The purpose of this study was to explore the effectiveness of teaching Basic Algebra at a university using an online, interactive learning system. This system, ALEKS (Assessment and Learning in Knowledge Spaces), accompanies the textbook, Elementary and Intermediate Algebra: A Unified Approach (Hutchison, Bergman, Hoelzle, 2000). The study was conducted in three Basic Algebra courses in the fall of 2001 at a small university in the Midwest; the same instructor taught all three courses. This research examined the ability of technology to help students practice the algebraic skills necessary to complete their mathematics coursework. Through this online, interactive learning system, students worked at their own pace, enhancing mathematical ideas they already knew and building on this knowledge.
New technologies are recognized today as a means for advanced learning. Designing these teaching modes for teaching with a systematic approach will lead to efficiency and effectiveness in education (Vrasidas, 2002). It would be a disservice if students were not instructed how to use technology (McMullin, 2001). McMullin encouraged instructors to concentrate on teaching mathematical ideas and the relationships between these ideas, suggesting that technology should be used not as a means to a quick answer, but to enhance understanding.
A study on the effectiveness of mastery learning showed that the extra time and work involved did not justify the results (Martinez & Martinez, 1999). Martinez and Martinez found that using a master teacher made a significant difference in the class, not time spent on mastery learning. To reduce the extra time spent on mastery learning, they suggested using computers and delegating students to manage details of tracking progress.
An online interactive learning system, ALEKS (Assessment and Learning in Knowledge Spaces), was studied to assess the feasibility of using such a web-based learning system (Canfield, 2001). Canfield's goal was to ascertain the general attitude of the students in his classes. Thirty students from National-Louis University participated in this study. Canfield wrote a five-point questionnaire to be completed by students at the beginning and again at the end of the term. The questions asked were generally about the course itself, with specific questions on how the online ALEKS system was/wasn't helping students. Students reported that they generally learned more with the help of ALEKS and appreciated the feedback and explanations that ALEKS provided, along with being able to work at their own pace. Some students even felt less stress with mathematics because of the online work, voicing that they liked working on material for which they were ready. Canfield viewed ALEKS as a good means to supplement classroom instruction, not as a replacement for a human teacher. Canfield recommended that instructors give written exams along with the online assessments, using ALEKS as a support to the learning happening in the classroom.
Extensive research by Jean-Claude Falmagne, Jean-Claude Doignon, and other scientists of Europe and the United States helped in developing the Knowledge Space Theory (Baker, 2000). The Knowledge Space Theory is a system that efficiently assesses information in domains using specific items consisting of several problems (instances). The Knowledge Structure set for each domain was developed through the careful study of standards, instructional materials, and input from instructors. Students choose items to work on within their 'knowledge state' established through assessments and previous work on the system. A knowledge state contains specific items in a domain that a student is capable of solving. There are approximately 40,000 knowledge states possible in the Basic math portion of ALEKS. Problems worked are open-ended, not multiple-choice, thus eliminating the possibility of guessing an answer. Each student has several paths she/he can take when mastering a mathematical concept. …