The Opportunity to Learn Euclidean Geometry in Two Mathematics Textbooks of Tenth Grade in South Africa

Ugorji I. Ogbonnaya

doi:10.32939/ejrpm.v4i2.976

Ugorji I. Ogbonnaya University of Pretoria

DOI: https://doi.org/10.32939/ejrpm.v4i2.976

Keywords: Euclidean Geometry, Mathematics Textbook, Opportunity to Learn

Abstract

Textbooks play a central role in the teaching and learning of mathematics. In some schools, textbooks serve as the only resource material available to teachers and students. Nevertheless, little is known about the learning opportunities in mathematics textbooks in most countries. This study investigated the opportunities to learn Euclidean Geometry in two textbooks of tenth-grade mathematics in South Africa. It examined the content coverage, content organization, and the types of tasks used in teaching the topic in the textbooks. This study followed a case study research design and a qualitative approach. The Curriculum and Assessment Policy Statement's (CAPS) grade 10 Euclidean geometry curriculum and Gracin's mathematical activity types served as frameworks for the analyses. The data were analyzed following the deductive content analysis approach. The result shows that the contents of Euclidean geometry were well covered in both textbooks following the curriculum, and the contents were presented in logical and sequential order to enhance learning. In addition, it was found that the tasks in the textbooks were predominantly of argumentation and reasoning type. It was concluded that the textbooks offer sufficient opportunities for learning Euclidean geometry as specified in the curriculum for the grade level. However, the inclusion of a broader range of tasks in the future editions of the textbooks was recommended.

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References

Adeniji, S. M., Ameen, S. K., Dambatta, B. U., & Orilonise, R. (2018). Effect of Mastery Learning Approach on Senior School Students’ Academic Performance and Retention in Circle Geometry. International Journal of Instruction, 11(4), 951-962. https://doi.org/10.12973/iji.2018.11460a

Akiba, M., LeTendre, G. K., & Scribner, J. P. (2007). Teacher quality, opportunity gap, and national achievement in 46 countries. Educational Researcher, 36(7), 369–387. https://doi.org/10.3102/0013189X07308739

Alex, J. K. (2019). The Preparation of Secondary School Mathematics Teachers in South Africa: Prospective Teachers’ Student Level Disciplinary Content Knowledge. Eurasia Journal of Mathematics, Science and Technology Education, 15(12), em1791. https://doi.org/10.29333/ejmste/105782

Artmann, B. (2020, September 10). Euclidean geometry. Encyclopedia Britannica. https://www.britannica.com/science/Euclidean-geometry

Banicky, L. (2000). Opportunity to learn. Education Policy Brief, 7. Retrieved from https://udspace.udel.edu/bitstream/handle/19716/2446/opp%20to%20learn.pdf?sequence=1

Bayaga, A., Mthethwa, M., BossÃ, M., J. & Williams, D. (2020). Impacts of implementing GeoGebra on eleventh grade students learning of Euclidean Geometry. South African Journal of Higher Education, 33(6), 32-54. https://doi.org/10.20853/33-6-2824

Boston, M. D. & Wilhelm, A. G. (2017). Middle School Mathematics Instruction in Instructionally Focused Urban Districts. Urban Education, 52(7), 829–861. https://doi.org/10.1177/0042085915574528

Campbell, J. & McPetrie, S. (2012). Platinum Mathematics Grade 10 Learner's Book. Cape Town, South Africa: Maskew Miller Longman

Charalambous, C. Y., Delaney, S., Hsu, H.Y., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12(2), 117–151. https://doi.org/10.1080/10986060903460070

Department of Basic Education. (2011). Curriculum Assessment Policy Statement grades 10 to 12 Mathematics. Pretoria Department of Basic Education.

Department of Basic Education, (2019). National Senior Certificate Diagnostic Report: Part 1. Retrieved from: https://www.education.gov.za/Resources/Reports.aspx

Fitriani, N., Suryadi, D. & Darhim, D. (2018). Analysis of mathematical abstraction on concept of a three-dimensional figure with curved surfaces of junior high school students. Journal of Physics: Conference Series, 1132, 1-7. https://doi.org/10.1088/1742-6596/1132/1/012037

Gracin, D. G. (2018). Requirements in mathematics textbooks: a five-dimensional analysis of textbook exercises and examples. International journal of mathematical education in science and technology, 49(7), 1003–1024. https://doi.org/10.1080/0020739X.2018.1431849

Graves, K. (2000). Designing Language Course, A Guide for Teachers. Boston. Heinle. Cengage Learning.

Hadar, L. L. (2017). Opportunities to learn: Mathematics textbooks and students’ achievements. Studies in Educational Evaluation, 55 (2017), 153–166. https://doi.org/10.1016/j.stueduc.2017.10.002

Hadar, L. L. & Ruby, T. L. (2019). Cognitive opportunities in textbooks: the cases of grade four and eight textbooks in Israel. Mathematical Thinking and Learning, 21(1), 54-77. https://doi.org/10.1080/10986065.2019.1564968

Hong, D. S. & Choi, K. M. (2018). A comparative analysis of linear functions in Korean and American standards-based secondary textbooks. International journal of mathematical education in science and technology, 49(7), 1025–1051. https://doi.org/10.1080/0020739X.2018.1440327

Hong, D. S., Choi, K. M., Runnalls, C. & Hwang, J. (2020). Examining curricular coverage of volume measurement: A comparative analysis. International Journal on Social and Education Sciences, 2(1), 1-19. https://www.ijonses.net/index.php/ijonses/article/view/22/18

Houang, R. T., & Schmidt, W. H. (2008). TIMSS international curriculum analysis and measuring educational opportunities. 3rd IEA International Research Conference. Taipei: Chinese Taipei. Retrieved from https://www.iea.nl/publications/presentations/timss-international-curriculum-analysis-and-measuring-educational

Jones, L. D. & Tarr, J. E. (2007). An examination of the levels of cognitive demand required by probability tasks in middle grades mathematics textbooks. Statistics Education Research Journal, 6(2), 4-27. https://www.stat.auckland.ac.nz/~iase/serj/SERJ6(2)_Jones_Tarr.pdf

Krippendorff, K. (2018). Content analysis: An introduction to its methodology (4th ed.). California: Sage.

Lemmer, M., Edwards, J. & Rapule S. (2008). Educators’ selection and evaluation of natural sciences textbooks. South African Journal of Education, 28,175-187. Retrieved from: https://files.eric.ed.gov/fulltext/EJ1149996.pdf

Matheou, A. A., & Panaoura, R. (2021). Young Students’Ability on Understanding and Constructing Geometric Proofs. Social Education Research, 2(2), 121-133. https://doi.org/10.37256/ser.222021784

McDonnell, L.M. (1995). Opportunity to Learn as a Research Concept and a Policy Instrument. Educational Evaluation and Policy Analysis, 17(3), 305-322. https://doi.org/10.3102/01623737017003305

Mesa, V. (2004). Characterizing practices associated with functions in middle school textbooks: An empirical approach. Educational Studies in Mathematics, 56, 255–286. https://link.springer.com/article/10.1023/B:EDUC.0000040409.63571.56

Mohale, N. & Mafumbate, R. (2019). Effects of Resource Materials on Implementation of Life Skills Education Programme in Manzini Region High Schools of Eswatini. Journal of Education and Practice, 10(27), 46-53. https://www.iiste.org/Journals/index.php/JEP/article/view/49710/51357

Mukamba, E., & Makamure, C. (2020). Integration of GeoGebra in Teaching and Learning Geometric Transformations at Ordinary Level in Zimbabwe. Contemporary Mathematics and Science Education, 1(1), ep20001. https://doi.org/10.30935/conmaths/8431

Ngirishi, H., & Bansilal, S. (2019). An exploration of high school learners’ understanding of geometric concepts. Problems of Education in the 21st Century, 77(1), 82–96. https://doi.org/10.33225/pec/19.77.82

Otten, S., Gilbertson, N. J., Males, L. M., & Clark, D. L. (2014). The Mathematical Nature of Reasoning-and proving Opportunities in Geometry Textbooks. Mathematical Thinking and Learning, 16(1), 51-79. https://doi.org/10.1080/10986065.2014.857802

Pike, M., Barnes, H., Jawurek, A. Kitto, A., Laridon, P., Myburgh, M., Rhodes-Houghton, R., Scheiber, J., Sigabi, M. & Wilson, H. (2011). Classroom Mathematics Grade 10, Learner’s book. Sandton, South Africa: Heinemann Publishers

Polikoff, M. S. (2015). How well aligned are textbooks to the common core standards in mathematics? American Educational Research Journal, 52(6), 1185–1211. https://doi.org/10.3102%2F0002831215584435

Remillard, J. T. & Heck, D. J. (2014). Conceptualizing the curriculum enactment process in mathematics education. ZDM, 46(5),705–718. https://link.springer.com/article/10.1007/s11858-014-0600-4

Sherman, M. F., Walkington, C., & Howell, E. (2016). Brief report: A comparison of symbol-precedence view in investigative and conventional textbooks used in algebra courses. Journal for Research in Mathematics Education, 47(2), 134-146. https://doi.org/10.5951/jresematheduc.47.2.0134

Shongwe, B. (2019). The quality of argumentation in a Euclidean geometry context in selected South African high schools: validation of a research instrument. In N. Govender, R. Mudaly, T. Mthethwa & A. Singh-Pillay (Eds.), Research for inclusive, relevant, and equitable quality Mathematics, Science and Technology Education: Promoting research-based opportunity for all. Proceedings of 27th Annual Conference of the Southern African Association for Research in Mathematics, Science and Technology Education (pp. 98-112). Durban, South Africa

Stols, G. (2013). An investigation into the opportunity to learn that is available to Grade 12 mathematics learners. South African Journal of Education, 33(1), 1-18. http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0256-01002013000100006

Stols, G., Kriek, J. & Ogbonnaya, U. I., (2008). The relationship between teaching practices and students’ achievement in mathematics in Lesotho. African Journal of Research in Mathematics, Science and Technology Education,12 (special issue), 107-118. https://hdl.handle.net/10520/EJC92689

Stylianides, G. J. (2009). Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11(4), 258–288. https://doi.org/10.1080/10986060903253954

Tachie, S. A. (2020). The challenges of South African teachers in teaching euclidean geometry. International Journal of Learning, Teaching and Educational Research, 19(8), 297-312. https://doi.org/10.26803/ijlter.19.8.16

Ubah, I., & Bansilal, S. (2019). The use of semiotic representations in reasoning about similar triangles in Euclidean geometry. Pythagoras, 40(1), a480. https://doi.org/10.4102/pythagoras.v40i1.480

Valverde, G., Bianchi, L., Wolfe, R., Schmidt, W. & Houang, R. (2002). According to the Book: Using TIMSS to Investigate the Translation of Policy into Practice through the World of Textbooks. London: Kluwer Academic Publishers.

van Steenbrugge, H., Valcke, M., & Desoete, A. (2013). Teachers’ views of mathematics textbook series in Flanders: Does it (not) matter which mathematics textbook series schools choose? Journal of Curriculum Studies, 45(3), 322-353. https://doi.org/doi:10.1080/00220272.2012.713995

van Zanten, M. & van den Heuvel‑Panhuizen, M. (2018). Opportunity to learn problem-solving in Dutch primary school mathematics textbooks, ZDM 50(5), 827–838. https://doi.org/10.1007/s11858-018-0973-x

Weiss, I. R., Pasley, J. D., Smith, P. S., Banilower, E. R., & Heck, D. J. (2003). Looking inside the classroom: A study of K-12 mathematics and science education in the United States. Chapel Hill, NC: Horizon Research, Inc.

Wijaya, A., van den Heuvel-Panhuizen, M. & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educ Stud Math, 89, 41–65. https://doi.org/10.1007/s10649-015-9595-1

Yin, R. K. (2018). Case study research and applications: Design and methods (6th ed). California: SAGE Publications.