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Getting Your Hands Dirty in Integral Calculus

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Conference

2020 ASEE Virtual Annual Conference Content Access

Location

Virtual On line

Publication Date

June 22, 2020

Start Date

June 22, 2020

End Date

June 26, 2021

Conference Session

Mathematics Division Technical Session 3: Diversity in Mathematics Education

Tagged Division

Mathematics

Page Count

23

DOI

10.18260/1-2--34707

Permanent URL

https://peer.asee.org/34707

Download Count

175

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Paper Authors

biography

Lee Singleton Whatcom Community College

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Lee Singleton is a professor at Whatcom Community College, in Bellingham, WA. He holds a BS in mathematics from Harding University, a MS in mathematics and PhD in biomedical mathematics from Florida State University. His current interests include 3D-printing, active learning, and infusing more physical activity into mathematics courses. Recent grant positions include principal investigator on the NSF-funded grant “EAGER: MAKER: Engaging Math Students with 3D-Printing for STEM Success and co-PI on the NSF-funded grant "Collaborative Research: Improving Representational Competence by Engaging with Physical Modeling in Foundational STEM Courses".

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biography

Eric Davishahl Whatcom Community College Orcid 16x16 orcid.org/0000-0001-9506-2658

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Eric Davishahl is assistant professor and engineering program coordinator at Whatcom Community College. His teaching and research interests include developing, implementing and assessing active learning instructional strategies and auto-graded online homework. Eric has been a member of ASEE since 2001. He currently serves as awards chair of the Pacific Northwest Section and was the recipient of the 2008 Section Outstanding Teaching Award.

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Todd Haskell Western Washington University

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Todd Haskell is a cognitive scientist interested in learning and the development of expertise, especially in STEM fields. He is currently Associate Professor of Psychology at Western Washington University. In previous projects Dr. Haskell has worked on understanding how chemistry novices and experts navigate between macroscopic, symbolic, and small particle representations, and how pre-service elementary teachers translate an understanding of energy concepts from physics to other disciplines.

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Abstract

The landscapes of many elementary, middle, and high school math classrooms have undergone major transformations over the last half-century, moving from drill-and-skill work to more conceptual reasoning and hands-on manipulative work. However, if you look at a college level calculus class you are likely to find the main difference is the professor now has a whiteboard marker in hand rather than a piece of chalk. It is possible that some student work may be done on the computer, but much of it contains the same type of repetitive skill building problems. This should seem strange given the advancements in technology that allow more freedom than ever to build connections between different representations of a concept.

Several class activities have been developed using a combination of approaches, depending on the topic. Topics covered in the activities include Riemann Sums, Accumulation, Center of Mass, Volumes of Revolution (Discs, Washers, and Shells), and Volumes of Similar Cross-section. All activities use student note outlines that are either done in a whole group interactive-lecture approach, or in a group work inquiry-based approach. Some of the activities use interactive graphs designed on desmos.com and others use physical models that have been designed in OpenSCAD and 3D-printed for students to use in class. Tactile objects were developed because they should provide an advantage to students by enabling them to physically interact with the concepts being taught, deepening their involvement with the material, and providing more stimuli for the brain to encode the learning experience. Web-based activities were developed because the topics involved needed substantial changes in graphical representations (i.e. limits with Riemann Sums).

Assessment techniques for each topic include online homework, exams, and online concept questions with an explanation response area. These concept questions are intended to measure students’ ability to use multiple representations in order to answer the question, and are not generally computational in nature. Students are also given surveys to rate the overall activities as well as finer grained survey questions to try and elicit student thoughts on certain aspects of the models, websites, and activity sheets. We will report on student responses to the activity surveys, looking for common themes in students’ thoughts toward specific attributes of the activities. We will also compare relevant exam question responses and online concept question results, including common themes present or absent in student reasoning.

Singleton, L., & Davishahl, E., & Haskell, T. (2020, June), Getting Your Hands Dirty in Integral Calculus Paper presented at 2020 ASEE Virtual Annual Conference Content Access, Virtual On line . 10.18260/1-2--34707

ASEE holds the copyright on this document. It may be read by the public free of charge. Authors may archive their work on personal websites or in institutional repositories with the following citation: © 2020 American Society for Engineering Education. Other scholars may excerpt or quote from these materials with the same citation. When excerpting or quoting from Conference Proceedings, authors should, in addition to noting the ASEE copyright, list all the original authors and their institutions and name the host city of the conference. - Last updated April 1, 2015