Mastery with Meaning: Access to Mathematics Online

Abstract

Mastery approaches with online internet platforms have been shown to alleviate many students' deficiencies and open the door to higher mathematics. [16, 17] This paper will detail some current programs using online learning for precalculus courses, and detail how the research affected the design, development, and implementation of a new online approach developed for the PACe precalculus mastery program at Colorado State University. Concluding considerations will consider the next steps of research and development. (PACe is an acronym for Paced Algebra to Calculus electronically.) The authors' encourage readers to communicate any questions or comments regarding these or other mathematics online programs to the email address above. ONLINE INSTRUCTION Online instruction systems for mathematics can be divided into two general categories: The carriers of instruction (Learning Management Systems, LMS) like BlackBoard, WebCT, and Angel and; the instruction-based systems (Interactive Learning Systems, ILS) like ActivStats, ALEKS, Thinkwell, and Plato. These systems have overlapping goals and features. LEARNING MANAGEMENT SYSTEMS All Learning Management Systems provide facilities for communication, grading and grade reporting, lesson design, and presentation. These features may or may not encourage effective instructional design, but they offer the basics for managing courses. Key features of LMSs are: * The communication features (e-mail, messaging, discussion boards, and white boards) include both synchronous and asynchronous features for the instructor to communicate with the entire class, with subgroups of the class, and with individual members of the class. Email, discussion sessions, and instant messaging may have mathematics palettes to allow for the transmission of mathematical symbols, expressions, and equations. * LMSs allow the creation or importation of quizzes, practice exams, and examinations with various types of questions that can be graded by the system, including multiple-choice, matching, and short-answer questions. * LMSs allow for lessons to be designed and presented. The instructional content can contain video clips, written textbook material, simulations, animations, spreadsheets, computer symbolic algebra systems, graphing utilities, and dynamic geometry software. INTERACTIVE LEARNING SYSTEMS Interactive Learning Systems, in contrast to the more general Learning Management Systems, are specific to particular courses and are usually stand alone instructional environments that students can use any time, and at their own pace. These systems can have all of the features of an LMS or just a few. Three of the current ILSs will be highlighted: ALEKS, Thinkwell, and Plato (Academic Systems). ALEKS [1, 2, 15] stands for Assessment and LEarning in Knowledge Spaces (The acronym refers to Knowledge Space Theory, a theory using Cognitive Psychology and Applied Mathematics to model and empirically describe particular fields of knowledge. It was developed in 1983 by two Belgian cognitive psychologists, Jean-Claude Falmagne and Jean-Paul Doignon, with a grant from the National Science Foundation). ALEKS has the ability to display video clips, textbook material, quizzes with instructor determined (but not created) question types, and glossary and dictionary entries. This program also contains: a communication capability that is built on an internal email system that has a symbol palette attached, and an artificial intelligence capability that looks at student entered responses (there are no multiple choice questions) on assessments, and determines what content a student is ready to access. This assessment capability is being imported to other ILSs as well. This capability allows students to take different paths through the material, rather than go through a pre-ordered list of topics. Thinkwell [18], in contrast, is a set of DVDs that contains video clips of lectures with associated quizzes. …