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On the Effectiveness of Designing Didactical Situations Targeting R^n to Teach the Concept of Subspace in Linear Algebra

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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 2: Poster Presentations

Tagged Division

Mathematics

Page Count

20

DOI

10.18260/1-2--35008

Permanent URL

https://cms.jee.org/35008

Download Count

51

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Paper Authors

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Anibal Sosa Universidad Icesi, Colombia

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Mathematician with a PhD in Computational Sciences from UTEP, and works as an Assistant Professor for the Dept. of Information Technology and Communications at Universidad Icesi (Colombia).

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Norha M. Villegas Universidad Icesi, Colombia Orcid 16x16 orcid.org/0000-0003-2872-3916

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Norha M- Villegas is an Associate Professor in the Department of Information and Communication Technologies, Director of the Software Systems Engineering Bachelor Program at Universidad Icesi, Cali, Colombia, an Adjunct Assistant Professor of the Department of Computer Science, University of Victoria, in Canada, and an IEEE Senior Member. Her research interests include engineering education, context-management, cyber physical systems, context-aware analytics, self-adaptive and self-managing systems, and runtime software evolution. She conducted her PhD at University of Victoria, between September 2009 and February 2013. In November 2011 she received the IBM Canada CAS Research Project of the Year 2011 for the application of context-awareness and self-adaptation to the improvement of on-line shopping systems. Over the last ten years she have co-authored an important number of scientific papers on software engineering, co-chaired several international workshops and conferences, and served in an important number of program committees for international conferences such as the International Conference on Software Engineering (ICSE) and the International Conference on Software Maintenance and Evolution (ICSME). She is the leader of the continuous improvement and accreditation processes for the Software Systems Engineering bachelor program of Universidad Icesi in Colombia.

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Stephanie Celis Gallego Universidad Icesi, Colombia

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She has a degree in mathematics from Universidad Santiago de Cali, a master's degree in mathematics education from Universidad del Valle and she is a specialist in university teaching at Icesi University. She has worked as a teaching coach for the public sector and advisor of pedagogical projects led by Universidad del Valle and the National Ministry of Education, with more than ten years of experience as a high school teacher at Colegio Bolivar. Her contributions in research in mathematics education, have focused mainly on the levels of difficulty associated with learning of school algebra, she has also led initiatives that contribute to inclusive curricular designs, based on the use of skills.

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Diego Antonio Bohórquez Universidad Icesi, Colombia

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Abstract

The concept of subspace, a subset of a vector space with two well-defined operations (sum and product by a scalar), can be considered as one of the most abstract, formal, and difficult concepts to learn by students, in an undergraduate linear algebra course for Science and Engineering programs. This paper presents the results of a case study in which we investigated how by using R^n to teach the concept of subspace, student learning performance can be improved. Our case study involved 36 students in 2 sections of a linear algebra course. One section in which the instructor used a conventional way to approach the subject by using traditional textbook-based lectures and examples, and a second section that uses the approach proposed in this paper. We evaluated the effectiveness of the proposed approach through qualitative evidence gathered by an external observer, the reflection made by the instructor himself, and through two tests that allowed us to assess student performance. The first test (diagnostic) was applied before the intervention to measure the level of attainment of prerequisites. The second test (closure) was applied after the intervention to measure the level of attainment of the learning objectives addressed in the case study. Findings demonstrate that our proposed approach effectively contributed to improve the level of attainment of learning objectives associated with the concept of subspace in linear algebra.

Sosa, A., & Villegas, N. M., & Gallego, S. C., & Bohórquez, D. A. (2020, June), On the Effectiveness of Designing Didactical Situations Targeting R^n to Teach the Concept of Subspace in Linear Algebra Paper presented at 2020 ASEE Virtual Annual Conference Content Access, Virtual On line . 10.18260/1-2--35008

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