Multiple Representations of Functions in a Calculus Open Educational Resource Compared to a Traditional Textbook
Presentation Type
Poster
Faculty Advisor
Joseph DiNapoli
Access Type
Event
Start Date
26-4-2023 9:45 AM
End Date
26-4-2023 10:44 AM
Description
Open educational resources (OERs) are often lauded as vehicles of educational equity because their open-licensed, cost-free publication online makes them a viable alternative to overpriced college textbooks. However, agreed-upon measures of their quality compared to more traditional textbooks are lacking. This research investigates one possible such measure by comparing the emphasis two calculus textbooks place on the coordination of multiple representations (CMR) of functions, a process that has been linked to conceptual learning in mathematics. The research question guiding this work is: How does the prevalence and nature of student tasks requiring CMR of functions in the OER Active Calculus compare to that found in the traditionally-published Calculus, Early Transcendentals? Between the two texts, 1,035 student tasks were analyzed and coded based on (1) whether or not they required CMR of functions, (2) which representations were to be coordinated (symbolic, graphic, numeric, or verbal), and (3) whether the task required construction of a new representation from a given one or perception of the relationship between two given representations. This analysis revealed that the OER was more likely than the traditional text to require students to make connections between multiple representations of functions. However, the traditional textbook was more likely to require the more cognitively demanding task of construction of a new representation. These results highlight the potential that OERs have to provide affordable access to mathematical resources of a quality comparable to (or perhaps even superior to) their traditionally-published counterparts.
Multiple Representations of Functions in a Calculus Open Educational Resource Compared to a Traditional Textbook
Open educational resources (OERs) are often lauded as vehicles of educational equity because their open-licensed, cost-free publication online makes them a viable alternative to overpriced college textbooks. However, agreed-upon measures of their quality compared to more traditional textbooks are lacking. This research investigates one possible such measure by comparing the emphasis two calculus textbooks place on the coordination of multiple representations (CMR) of functions, a process that has been linked to conceptual learning in mathematics. The research question guiding this work is: How does the prevalence and nature of student tasks requiring CMR of functions in the OER Active Calculus compare to that found in the traditionally-published Calculus, Early Transcendentals? Between the two texts, 1,035 student tasks were analyzed and coded based on (1) whether or not they required CMR of functions, (2) which representations were to be coordinated (symbolic, graphic, numeric, or verbal), and (3) whether the task required construction of a new representation from a given one or perception of the relationship between two given representations. This analysis revealed that the OER was more likely than the traditional text to require students to make connections between multiple representations of functions. However, the traditional textbook was more likely to require the more cognitively demanding task of construction of a new representation. These results highlight the potential that OERs have to provide affordable access to mathematical resources of a quality comparable to (or perhaps even superior to) their traditionally-published counterparts.