Handling Difficult Topics in Linear Algebra Through Pedagogical Approaches

Abstract: Linear algebra is a fundamental branch of mathematics that plays a crucial role with a wide range of applications to the natural sciences, to engineering, to computer sciences, to management and social sciences, and more various fields. However, for many students, certain topics within linear algebra including include eigenvalues and eigenvectors, determinants, and abstract vector spaces. can be challenging to grasp. This paper explores nine (9) pedagogical approaches to effectively teach and learn these difficult topics, aiming to enhance students' understanding and retention of linear algebra concepts.

Linear algebra, difficult topics, pedagogical approaches

1. Abdurrahman, M. S., Abdullah, A. H., & Osman, S. (2020). Design and development of linear algebra peer tutoring strategy to develop students mathematical thinking processes based on experts’ evaluation. Universal journal of educational research, 8(8), 3592-3607. [Google Scholar] [Crossref]

2. Al-Mutawah, M. A., Thomas, R., Eid, A., Mahmoud, E. Y., & Fateel, M. J. (2019). Conceptual Understanding, Procedural Knowledge and Problem-Solving Skills in Mathematics: High School Graduates Work Analysis and Standpoints. International journal of education and practice, 7(3), 258-273. [Google Scholar] [Crossref]

3. Amiripour, P., Amir-Mofidi, S., & Shahvarani, A. (2012). Scaffolding as effective method for mathematical learning. Indian Journal of Science and Technology, 5(9). [Google Scholar] [Crossref]

4. Andam, E. A., Atteh, E., & Obeng-Denteh, W. (2016). The cooperative learning approach of solving word problems involving algebraic linear equations at Institute for Educational Development and Extension (IEDE), University of Education, Winneba, Ghana. Journal of Mathematical Acumen and Research, 1(1). [Google Scholar] [Crossref]

5. Bonanzinga, V. (2022). Some applications of linear algebra and geometry in real life. arXiv preprint arXiv:2202.10833. [Google Scholar] [Crossref]

6. Boyce, S., & O’Halloran, J. (2020). Active learning in computer-based college algebra. Primus, 30(4), 458-474. [Google Scholar] [Crossref]

7. Carlson, D., Johnson, C. R., Lay, D. C., & Porter, A. D. (1993). The Linear Algebra Curriculum Study Group recommendations for the first course in linear algebra. The College Mathematics Journal, 24(1), 41-46. [Google Scholar] [Crossref]

8. Harel, G. (2000). Principles of Learning and Teaching of Linear Algebra: Old and New Observations. (edit. J.-L. Dorier). On the Teaching of Linear Algebra (ss. 177-189). [Google Scholar] [Crossref]

9. Jimoyiannis, A. (2010). Designing and implementing an integrated technological pedagogical science knowledge framework for science teachers professional development. Computers & Education, 55(3), 1259-1269. [Google Scholar] [Crossref]

10. Konyalıoğlu, A. C. (2003). Investigation of effectiveness of visualization approach on understanding of concepts in vector spaces at the university level. Unpublished Doctoral Dissertation, Atatürk University, Institute of Natural and Applied Sciences, Erzurum. [Google Scholar] [Crossref]

11. Konyalioglu, A. C., Isik, A., Kaplan, A., Hizarci, S., & Durkaya, M. (2011). Visualization approach in teaching process of linear algebra. Procedia-Social and Behavioral Sciences, 15, 4040-4044. [Google Scholar] [Crossref]

12. Nachowitz, M. (2018). Scaffolding progressive online discourse for literary knowledge building. Online Learning, 22(3), 133-156. [Google Scholar] [Crossref]

13. National Research Council. (1993). Measuring what counts: A conceptual guide for mathematics assessment. National Academies Press. [Google Scholar] [Crossref]

14. Stacey, K., & Wiliam, D. (2012). Technology and assessment in mathematics. Third international handbook of mathematics education, 721-751. [Google Scholar] [Crossref]

15. Yilmaz, F., & Mierlus Mazilu, I. (2020). Some practical applications of matrices and determinants in real life. In 19th Conference on Applied Mathematics, Aplimat (pp. 814-823). [Google Scholar] [Crossref]

16. YILMAZ, F., Mierlus Mazilu, I., & Rasteiro, D. (2020). Solving real life problems using matrices and determinants. [Google Scholar] [Crossref]

• Anomaly Based Detection of Chronic Obstructive Pulmonary Disease Using Machine Learning
• Carbon Dioxide (CO2) Emission on Agricultural Land Use and its Impact on food Production
• Structural Characterization of High Resolution Aeromagnetic Data for Potentially Mineralized Zones Identification Within the North-Central Basement Complex of Nigeria
• Advancing U.S. Business Interests Abroad: Leveraging Technology to Optimize Cross-Border Operations
• Semi-Dynamic Mobile-Based Virtual Reality System for University