Illustrating Productive and Unproductive Cognitive Interactions in an Online Intermediate Algebra Course

Abstract

Universities have drawn on an assortment of strategies to address the learning challenges and high attrition rates of developmental mathematics students. One of those strategies has been utilizing computer adaptive instruction (CAI) mathematics software. Reports about the efficacy of CAI vary from glowing to unfavorable. This article presents an instrumental case study, meaning that the purpose is to examine and describe a single case in depth to explain observed phenomena and illustrate a theory [Baxter and Jack 2008. Qualitative case study methodology: Study design and Implementation for novice researchers. The Qualitative Report. 14(4): 544–559]. The phenomena described in this article is productive and unproductive student interactions with a CAI environment. The vignettes in this article illustrate how students, even the same student, can have both productive and unproductive interactions with a CAI system. The vignettes are followed by recommendations for curriculum, instruction, assessment, and further research. Although these recommendations are gathered from observations of student interactions with CAI software in an asynchronous online Intermediate Algebra course, the observations have implications for different modes of instruction (e.g., synchronous online, flipped, hybrid, or face-to-face) that utilize online homework systems.

Keywords:

• Developmental mathematics
• intermediate algebra
• computer-adaptive instruction
• online instruction
• online homework
• productive and unproductive learning
• cognitive interactions
• case study

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Jennifer L. Nimtz

Jennifer L. Nimtz has over 25 years of experience in mathematics education, with more than 15 years teaching developmental and first-year undergraduate mathematics. Jen has also taught grades 7–12 mathematics and held K–12 leadership positions. Jen earned her Ph.D. in mathematics education at Michigan State University, with a focus on curriculum development and undergraduate mathematics teaching and learning. Currently, Jen is an assistant professor and director of First Year Mathematics Instruction at Western Washington University.