Article Sidebar

Download
PDF
Statistic
Read Counter : 901 Download : 561

Downloads

Download data is not yet available.

Main Article Content

Abstract

In this paper, we explored the type of mathematical connections Grade 11 learners make when solving two-dimensional (2D) trigonometric problems in an Activity-Based Learning (ABL) environment. We followed a qualitative case study design within an interpretive paradigm. Convenience sampling was used to select a whole class of 45 Grade 11 learners from one of the public non-fee-paying secondary schools in Capricorn District, Limpopo Province of South Africa. Group work presentations and classroom interactions were used to collect data. Data were analyzed using deductive thematic analysis guided by the mathematical connections’ framework. The findings indicated that learners managed to make procedural, meaning, reversibility, different representations, feature, and inclusion part whole as well as integrated connections as they worked on 2D trigonometric problems in an ABL environment. We established that learners did not make generalization part-whole connections. In addition, we found that some learners lacked mathematical connections skills and failed to solve the problems. Engaging learners in an ABL environment provided a fine-grained approach that allowed them to make mathematical connections. We, therefore, recommend that teachers should create an ABL environment to enable learners to make different types of mathematics connections during the teaching and learning of trigonometric concepts.

Keywords

Activity-Based Learning environment Deductive Thematic Analysis Integrated Mathematical Connections Mathematical Connection Skills Two-Dimensional Trigonometry

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite
Maphutha, K., Maoto, S., & Mutodi, P. (2023). Exploring grade 11 learners’ mathematical connections when solving two-dimensional trigonometric problems in an activity-based learning environment. Journal on Mathematics Education, 14(2), 293–310. https://doi.org/10.22342/jme.v14i2.pp293-310
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX

References

  1. Akkuş, Z. (2015). Activity-based teaching in social studies education: An action research. Educational Research and Reviews, 10(14), 1911-1921. https://doi.org/10.5897/ERR2015.2261
  2. Andrade, C. (2021). The inconvenient truth about convenience and purposive samples. Indian Journal of Psychological Medicine, 43(1), 86-88.
  3. Anwer, F. (2019). Activity-based teaching, student motivation and academic achievement. Journal of Education and Educational Development, 6(1), 154-170.
  4. Ayunani, D. S., & Indriati, D. (2020). Analyzing mathematical connection skills in solving a contextual problem. Journal of Physics: Conference Series, 1511(1), 012095. https://doi.org/10.1088/1742-6596/1511/1/012095
  5. Bayu, C. P., Yohanie, D. D., & Handayani, A. D. (2021). Analysis of student errors in solving comparative trigonometry problems of right-angled triangles based on Watson’s criteria. Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah di Bidang Pendidikan Matematika, 7(2), 161-171. https://doi.org/10.29407/jmen.v7i2.16247
  6. Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative research in psychology, 3(2), 77-101.
  7. Brophy, J., & Alleman, J. (1991). Activities as instructional tools: A framework for analysis and evaluation. Educational researcher, 20(4), 9-23.
  8. Businskas, A. (2008). Conversations about connections: How secondary mathematics teachers conceptualise and contend with mathematical connections. Unpublished doctoral dissertation. Simon Fraser University, Burnaby, Canada. Available from http://ir.lib.sfu.ca/handle/1892/10579
  9. Cai, J. & Ding, M. (2017). On mathematical understanding: perspectives of experienced Chinese mathematics teachers. Journal of Mathematics Teacher Education, 20, 5–29. https://doi.org/10.1007/s10857-015-9325-8
  10. Çelik, H. C. (2018). The effects of activity-based learning on sixth-grade students’ achievement and attitudes towards mathematics activities. Eurasia Journal of Mathematics, Science and Technology Education, 14(5), 1963-1977. https://doi.org/10.29333/ejmste/85807
  11. Davis, R. B., & Maher, C. A. (2013). How students think: The role of representations. In Mathematical Reasoning (pp. 101-124). Routledge
  12. Department of Basic Education (DBE). (2011). Curriculum and Assessment Policy Statement (CAPS) Grades 10−12: Government printing works.
  13. Department of Basic Education (DBE). (2018). Mathematics Teaching and Learning Framework for South Africa. Teaching Mathematics for Understanding: Government printing works.
  14. Department of Basic Education (DBE). (2022). 2021 National Senior Certificate- diagnostic report. Pretoria: Government printing works.
  15. Department of Education (DoE). (2003). Mathematics Subject Assessment Guidelines: Grades 10-12 (General). Pretoria: Department of Education
  16. Dudung, A., & Oktaviani, M. (2020). Mathematical connection ability: An analysis based on test forms. International Journal of Advanced Science and Technology, 29(6), 4694-4701.
  17. Festus, A. B. (2013). Activity-Based learning strategies in the mathematics classrooms. Journal of Education and Practice, 4(13), 8 - 14.
  18. Fujita, T., Kondo, Y., Kumakura, H., Kunimune, S., & Jones, K. (2020). Spatial reasoning skills about 2D representations of 3D geometrical shapes in grades 4 to 9. Mathematics Education Research Journal, 32, 235-255.
  19. García-García, J., & Dolores-Flores, C. (2018). Intra-mathematical connections made by high school learners in performing Calculus tasks. International Journal of Mathematical Education in Science and Technology, 49(2), 227-252. https://doi.org/10.1080/0020739X.2017.1355994
  20. García-García, J., & Dolores-Flores, C. (2021). Pre-university learners’ mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33(1), 1-22. https://doi.org/10.1007/s13394-019-00286-x
  21. González-Martín, A. S., Gueudet, G., Barquero, B., & Romo-Vázquez, A. (2021). Mathematics and other disciplines, and the role of modelling: Advances and challenges. Research and Development in University Mathematics Education, 169-189.
  22. Hasbi, M., Lukito, A., Sulaiman, R., & Muzaini, M. (2019). Improving the mathematical connection ability of middle-school students through realistic mathematics approach. Journal of Mathematical Pedagogy (JoMP), 1(1), 37-46. https://doi.org/10.26740/jomp.v1n1.p37-46
  23. Hatisaru, V. (2022). Mathematical connections are established in the teaching of functions. Teaching Mathematics and its Applications: An International Journal of the IMA. 1-21.
  24. Hine, G. (2021). Making mathematical connections. Teaching Secondary Mathematics, 61. https://doi.org/10.1093/teamat/hrac013
  25. Huang, R., Spector, J. M., & Yang, J. (2019). Designing learning activities and instructional systems. In Educational Technology (pp. 125-147). Springer. https://doi.org/10.1007/978-981-13-6643-7_8
  26. Iyamuremye, E., Ndayambaje, I., & Muwonge, C. M. (2021). Influence of teaching approaches on students’ performance in mathematics: A meta-analysis of quasi-experimental studies in Africa. African Journal of Educational Studies in Mathematics and Sciences, 17(2), 73-94.
  27. Jackson, D., Fleming, J., & Rowe, A. (2019). Enabling the transfer of skills and knowledge across classroom and work contexts. Vocations and Learning, 12(3), 459-478. https://doi.org/10.1007/s12186-019-09224-1
  28. Jawad, L. F. (2022). Mathematical connection skills and their relationship with productive thinking among secondary school students. Periodicals of Engineering and Natural Sciences, 10(1), 421-430
  29. Kamber, D., & Takaci, D. (2018). On problematic aspects in learning trigonometry. International Journal of Mathematical Education in Science and Technology, 49(2), 161-175. https://doi.org/10.1080/0020739X.2017.1357846
  30. Karapetian, A. O. (2020). Creating ESP-based language learning environment to foster critical thinking capabilities in students' papers. European Journal of Educational Research, 9(2), 717-728. https://doi.org/10.12973/eu-jer.9.2.717
  31. Karnasih, I., & Sinaga, M. (2014). Enhancing mathematical problem-solving and mathematical connection through the use of dynamic software autograph in cooperative learning think-pair-share. The Journal of the Association for Science and Mathematics Education, 17, 51-71.
  32. Kenedi, A. K., Helsa, Y., Ariani, Y., Zainil, M., & Hendri, S. (2019). Mathematical connection of elementary school students to solve mathematical problems. Journal on Mathematics Education, 10(1), 69-80. https://doi.org/10.22342/jme.10.1.5416.69-80
  33. Khairunnisak, C., Hasbi, M., Mustika, A., & Elizar, E. (2020). Students’ mathematical connection ability in the learning employing contextual teaching and learning. Journal of Physics: Conference Series, 1460(1), 012028. https://doi.org/10.1088/1742-6596/1460/1/012028
  34. Khurana, S. (2015). Activity-Based Learning (ABL): How it can be a recipe for success in mathematics? International Journal of Education and Psychological Research (IJEPR), 4(3), 91–95.
  35. Kleden, M. A., Sugi, Y., & Samo, D. D. (2021). Analysis of mathematical connections ability on junior high school students. International Journal of Educational Management and Innovation, 2(3), 261-271.
  36. Liljedahl, P., Santos-Trigo, M., Malaspina, U, & Bruder, R. (2016). Problem-solving in Mathematics Education, ICME-13 Topical Surveys, Springer. https://doi.org/10.1007/978-3-319-40730-2
  37. Mabena, N., Mokgosi, P. N., & Ramapela, S. S. (2021). Factors contributing to poor learner performance in mathematics: A case of selected schools in Mpumalanga Province, South Africa. Problems of Education in the 21st Century, 79(3), 451. https://doi.org/10.33225/pec/21.79.451
  38. Maphutha, K., Maoto, S., & Kibirige, I. (2022). The effect of the activity-based approach on grade 11 learners’ performance in solving two-dimensional trigonometric problems. Eurasia Journal of Mathematics, Science and Technology Education, 18(10), em2155. https://doi.org/10.29333/ejmste/12405
  39. Marufi, M., Ilyas, M., Ikram, M., Rosidah, R., & Kaewhanam, P. (2022). Exploration of high school students' reasoning in solving trigonometric function problems. Al-Jabar: Jurnal Pendidikan Matematika, 13(2), 231-249. https://doi.org/10.24042/ajpm.v13i2.12972
  40. Menanti, H., & Sinaga, B. (2018). Improve mathematical connections skills with realistic mathematics education based learning. In 3rd Annual International Seminar on Transformative Education and Educational Leadership (AISTEEL 2018) (pp. 29-35). Atlantis Press. https://doi.org/10.2991/aisteel-18.2018.7
  41. Nabilah, R. G. S., Suhendra, S., & Yulianti, K. (2019). The efforts of improving the mathematical connection ability of senior high school students with the 7e learning cycle model. Journal of Physics: Conference Series, 1157(4), 042096. https://doi.org/10.1088/1742-6596/1157/4/042096
  42. Nanmumpuni, H. P., & Retnawati, H. (2021). Analysis of senior high school students’ difficulty in resolving trigonometry conceptual problems. Journal of Physics: Conference Series, 1776(1), 012012. https://doi.org/10.1088/1742-6596/1776/1/012012
  43. Ngu, B. H., & Phan, H. P. (2020). Learning to solve trigonometry problems that involve algebraic transformation skills via learning by analogy and learning by comparison. Frontiers in Psychology, 11, 558773. https://doi.org/10.3389/fpsyg.2020.558773
  44. Noreen, R., & Rana, A. M. K. (2019). Activity-based teaching versus traditional method of teaching in mathematics at elementary level. Bulletin of Education and Research, 41(2), 145-159.
  45. Nwoke, B. L. (2021). Enhancing primary school pupils' mathematics creative ability through activity-based learning approach. Malikussaleh Journal of Mathematics Learning (MJML), 4(2), 70-76. https://doi.org/10.29103/mjml.v4i2.5707
  46. Pambudi, D. S., Budayasa, I. K., & Lukito, A. (2020). The role of mathematical connections in mathematical problem-solving. Jurnal Pendidikan Matematika, 14(2), 129-144. https://doi.org/10.22342/jpm.14.2.10985.129-144
  47. Pokhrel, T. R. (2018). Activity-Based Mathematics Instruction: Experiences in Addressing the 21st-Century Skills. Journal of Mathematics Education, 11(1), 46-61. https://doi.org/10.26711/007577152790020
  48. Putra, H. D., Setiawan, W., & Afrilianto, M. (2020). Indonesian high scholars difficulties in learning mathematics. International Journal of Scientific & Technology Research, 9(1), 3466-3471.
  49. Quilang, L. J. L., & Lazaro, L. L. (2022). Mathematical Connections Made during Investigative Tasks in Statistics and Probability. International Journal of Evaluation and Research in Education, 11(1), 239-249. https://doi.org/10.11591/ijere.v11i1.21730
  50. Richards, A. J., Jones, D. C., & Etkina, E. (2020). How learners combine resources to make conceptual breakthroughs. Research in Science Education, 50(3), 1119-1141. https://doi.org/10.1007/s11165-018-9725-8
  51. Rodríguez-Nieto, C. A., Font Moll, V., Borji, V., & Rodríguez-Vásquez, F. M. (2022). Mathematical connections from the networking of theories between the extended theory of mathematical connections and the onto-semiotic approach. International Journal of Mathematical Education in Science and Technology, 53(9), 2364-2390. https://doi.org/10.1080/0020739X.2021.1875071
  52. Rohmah, S., Kusmayadi, T. A., & Fitriana, L. (2020). Mathematical connections ability of junior high school students viewed from mathematical resilience. Journal of Physics: Conference Series, 1538(1), 012106. https://doi.org/10.1088/1742-6596/1538/1/012106
  53. Saleh, S., Purwanto, P., Sudirman, S., Hidayanto, E., & Susiswo, S. (2018). Elementary School Teachers' Mathematical Connections in Solving Trigonometry Problem. Research in Social Sciences and Technology, 3(3), 32-41. https://doi.org/10.46303/ressat.03.03.3
  54. Saminanto, K., & Kartono, K. (2015). Analysis of mathematical connection ability in linear equation with one variable based on connectivity theory. International Journal of Education and Research, 3(4), 259-270.
  55. Sarkam, S. F., Abas, N., Daud, S. R., Mohamed, N. A., & Wahab, N. A. (2019). Lecturer support and self-efficacy on students’ off-classroom training effectiveness. Jurnal Intelek, 14(2), 58-67. https://doi.org/10.24191/ji.v14i2.8518
  56. Selvianiresa, D., & Prabawanto, S. (2017). Contextual teaching and learning approach of mathematics in primary schools. Journal of Physics: Conference Series, 895(1), 012171. https://doi.org/10.1088/1742-6596/895/1/012171
  57. Setiawan, Y. E. (2022). Prospective teachers’ representations in problem-solving of special angle trigonometry functions based on the level of ability. Infinity Journal, 11(1), 55-76. https://doi.org/10.22460/infinity.v11i1.p55-76
  58. Setiawan, Y. E., & Surahmat, S. (2021). Error analysis of prospective mathematics teachers in solving of applying radian measurement problem in trigonometry courses. Al-Jabar: Jurnal Pendidikan Matematika, 12(2), 343-357. https://doi.org/10.24042/ajpm.v12i2.9874
  59. Spangenberg, E. D. (2021). Manifesting of pedagogical content knowledge on trigonometry in teachers' practice. Journal of Pedagogical Research, 5(3), 135-163.
  60. Stake, R. E. (1995). The art of case study research. Sage.
  61. Tularam, G. A. (2018). Traditional vs Non-traditional Teaching and Learning Strategies-the case of E-learning!. International Journal for Mathematics Teaching and Learning, 19(1), 129-158.
  62. Wardhani, T. A. W., & Argaswari, D. P. (2022). High School Students’ error In Solving Word Problem Of Trigonometry Based On Newman Error Hierarchical Model. Infinity Journal, 11(1), 87-102. https://doi.org/10.22460/infinity.v11i1.p87-102
  63. Williams, J., & Choudry, S. (2016). Mathematics capital in the educational field: Bourdieu and beyond. Research in Mathematics Education, 18(1), 3-21.
  64. Zengin, Y. (2019). Development of mathematical connection skills in a dynamic learning environment. Education and Information Technologies, 24(3), 2175-2194. https://doi.org/10.1007/s10639-019-09870-x