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

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.