VARIETY OF ARRANGEMENTS OF NUMERICAL DATA FOR A DEEPER UNDERSTANDING OF MATHEMATICS

Pēteris Daugulis, Elfrīda Krastiņa, Anita Sondore, Vija Vagale

Abstract


Effective arranging of numerical data and design of associated computational algorithms are important for any area of mathematics for teaching, learning and research purposes. Usage of various algorithms for the same area makes mathematics teaching goal-oriented and diverse. Matrices and linear-algebraic ideas can be used to make algorithms visual, two dimensional (2D) and easy to use. It may contribute to the planned educational reforms by teaching school and university students deeper mathematical thinking. In this article we give novel data arranging techniques (2D and 3D) for matrix multiplication. Our 2D method differs from the standard, formal approach by using block matrices. We find this method a helpful alternative for introducing matrix multiplication. We also give a new innovative 3D visualisation technique for matrix multiplication. In this method, matrices are positioned on the faces of a rectangular cuboid. Computerized implementations of this method may be considered as student project proposals.

 


Keywords


block matrix; data arranging; linear algebra; mathematics education; matrix multiplication; rectangular cuboid; scalar product

Full Text:

PDF

References


Agarwal, R.P., & Sen, S.K. (2014). Creators of Mathematical and Computational Sciences. New York: Springer.

Andrilli, S., & Hecker, D. (2003). Elementary linear algebra. USA: Elsevier.

Blyth, T., & Robertson, E. (2002). Basic linear algebra (2nd edition).UK: Springer Verlag London Limited.

Boag, E. (2007). Lattice Multiplication. BSHM Bulletin: Journal of the British Society for the History of Mathematics, 22(3), 182-184.

Curtis, C. (1984). Linear algebra - an introductory approach. USA: Springer Science Business Media.

Daugulis, P. (1998). Stable endomorphism rings of idempotent E-modules. PhD thesis, University of Georgia, Athens, USA.

Daugulis, P., & Sondore, A. (2017). Visualizing matrix multiplication. PRIMUS. 28(1),90-95.

Kangro, A., & Kiseļova, R. (2019). Latvija OECD Starptautiskajā skolēnu novērtēšanas programmā PISA 2018 – pirmie rezultāti un secinājumi. Rīga. Pieejams: https://www.izm.gov.lv/images/aktualitates/2019/OECD_PISA_2018.pdf

KM (2018). Kolektīvā monogrāfija „Mācīšanās lietpratībai”. LU Akadēmiskais apgāds. Zin., red. D. Namsone. Pieejams: https://www.siic.lu.lv/petnieciba/monografija-macisanas-lietpratibai/

Mārtinsone, K., Pipere, A., & Kamerāde D. (2016). Pētniecība: teorija un prakse. Rīga: Raka.

Matrix-Matrix Multiplication on the GPU with Nvidia CUDA. (2019). Retrieved from

https://www.quantstart.com/articles/Matrix-Matrix-Multiplication-on-the-GPU-with-Nvidia-CUDA

NRC (2012). Education for Life and Work: Developing transferable knowledge and skills in the 21st century. In Pellegrino, J. W., & Hilton, M. L. (eds.). Committee on Defining Deeper Learning and 21st Century Skills, National Research Council (NRC). Retrieved from https://www.nap.edu/resource/13398/dbasse_070895.pdf

Robinson, D. (2006). A course in linear algebra (2nd edition). Singapore: World Scientific Publishing.

Skola2030. (2019). Mācīšanās iedziļinoties. Pieejams: https://www.skola2030.lv/lv/istenosana/macibu-pieeja/macisanas-iedzilinoties

Sondore, A., Krastiņa, E., Daugulis, P., Drelinga, E. (2016). Pamatjēdzienu izpratne skolas matemātikas kompetenču apguvē. Society.Integration.Education. Proceedings of the International Scientific Conference, Volume II, 330-342. DOI: http://dx.doi.org/10.17770/sie2018vol1.3276

Sondore, A., Krastiņa, E., Daugulis, P., & Drelinga, E. (2017). Improving Mathematical Competence in Primary School to Enable Skill Transfers in New Situations. Proceedings of the International Scientific Conference "Society.Integration.Education", Volume II, 208-218. DOI: http://dx.doi.org/10.17770/sie2018vol1.3276

Strazdiņš, I. (1980). Diskrētās matemātikas pamati. Rīga: Zvaigzne.

Šteiners, K., Siliņa, B. (1997). Augstākā matemātika. I daļa. Rīga: Zvaigzne ABC.




DOI: http://dx.doi.org/10.17770/sie2020vol1.5081

Refbacks

  • There are currently no refbacks.