Abstract

Full paper prices: €32 / €24 / €60

Open Access price: €100

Symmetry: Culture and Science
Volume 34, Number 3, pages 251-280 (2023)
https://doi.org/10.26830/symmetry_2023_3_251

PUPILS’ RECOGNITION OF GEOMETRIC TESSELLATIONS AS PATTERNS OF TRADITIONAL CULTURE

Clement Ayarebilla Ali^1*, Ernest Kofi Davis²

¹ Department of Basic Education, University of Education, Winneba, GHANA
Email: ayarebilla@yahoo.com
ORCID: 0000-0002-3268-6452

² College of Education Studies, University of Cape Coast, GHANA
Email: ekdavis@ucc.edu.gh
ORCID: 0000-0001-5682-5835

^* corresponding author

Abstract: Tessellation is barely tackled in many primary schools. However, the curricula expect pupils to bridge the gaps between home mathematics and school mathematics. In this study, we explore geometric tessellations in the primary school mathematics. Even though there could exist other forms of tessellations, we present three main types of tessellations that could be explored for conceptual analysis of geometric tessellations. With a case study design involving 15 pupils through interviews and observations, the findings show that there abound many tessellations as patterns in Adinkra, Kente, Baskets and Smocks that could be harnessed to learn and apply geometric tessellations. We conclude that geometric tessellations present ample construct as patterns of traditional culture. We therefore recommend that many of the traditional cultures should be brought to bear on geometric tessellations. This will help primary pupils to extend learning and bridge the yawning gaps of home and school mathematics.

Keywords: Geometric tessellations, patterns, pupils’ cognition, traditional culture

References:
Acquaah, S., Amissah, E. R. K., and Yankson, P. G. (2017) Dress aesthetics of smock in northern Ghana: form, function, and context, Journal of Textile Engineering and Fashion Technology, 1(2), 68-77; doi: 10.15406/jteft.2017.01.00013

Adjei, K. and Ampong, R. A. (2021) Exploring Fry and Drew’s application of Ghanaian symbolism in architectural ornamentations: Case Study of Opku Ware and Prempeh Senior High Schools in Kumasi, Ghana, Journal of Science and Technology, 39 (1 and2), 88-99; http://dx.doi.org/10.4314/just.v39i1.7.

Adovasio, J.M. (1977) Basketry Technology: a guide to identification and analysis, Aldine, Chicago, available at https://core.tdar.org/document/117707/basketry-technology-a-guide-to-identification-and-analysis.

Ali, C. A., Adzifome, N. S., and Amihere, K. A. (2021) Learning, Teaching, and Applying Geometric and Handling Data, College of Distance and e-Learning, University of Education, Winneba.

Ali, C. A., and Davis, E. K. (2022) Applications of Basketry to Geometric Tessellations. 16thInternational Conference of the Mathematics Education for the Future Project, King’s College, Cambridge University, Aug 8-13, 2022.

Ali, C. A., and Davis, E. K. (2018) Harnessing Indigenous Basketry Resources for Prenumber and Early Number Work, Journal of Education and Learning, 7(2), 201-220; https://doi.org/10.5539/jel.v7n2p210.

Ampadu, J., Acquaye, R., and Adjei Appoh, G. (2022) Textile Design and Product Innovations from Adinkra and Bogolanfini Ideographic Mergers, Journal of Art and Design, 1(1), 28-45; https://doi.org/10.31586/jad.2022.231.

Aydın-Güç, F.; and Hacısalihoğlu-Karadeniz, M. (2020) Determination of Students’ Performance in Tessellations, Acta Didactica Napocensia, 13(1), 189-200; https://doi.org/10.24193/adn.13.1.17.

Baker, T. (2011) Zome Symmetry and Tilings, San Francisco State.

Cherry, K. (2022) What is a Case Study? An in-depth study of one person, group, or event. Retrieved from https://www.verywellmind.com/how-to-write-a-psychology-case-study-2795722.

Creswell, J.W. (2014). Research design: qualitative, quantitative, and mixed methods approach (4ed), Washington DC: SAGE Publications, Inc.

Davis, E. K., Bishop, A. J. and Seah, W.T. (2009) Gaps between inside school and out‐of‐school mathematics in Ghana, Mathematics Connection, 8(1), 1-16; https://doi.org/10.4314/mc.v8i1.61539.

Deger, K. O., and Deger, A. H. (2012) An application of mathematical tessellation method in interior designing, Procedia - Social and Behavioural Sciences, 51, 249-256; https://doi.org/10.1016/j.sbspro.2012.08.154.

Guo, Y. and Li, C. K. (2020) A Mathematical Study of Tessellations: The Art of Space Filling.

Leon, R., Nagel, W., Ohser, J., and Arscott, S. (2020) Modelling Crack Patterns by Modified STIT Tessellations, Image Analysis and Stereology, 39(1), 33-46, https://doi.org/10.5566/ias.2245.

Lloyd, K. (2017) Everything You Need To Know About Kente, Retrieved from KenteCloth.net.

Meyer, S, and Aikenhead, G. (2021) Indigenous Culture-Based School Mathematics in Action Part II: The Study’s Results: What Support Do Teachers Need? The Mathematics Enthusiast, 18(1-2), 119-138; https://doi.org/10.54870/1551-3440.1517.

Ministry of Education (2019) New Curriculum for Upper Primary (Basic 4-6). Accra: National Council for Curriculum and Assessment (NaCCA).

Mitchell, K. (1996) General Theorems: Regular and Semi-Regular Tilings; available at http://people.hws.edu/mitchell/tilings/Part3.html.

Mohammed, W. F. (2018) The Northern Smock: Threading, colour and design, Popula, retrieved from https://popula.com/2018/10/15/the-northern-smock/.

Panidapu, A. (2021) Many Symmetries of Tessellations ft. Harry’s Tiles, In: Gems in STEM: Tessellations, retrieved from https://www.cantorsparadise.com/tessellations-ft-harrys-tiles-4c41315649c8.

Saunders, M., Lewis, P. and Thornhill, A. (2012) Research Methods for Business Students (6thedition), Pearson Education Limited.

Thakur, S. and Chetty, P. (2020) How to establish the validity and reliability of qualitative research? retrieved from https://www.projectguru.in/how-to-establish-the-validity-and-reliability-of-qualitative-research/.

Twinkl.com (2023). Tessellation retrieved from https://www.twinkl.com.gh/teaching-wiki/tessellation.

Yu, L., and Zhang, H. (2018) Research on tessellation with triangle strip, AIP Conference Proceedings 1955, https://doi.org/10.1063/1.5033624.