June 15, 2014
June 15, 2014
June 18, 2014
24.619.1 - 24.619.8
Flipping the Classroom to Address Cognitive ObstaclesEngineering students have difficulty transitioning to post-calculus courses, in part, becausehow calculus is expected to be known at the end of calculus differs from how it is expected tobe used in later courses like differential equations (Authors: Year). Our concern was toidentify cognitive obstacles for engineering students as they transition from calculus todifferential equations and to adapt the differential equations course to address them. Thepurpose of this paper is to describe a way of exploiting the flipped classroom model toeliminate cognitive obstacles and to increase conceptual coherence in the mathematicsclassroom.Though implementation of the flipped classroom varies from instructor to instructor, themodel moves lecture content to be work done at home as preparation for class while classtime is used for problem solving. Typically, instructors accomplish the “flip” by usinginstructional technology to deliver lectures or learning modules out-of-class. Difficulties arisefrom this model: a failure to address student misconceptions, poorly designed activities thatrequire only recall, disconnect between active-learning components and other material1, andpersistence of lecture use during class time2. These difficulties leave students with a feelingof incoherence in their learning. That is, the flipped classroom instructional model is itself apotential source of incoherence in the curriculum. A cognitive obstacle is a way of thinking about a mathematical structure or object that isappropriate in one situation and inappropriate in another. They are a source of conceptualincoherence in the mathematics curriculum. We made these the basis of out-of-class learningmodules. Built in Articulate Storyline, the modules asked questions about pre-calculus andcalculus content in ways consistent with how those concepts needed to be used in upcomingin-class activities. For example, since students have difficulty thinking about ways to measurechange in a data set (e.g., absolute change, relative change, average change, etc.), out-of-classmaterials asked students to decide among appropriate ways to measure change in a data setwhile in-class activities centered on how measurement of change is used to derive differenceequations. The pre-class materials provided a link from students’ prior calculus knowledge tohow that knowledge was expected to be used in the upcoming activities. We developedsurveys to gather feedback from the students on their perceptions of conceptual coherence.Results indicated that students found the pre-class materials coherent with the in-classmaterials as well as coherent from prerequisite material to differential equations. Whenasked to give a specific example of from prelectures, students highlighted the usefulness of areview of implicit differentiation. We thus reduced incoherence in mathematics contentalong two fronts: addressing cognitive obstacles to differential equations learning andconnecting in-class to out-of-class content. We will continue to adapt technology to increasemathematical coherence in our flipped model and we urge other instructors to first questionwhat the goals of their courses are before they construct their own flipped classroom model. Andrews, T. M., Leonard, M. J., Colgrove, C. A., & Kalinowski, S. T. (2011). Active learning not associated with student learning in a random sample of college biology courses. CBE – Life Sciences Education, 10, 394-405. Bowers, J., & Zazkis, D. (2012). Do students flip over the flipped classroom model for learning college calculus? Proceedings of the 34th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Kalamazoo, MI: Western Michigan University.
Tague, J., & Baker, G. R. (2014, June), Flipping the Classroom to Address Cognitive Obstacles Paper presented at 2014 ASEE Annual Conference & Exposition, Indianapolis, Indiana. 10.18260/1-2--20510
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