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Incorporating EFFECTs into Content-Rich Courses: A Journey

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Conference

2016 ASEE Annual Conference & Exposition

Location

New Orleans, Louisiana

Publication Date

June 26, 2016

Start Date

June 26, 2016

End Date

August 28, 2016

ISBN

978-0-692-68565-5

ISSN

2153-5965

Conference Session

Mathematics Division Technical Session 1

Tagged Division

Mathematics

Page Count

8

DOI

10.18260/p.25652

Permanent URL

https://peer.asee.org/25652

Download Count

100

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Paper Authors

biography

Rebecca Bourn University of Wisconsin - Milwaukee

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Dr. Bourn is the Calculus Coordinator at the University of Wisconsin-Milwaukee. She earned her Ph.D. in Applied Mathematics from the University of Virginia School of Engineering and Applied Science.

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Sarah Baxter University of St. Thomas

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Dr. Baxter is a Professor of Mechanical Engineering in the School of Engineering at the University of St, Thomas in St. Paul, MN. She received her PhD in Applied Mathematics from the University of Virginia School of Engineering and Applied Science.

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Abstract

Incorporating EFFECTs into Content-Rich Courses: A Journey

Many foundation courses in mathematics are considered “content-rich,” meaning they must cover a significant amount of material to build skills and knowledge for subsequent courses. These courses are tightly scheduled surveys of multiple topics, all of which are considered “essential”. Often the presumption is that students will develop expertise in these foundation skills and be able to recall and use them as they are presented at a later date in a future course. Upon occasion, however, students do well in the initial course but retain little familiarity with the content in later courses, when context, application and sometimes even notation can be quite different. This is often true for engineering students with respect to the Calculus sequence.

A faculty group at the University of ___ developed a pedagogical structure to assist students in deepening their conceptual understanding of new and challenging ideas. This structure, named EFFECTs, Environments For Fostering Effective Critical Thinking Skills, was originally aimed at introductory engineering students, but has been extended to upper division engineering classes as well. The format intertwines multiple learning modules and written journal entries into a multi-session exploration of a large-scale physical problem, which often has no unique solution, perhaps only a best design. Critical thinking skills are enhanced through student reflection, on ideas and implications, or on the inherent challenges, prior to and along with, formal solution techniques. In their research they have demonstrated improvements in student engagement, technical skills, and deeper growth of understanding of core knowledge.

In previous work, the current authors proposed an adaption of the EFFECTs framework to the math classroom (Math-EFFECTs) by incorporating physical applications, geometry-based problems and estimation techniques into solution processes to contribute to the “does this answer make sense” aspect of critical thinking. These Math-EFFECTs modules were proposed for courses with flexible content requirements that allowed for free-form exploration. Students’ reported more enjoyment in learning and that their feelings of creativity in using mathematics increased significantly as they completed realistically modeled problems and were given the opportunity to make choices regarding approaches to problem solving. The response to the presentation of this work was positive, however the audience pointed out the difficulty of finding time in content rich classes for the more extended time required to implement an EFFECTs module. In the current work, sample Math-EFFECTs problems/modules, that fit more realistically into content-driven courses, are proposed. These modules retain key elements of the EFFECTs framework that seem to may help increase critical thinking and help students internalize concepts, but look to minimize added time. In particular, the topics of solids of revolution and cross-products are cast in an EFFECTs-like framework. The key components retained from the original EFFECTs framework are an enhanced component of physical visualization and aspects of reflection as to what type of solutions students should expect. The paper also describes details of the EFFECTs framework and presents possible approaches to assess the higher-level cognitive outcomes of the method.

Bourn, R., & Baxter, S. (2016, June), Incorporating EFFECTs into Content-Rich Courses: A Journey Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.25652

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