From Scholarly Knowledge to Knowledge to be Taught: The Case of Vector Introduction

Enjun Junaeti, Dadang Juandi, Eka Fitrajaya Rahman, Joey Miranda Suba

Abstract


The incorporation of the contextualization and tangible instances in the diffusion of vector concepts in a textbook can lead to students forming a concept image that differs from the scientific understanding due to their perceptions and actions towards the learning environment. This study aims to expose potential learning obstacles in vector introduction caused by external didactic transposition through the study of textbook analysis. Meta-discourse served as the methodological analysis. Two textbooks were analyzed based on concept declaration, the changing environment, and didactic phenomena. Based on the concept declaration, the presence of an epistemological obstacle is a potential learning barrier. Additionally, changes in the learning environment can contribute to ontogenic obstacles. In conclusion, the analysis of the three textbooks reveals that potential learning obstacles encompass both ontogenic and epistemological aspects.


Keywords


Vector introduction; Scholarly knowledge; Knowledge to be taught; Didactic transposition; Concept declaration; Changing environment; Didactic phenomena

Full Text:

PDF

References


Andrilli, S., & Hecker, D. (2010). Elementary linear algebra 4th Edition. Academic Press Elsevier.

Anton, H., Rorres, C., & Kaul, A. (2019). Elementary linear algebra: applications version. John Wiley & Sons.

Açikyildiz, G., & Temel, K. Ö. S. A. (2021). Creating design principles of a learning environment for teaching vector spaces. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 12(1), 244-289.

Bækkelie, A. K. (2019). Can Computing Help Undergraduate Students Learn Linear Algebra? (Master's thesis).

Bianchini, B. L., de Lima, G. L., & Gomes, E. (2019). Linear algebra in engineering: an analysis of Latin American studies. ZDM, 51(7), 1097-1110.

Bouhjar, K., Andrews-Larson, C., & Haider, M. Q. (2021). An analytical comparison of students’ reasoning in the context of Inquiry-Oriented Instruction: The case of span and linear independence. The Journal of Mathematical Behavior, 64, 100908.

Boyd, S., & Vandenberghe, L. (2018). Introduction to applied linear algebra: vectors, matrices, and least squares. Cambridge university press.

Brousseau, G. (2002). Epistemological obstacles, problems, and didactical engineering. Theory of Didactical Situations in Mathematics: Didactique des Mathématiques, 1970–1990, 79-117.

Chaudhuri, A., Sinhababu, N., Sarma, M., & Samanta, D. (2021). Hidden features identification for designing an efficient research article recommendation system. International Journal on Digital Libraries, 22(2), 233-249.

Chevallard, Y. (2007). Readjusting didactics to a changing epistemology. European Educational Research Journal, 6(2), 131-134.

Chevallard, Y., & Bosch, M. (2020). Didactic transposition in mathematics education. Encyclopedia of mathematics education, 214-218.

Connell, E. H. (2002). Elements of abstract and linear algebra. EH Connell.

Dillon, M. I. (2022). Linear Algebra: Vector Spaces and Linear Transformations (Vol. 57). American Mathematical Society.

Friedberg, S. H., Insel, A. J., & Spence, L. E. (2019). Linear Algebra: Pearson New International Edition. Pearson Higher Ed.

Golan, J. S. (2007). The Linear Algebra. Springer.

Gosztolya, G. (2020). Using the fisher vector representation for audio-based emotion recognition. Acta Polytechnica Hungarica, 17(6), 7-23.

Groves, J. R. J., Hodgson, C. D., & Ghitza, A. (2015). Group Theory and Linear Algebra. Department of Mathematics and Statistics University of Melbourne.

Hefferon, J. (2006). Linear algebra. Saint Michael’s College Colchester, Vermont USA.

Hui, B., Zhang, L., Zhou, X., Wen, X., & Nian, Y. (2022). Personalized recommendation system based on knowledge embedding and historical behavior. Applied Intelligence, 1-13.

Kang, W., & Kilpatrick, J. (1992). Didactic transposition in mathematics textbooks. For the learning of Mathematics, 12(1), 2-7.

Kwak, J. H., & Hong, S. (2004). Linear algebra. Springer Science & Business Media.

Lang, S. (2010). Linear algebra. Springer.

Liesen, V. M. J., & Mehrmann, V. (2015). Linear Algebra. Wiesbaden, Germany: Springer.

Lyse-Olsen, E., & Fleischmann, Y. (2022). Modes of description and indicators of formalism in students' descriptions of eigenvectors. In Fourth conference of the International Network for Didactic Research in University Mathematics.

Matthews K.R. (1998). Elementary Linear Algebra. Department of Mathematics University of Queensland.

Maudy, S. Y. (2023). Transposisi Didaktik Berpikir Aljabar Awal (Doctoral dissertation, Universitas Pendidikan Indonesia).

Mutambara, L. H., & Bansilal, S. (2018). Dealing with the abstraction of vector space concepts. Challenges and strategies in teaching linear algebra, 147-173.

Oliveira, L. (2022). Linear Algebra. CRC Press_Chapman & Hall.

Panda, D. K., & Ray, S. (2022). Approaches and algorithms to mitigate cold start problems in recommender systems: a systematic literature review. Journal of Intelligent Information Systems, 59(2), 341-366.

Shah, A. (2021). Sentiment analysis of product reviews using supervised learning. Reliability: Theory & Applications, 16(SI 1 (60)), 243-253.

Suryadi, D. (2019). Landasan filosofis penelitian desain didaktis (DDR). Bandung: Pusat Pengembangan DDR Indonesia.

Tran, D. V. K. (2022). Basic Linear Algebra: An Introduction with an Intuitive Approach. Texas USA.

Wang, T., Li, J., Zhou, J., Li, M., & Guo, Y. (2022). Music Recommendation Based on “User-Points-Music” Cascade Model and Time Attenuation Analysis. Electronics, 11(19), 3093.

Wilson, E. B., & Gibbs, J. W. (1901). Vector analysis: a text-book for the use of students of mathematics and physics; founded upon the lectures of J. Willard Gibbs. C. Scribner's sons.




DOI: https://doi.org/10.17509/jds.v1i1.59019

Refbacks

  • There are currently no refbacks.


Journal of Didactic Studies https://ejournal.upi.edu/index.php/jds is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License

All rights reserverd. p-ISSN 2987-856X e-ISSN 2987-7512

Copyright © Universitas Pendidikan Indonesia (UPI)

Indonesian DDR Development Center
Directorate of Innovation and University Center of Excellence
Universitas Pendidikan Indonesia

 

Secretariat:
Building of CeO, 6th Floor
Jalan Dr. Setiabudhi 229, Bandung, West Java, 40154 Indonesia