Can Computing Help Undergraduate Students Learn Linear Algebra
Anne Katrine Bækkelie · Duo Research Archive (University of Oslo) · 2019
Computers have over the last century become a vital part of human society in many different aspects.As a result, computers have had a major impact on scientific research as a vital tool for solving problems, which before were unsolvable.In this thesis, I investigate how computational thinking may be beneficial for undergraduate students in understanding the concept rank in linear algebra.In order to explore this question, a qualitative study of four second-year students was performed.I found that working with programming exercises designed around exploring the concept rank, resulted in that the students' expanded their understanding of the concept.The study is analysed in light of theory of learning, theory of computational thinking and discussed in the context of the historical development of linear algebra.Specifically, the theory of Concept Image and the Structure of Observed Learning Outcomes(SOLO) taxonomy is used as an analytical and theoretical framework along with the concept tinkering, connected to computational thinking.The analytical framework worked well as a tool to investigate how the students were able to expand their concept image of rank.Something interesting to investigate further is how computations through mechanisms of tinkering can be used as a framework for exploring different subjects in undergraduate mathematics.i A special thanks go to the students participating in this research.It was enjoyable seeing how you had some fun while doing the exercises.Thank you, Geir for helping me out with creating the python script for the image compression, and to Konrad for all the times spent bouncing ideas back and forth.I am so grateful for Marte, Ingvild, Jakob and Arne who helped me by reading through the thesis and helping me improve it.Lastly, I need to thank all my friends and family who have supported me through this process.Especially Tor-Martin, I know you have been patient