting.
Student behaviors directed towards achievement in college algebra like effort, task persistence, and self-regulatory decision-making are shaped by two factors: their beliefs about the tasks at hand and their perceptions about their abilities to be successful in completing the tasks (Bandura, 1997; Updegraff & Eccles, 1996; Warton, 2001). In particular, the use of WBH may foster positive feelings towards it and influence motivation to use it (Liaw, 2002). This study examines student beliefs and perceptions about using WBH for learning mathematics. The WBH tool used was WeBWorK.
As Warton (2001) noted, homework is a complex research topic in which the views of students and styles of teachers should not be ignored. Therefore, to investigate the impact of the web-based homework interface WeBWorK on college algebra learning, at least the following must be addressed:
1. Student Perception: What are student perceptions of the nature, purpose, and use of WBH, particularly of their efforts and degree of success using WeBWorK?
2. Instructional Style: What contributions to differences in students' perceptions and performance might be attributable to instructor style?
After a brief description of the WeBWorK interface and an overview of the theoretical framing for the study, the methods used are summarized. The study was qualitative, so the results include descriptive (not inferential) statistics. The focus is on reporting and analyzing the interaction of WBH with student perceptions, intentions, and beliefs along with examination of the possible influences of instructor style. The presentation of results is followed by a discussion of the limitations of the study and possible implications for college teaching practice.
Overview of WeBWorK
The goal of the WBH system called WeBWorK is immediate "correct" or "incorrect" feedback. The WeBWorK interface does not correct a student's errors or give hints. WeBWorK simply lets students know whether they have submitted a correct answer and provides the opportunity to try again. If students need help, they are encouraged to seek out a fellow student, a tutor, or the instructor. They can do this in person or by email (there is a "Feedback" button to generate email to the instructor built into the WebWorK interface--see Figure 1).
[FIGURE 1 OMITTED]
WeBWorK is an open-source, non-proprietary web-based interface developed at the University of Rochester (Gage, Pizer & Roth, 2001). It uses problem libraries to create similar but personalized problems for each student. WeBWorK has the potential to provide individualized graphical questions and interactive mathematical experiments for students to manipulate. Course management capabilities of the program for use by instructors include: (a) statistical information on individual student and whole-class progress, (b) adjustable due dates for individuals or groups, (c) group email lists for a class, and (d) exporting of grade data to spreadsheet programs. In the semester of this study, Fall 2002, instructors incorporating WeBWorK into their courses rarely used capabilities (a)-(c) but did make use of grade exporting.
To use WBH, students signed on to the WeBWorK server. From there they could (and were encouraged to) download and print a hard copy of their assignment. Once their work was complete, students entered solutions into WeBWorK through a text window using standard computer algebra software syntax (see Figure 1). After the WeBWorK due date, they could go back and review their submitted homework and view correct answers. Students might also re-work old assignments to review for exams.
THEORETICAL FRAMEWORK
The educational philosophy underpinning both the development of WeBWorK and this study is constructivist: understandings are conceptual structures built mentally by a learner. Such construction is generated by personal and social interaction...
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