A constructivist approach to trigonometry problem solving using Manipulatives: a case study of a South African secondary school

Abstract

Trigonometry is currently an examinable section in the subject of mathematics and is assessed in grade 12 examinations. This study addresses the challenge that teachers’ knowledge and the supply of quality learning support material is inadequate in trigonometry in secondary schools The purpose is to determine how Mathematical models/manipulatives helped grade 12 learners adopt more interactive approaches toward the learning of three-dimensional trigonometric problems and whether the use of models improves the learning of mathematics. The study used a qualitative approach with a case study research design. The interpretive paradigm framed the analysis of the learners' interactions with the Mathematical manipulatives. This case study was conducted at a school in KwaZulu-Natal (n=16) in South Africa. Grade 12 mathematics learners participated in the research, engaging in qualitative assessments in structured activity worksheets consisting of questions on 3-dimensional trigonometric problems and semi-structured interviews. Findings emanating from the data analysis reveal that the use of manipulatives is beneficial to learners when solving 3D trigonometric problems and suggest that the use of manipulatives shows a reduction in task difficulty by linking the concrete to the abstract, and manipulatives encourage mathematical fluency.

Keywords: {'name': 'Empowerment; Model Design; Cocoa Oil Small-sized Industries; Problems and Solution; Business Perspective'}

Authors & affiliations

Caresse Niranjan
University of South Africa

Deonarain Brijlall
Durban University of Technology

Deposited references

Supplied references, not a list of publications citing this article.

DOI: 10.29333/mathsciteacher/13698

DOI: 10.1080/18146627.2015.1110893

Bruner, J. S. (1966). Toward a theory of instruction (Vol. 59). Harvard University Press.

DOI: 10.1080/09500693.2011.645514

DOI: 10.12973/eurasia.2015.1396a

DOI: 10.1080/2331186X.2024.2379712

DOI: 10.1177/10534512050410010501

DOI: 10.29333/iji.2021.14132a

DOI: 10.1088/1742-6596/1918/4/042148

Jones, J. P., & Tiller, M. (2017). Using concrete manipulatives in mathematical instruction. Dimensions of Early Childhood, 45(1), 18–23.

Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. The National Academies Press.

DOI: 10.5539/jel.v5n3p10

DOI: 10.26711/007577152790026

Luneta, K., & Makonye, J. P. (2011). Undergraduate students' preferences of knowledge to solve particle mechanics problems. Journal of Science and Mathematics Education in Southeast Asia, 34(2), 237–261.

DOI: 10.1080/00405840701593899

Motshekga, A. (2012, January 30). Keynote address at the Public Sector Managers Forum. Department of Basic Education. http://www.education.gov.za

National Senior Certificate School Subject Report. (2019). Department of Basic Education. http://www.education.gov.za

Niranjan, C. (2022). The use of models to develop skills to solve 3D trigonometry problems: A case study of Grade 12 learners in a selected school in the Pinetown District [Doctoral dissertation, Durban University of Technology].

DOI: 10.63301/tme.v18i1.1923

DOI: 10.1007/978-3-642-46323-5_2

DOI: 10.1080/0020739X.2011.622798

DOI: 10.1007/BF03217474

DOI: 10.1177/01626434241263055

DOI: 10.1111/j.1949-8594.2010.00046.x

Witzel, B. S. (2005). Using CRA to teach algebra to students with math difficulties in inclusive settings. Learning Disabilities: A Contemporary Journal, 3(2), 49–60.