Mathematical Symbolization in Relation to Arts and Culture

Peter Okoth Oyoo

doi:10.37284/eajes.8.1.2588

Peter Okoth Oyoo Jaramogi Oginga Odinga University of Science and Technology

DOI: https://doi.org/10.37284/eajes.8.1.2588

Keywords: Constructivist, Ecological System, Mathematical Symbol, Multiple Representation

Share Article:

Abstract

This paper stems from an analysis of a larger study that explored proficiency in mathematical symbolization and presents students’ representational fluency in using mathematical symbols concerning arts and culture. The research had the potential of revealing the conception of symbols by students, the thick line interconnection between mathematics and arts and underscoring mathematics symbols in the perspective of arts. The study objectives comprised finding out whether culture has mathematical concepts and how students conceive mathematical symbols concerning culture and traditions. The analysis made use of constructivist learning and ecological system theory as conceptual frameworks in lensing the study. The qualitative case study research design examined multiple representations of symbols among students in secondary schools and reported in light of symbols’ interconnections to the perspective of the arts. The findings of the study show that students are aware of mathematics concepts and their origin in the communities’ culture and prior knowledge of symbols contributes to challenges and tenacity in multiple representations of symbols in aspects of supportive and problematic conception. Discussion of these findings concerning performance in mathematics in the Kenya Certificate of Secondary Education (KCSE) may be owed to long-term negative effects on students’ understanding of mathematical symbolizations which in turn could impact achievement in mathematics. The study may be useful in recommending that emphasis could be put on better ways of integrating diverse cultures in the mathematics curriculum through curriculum documentation such as textbooks to enhance mathematical symbols’ conceptual understanding among students and reduce symbol cognitive load through proper pedagogical design

Downloads

Download data is not yet available.

References

Arcavi, A. (1994). Symbol Sense: Informal Sense-making in Formal Mathematics. FLM Publishing Association, 14(3), 24–25.

Arisetyawan, A., Suryadi, D., Herman, T., & Rahmat, C. (2014). Study of Ethnomathematics: A lesson from the Baduy Culture. 2(10), 8.

Bardini, C., & Pierce, R. (2015). Assumed Mathematics Knowledge: The Challenge of Symbols. International Journal of Innovation in Science and Mathematics Education (Formerly CAL-Laborate International), 23(1), 1–9.

Barton, B. (1996). Making sense of ethnomathematics: Ethnomathematics is making sense. Educational Studies in Mathematics, 31(1–2), 201–233.

Bishop, A. H. (1988). Mathematics enculturation. Kluwer Academic Publisher.

Bowen, G. A. (2009). Document Analysis as a Qualitative Research Method. Qualitative Research Journal, 9(2), 27–40. https://doi.org/10.3316/QRJ0902027

Chin, K. E., & Pierce, R. (2019). University Students’ Conceptions of Mathematical Symbols and Expressions. EURASIA Journal of Mathematics, Science and Technology Education, 15(9), 1–12. https://doi.org/10.29333/ejmste/103736

Cobb, P. (2002). Modeling, Symbolizing, and Tool Use in Statistical Data Analysis. In K. Gravemeijer, R. Lehrer, B. Van Oers, & L. Verschaffel (Eds.), Symbolizing, Modeling and Tool Use in Mathematics Education (pp. 171–195). Springer Netherlands. https://doi.org/10.1007/978-94-017-3194-2_11

d’Entremont, Y. (2015). Linking Mathematics, Culture and Community. Procedia - Social and Behavioral Sciences, 174, 2818–2824. https://doi.org/10.1016/j.sbspro.2015.01.973

De Cruz, H., & De Smedt, J. (2013). Mathematical Symbols as Epistemic Actions. Synthese, 190(1), 3–19. https://doi.org/10.1007/s11229-010-9837-9

Erfle, S. E. (2021). Using Archimedean Spirals to Explore Fractions. 6.

Ezeife, A. N. (2013). Culture-sensitive Mathematics: The Walpole Island Experience. 3, 17.

Fonger, N. L. (2019). Meaningfulness in representational fluency: An analytic lens for students’ creations, interpretations and connections. 5.

Godino, J. D., & Batanero, C. (2003). Semiotic Functions in Teaching and Learning.

Gray, E., & Tall, D. (1994). Relationships between embodied objects and symbolic procepts: An explanatory theory of success and failure in mathematics. 8.

Harris, H. (2001). Content Analysis of Secondary Data: A Study of Courage in Managerial Decision Making. Journal of Business Ethics, 191–208.

Jiew, F. F., & Chin, K. E. (2020). Supportive and Problematic Conceptions in Making Sense of Multiplication: A Case Study. 17(1), 141–165.

Kaput, J. J., & Shaffer, D. W. (2002). On the Development of Human Representational Competence from an Evolutionary Point of View. In K. Gravemeijer, R. Lehrer, B. Van Oers, & L. Verschaffel (Eds.), Symbolizing, Modeling and Tool Use in Mathematics Education (pp. 277–293). Springer Netherlands. https://doi.org/10.1007/978-94-017-3194-2_17

Kharde, U. D. (2016). The Symbolic Language of Mathematics. 01(1), 3.

KIE. (2002). Secondary Education Syllabus. KIE, Nairobi, Kenya, 2.

Kilpatrick, J., Swafford, J., Findell, B., National Research Council (U.S.), & Mathematics Learning Study Committee. (2001). Adding it up: Helping children learn mathematics. National Academy Press. https://openlibrary.org/books/OL17062503M

Mamolo, A. (2010). Polysemy of Symbols: Signs of Ambiguity. The Montana Mathematics Enthusiast, 7(2), 247–262.

Mbugua, Z. K. (2012). Influence of Mathematical Language on Achievement in Mathematics by Secondary School Students in Kenya. International Journal of Education and Information Studies, 2(1), 1–7.

Momanyi, B. D. (2018). Application of Abagusii Cultural Practices into Teaching and Learning of Mathematics in Secondary Schools in Masaba North Sub-County, Kenya. Kenyatta University.

Moschkovich, J. (2006). Using Two Languages When Learning Mathematics. Educational Studies in Mathematics, 64(2), 121–144. https://doi.org/10.1007/s10649-005-9005-1

Moschkovich, J. N. (2008). “I Went by Twos, He Went by One”: Multiple Interpretations of Inscriptions as Resources for Mathematical Discussions. Journal of the Learning Sciences, 17(4), 551– 587. https://doi.org/10.1080/10508400802395077

Mulwa, E. C. (2014). The Role of the Language of Mathematics in Students’ Understanding of Number Concepts in Eldoret Municipality, Kenya. International Journal of Humanities and Social Science, 4(3), 11.

Mulwa, E. C. (2015). Difficulties Encountered by Students in the Learning and Usage of Mathematical Terminology: A Critical Literature Review. 6(13), 12.

Nogueira de Lima, R., & Tall, D. (2008). Procedural Embodiment and Magic in Linear Equations. Educational Studies in Mathematics, 67(1), 3–18. https://doi.org/10.1007/s10649-007-9086-0

Paquette, D., & Ryan, J. (2001). Bronfenbrenner’s Ecological Systems Theory. 59.

Peter, E. E., & Olaoye, A. A. (2013). Symbolic notations and students’ achievements in algebra. 8(15), 1294–1303.

Pierce, R., & Stacey, K. (2004). Monitoring Progress in Algebra in a CAS Active Context: Symbol Sense, Algebraic Insight and Algebraic Expectation. International Journal for Technology in Mathematics Education, 11(1).

Rosa, M., & Orey, D. (2013). Culturally relevant pedagogy as an ethnomathematical approach. Journal of Mathematics and Culture, 7(1), 74–97.

Serfati, M. (2005). La constitution de la pensee symbolique mathematique. Une etude epistemologique. 1192–1207.

Skemp, R. R. (1976). Relational and instrumental understanding.Mathematics Teaching. 77, 16.

Sullivan, P. (2013). Characterizing the Nature of Students’ Feature Noticing-and-Using with Respect to Mathematical Symbols Across Different Levels of Algebra Exposure. Pennsylvania State University.

Tegegne, H. R. (2015). Everyday Mathematics in Ethiopia: The Case of the Khimra People. 270.