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Research Article

An Error Analysis of TVET Students’ Responses to Optimisation Problems

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References

  • Baroody, A. J., Brach, C., & Tai, Y. C. (2006). The application and development of an addition goal sketch. Cognition and Instruction, 24(1), 123–170.
  • Bassarear, T. 2012. Mathematics for elementary school teachers (5th edn). Brooks/Cole.
  • Brijlall, D., & Ndlovu, Z. (2013). High school learners’ mental construction during solving optimisation problems in Calculus: A South African case study. South African Journal of Education, 33(2), 1–18, https://hdl.handle.net/10520/EJC134992
  • Berry, J. S., & Nyman, M. A. (2003). Promoting students’ graphical understanding of the calculus. The Journal of Mathematical Behavior, 22(4), 479–495.
  • Brijlall, D. (2015). Exploring the Gurteen Knowledge Café approach as an innovative teaching for learning strategy with first-year engineering students. Groupwork, 24(3), 26–45, https://doi.org/10.1921/13801240303272713801240303
  • Bezuidenhout, J. (2001). Limits and continuity: Some conceptions of first-year students. International journal of mathematical education in science and technology, 32(4), 487–500.
  • Chusnul, Rr. C., Mardiyana, & Retno, D. S. (2017). Errors Analysis of Problem Solving Using the Newman Stage After Applying Cooperative Learning of TTW Type. AIP Conference Proceedings, 1913, 020028-1–020028-7
  • Curriculum and Assessment Policy Statement Grades CAPS). (2011). 10–12: Mathematics. Pretoria: Government Press
  • Chusnul, C., Mardiyana, S., & Retno, D. (2017). Error analysis of problem solving using the Newman stage after applying cooperative learning of TTW type. Proceedings of Mathematical analysis and its applications, 1913(1), 020028, https://doi.org/10.1063/1.5016662
  • Devetak, I., Glažar, S. A., & Vogrinc, J. (2010). The role of qualitative research in science education. Eurasia Journal of Mathematics, Science and Technology Education, 6(1), 77–84, https://doi.org/10.12973/ejmste/75229
  • Douglas, S. R. (2010). Non-native English speaking students at university: Lexical richness and academic success (Doctoral dissertation, University of Calgary, Graduate Division of Educational Research).
  • Department of Higher Education and Training (DHET). (2013). Mathematics Subject Assessment Guidelines. Pretoria. Department of Higher Education and Training.
  • Department of Higher Education and Training (DHET). 2013. Mathematics Subject Assessment Guidelines. Pretoria. Department of Higher Education and Training.
  • Hasanah, A.N., & Yulianti, K. (2020). Error analysis in solving prism and pyramid prisms. Proceedings of Journal of Physics, 1521(3), 032035, https://doi.org/10.1088/1742-6596/1521/3/032035
  • Hadjidemetriou, C., & Williams, J. (2002). Teachers' pedagogical content knowledge: Graphs from a cognitivist to a situated perspective. In Pme conference (Vol. 3, pp. 3-057).
  • Hill, C. J., Bloom, H. S., Black, A. R., & Lipsey, M. W. (2008). Empirical benchmarks for interpreting effect sizes in research. Child Development Perspectives, 2, 172–177.
  • James, F. (1998). MINUIT: function minimization and error analysis reference manual (No. CERNLIB-D506). CERN.
  • Kieran, C. (1992). The Learning and Teaching of School Algebra. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 390–419). New York: Macmillan Publishing Company.
  • Kirschner, F., Paas, F., & Kirschner, P. A. (2009). A cognitive load approach to collaborative learning: United brains for complex tasks. Educational psychology review, 21, 31–42.
  • Khan, N. N., Boyle, J. A., Lang, A. Y., & Harrison, C. L. (2019). Preconception health attitudes and behaviours of women: a qualitative investigation. Nutrients, 11(7), 1490.
  • Kirschner, F., Paas, F., & Kirschner, P. A. (2009). A cognitive load approach to collaborative learning: United brains for complex tasks. Educational psychology review, 21, 31–42.
  • Kinley, M. (2016). Grade 12 students establishing the relationship between differentiation and integration using graphs. IEJME – Mathematics Education, 11(9), 3371–3385.
  • Laborde, C. (1990). Language and mathematics. Mathematics and cognition, 53-69.
  • Laborde, C. (2007). Towards theoretical foundations of mathematics education. ZDM, 39, 137–144.
  • Legutko, M. (2008) . An analysis of students’ mathematical errors in the teaching-research process. In Handbook for mathematics teaching: Teacher experiment. A tool for research (pp. 141–152) Drukarnia Cyfrowa KSERKOP, Kraków, Poland.
  • Loc, N. P., & Hoc, T. C. T. (2014). A Survey Of 12 th Grade Students’ Errors In Solving Calculus Problems. TC, 1(49), 49.
  • Loc, N. P. (2008). Non-traditional teaching trends curriculum. Can Tho University (unpublished doctoral thesis). Vietnam.
  • Luneta, K., & Makonye, P. J. (2010). Learner Errors and Misconceptions in Elementary Analysis: A Case Study of a Grade 12 Class in South Africa. Acta Didactica Napocensia, 3(3), 35-46.
  • Luneta, K. (2008). Error discourse in fundamental physics and mathematics: Perspectives of students’ misconceptions. Proceedings of International Council on Education for Teaching (pp. 386–400). 17–22 April, Braga, Portugal.
  • Luneta, K. (2015). Understanding students’ misconceptions: An analysis of final Grade 12 examination questions in geometry. Pythagoras, 36(1), 1–11, https://hdl.handle.net/10520/EJC172894
  • Luneta K (2022). Learners’ computational strategies and errors exhibited when adding and subtracting multiple-digit whole numbers in lower primary school. International Journal of Science Mathematics and Technology Learning, https://doi.org/10.18848/2327-7971/CGP/v30i01/67-86
  • Luneta, K., & Makonye, J. (2010). Learner errors and misconceptions in elementary analysis: A case study of a Grade 12 class in South Africa. Acta Didactica Napocensia, 3(3), 35–46.
  • Maharaj, A., & Ntuli, M. (2018). Students’ ability to correctly apply differentiation rules to structurally different functions. South African Journal of Science, 114(11–12), 1–7, http://doi.org/10.17159/sajs.2018/5008
  • Mbusi, N. (2016).  Misconceptions and related errors displayed by pre-service foundation phase teachers in transformation geometry. In J. Kriek, B. Bantwini, JJ Dhlamini, C. Ochonogor & L. Goosen (Eds.) Proceedings of ISTE International conference on Mathematics Science and Technology (pp. 67–77) UNISA Press.
  • Maharaj, A. (2010). An APOS analysis of students' understanding of the concept of a limit of a function. Pythagoras, 71, 41–52.
  • Maharaj, A., & Ntuli, M. (2018). Students' ability to correctly apply differentiation rules to structurally different functions. South African Journal of Science, 114(11-12), 1–7.
  • Mbusi, N. (2016). Misconceptions and related errors displayed by pre-service foundation phase teachers in transformation geometry. In International Conference on Mathematics, Science and Technology Education (pp. 386-400). Mopane Camp, Kruger National Park, South Africa. Unisa Press.
  • Mendezabal, M.J.N, & Tindowen, D.J.C. (2018). Improving students’ attitude, conceptual understanding, and procedural skills in differential calculus through Microsoft Mathematics. JOTSE, 8(4), 385–397.
  • Mensah, F.S. (2017). Ghanaian senior high school students’ error in learning of trigonometry. International Journal of Environmental & Science Education, 12(8), 1709–1717.
  • Motseki, P.D. (2021). Identifying and addressing errors and misconceptions in differential calculus: A case study of National Vocational (Certificate) students at Technical Vocational and Education. Unpublished PhD thesis, Department of Childhood Education, University of Johannesburg.
  • Muzangwa, J., & Chifamba, P. (2012). Analysis of errors and misconceptions in the learning of calculus by undergraduates Students. Acacta Didactica Napocensia, 5(2), 1–10.
  • Newman, M. A. (1977). An analysis of sixth-grade pupil's error on written mathematical tasks. Victorian Institute for Educational Research Bulletin, 39, 31–43.
  • Oktaviyanthi, R., Agus, R. N., Supriani, Y., & Sholahudin, U. (2019). Is functional skills mathematics approach relevant to stimulate students’ mathematical problem solving? Journal of Physics: Conference Series, 1280(4), 042029.
  • Oktaviyanthi, R., Agus, R. N., Supriani, Y., & Sholahudin, U. (2019, November). Is functional skills mathematics approach relevant to stimulate students’ mathematical problem solving?. In Journal of Physics: Conference Series (Vol. 1280, No. 4, p. 042029). IOP Publishing.
  • Parameswaran, R. (2007). On understanding the notion of limits and infinitesimal quantities. International Journal of Science and Mathematics Education, 5(2), 193–216.
  • Pólya, G. (1945). How to solve it: A new aspect of mathematics. New Jersey: Princeton University Press. https://doi.org/10.1515/9781400828678
  • Pham, L.T.M. (2018). Qualitative approach to research: A review of advantages and disadvantages of three paradigms: Positivism, interpretivism and critical inquiry. University of Adelaide.
  • Rashid, Y., Rashid, A., Warraich, M. A., Sabir, S. S., & Waseem, A. (2019). Case study method: A step-by-step guide for business researchers. International Journal of Qualitative Methods, 18, https://doi.org/10.1177/1609406919862424
  • Rabadi, N. (2015). Overcoming difficulties and misconceptions in calculus (Doctoral dissertation, Teachers College, Columbia University).
  • Richards, J. (1971). Error analysis and second language strategies.
  • Robinson, O.C. (2014). Sampling in interview-based qualitative research: A theoretical and practical guide. Qualitative Research in Psychology, 11(1), 25–41, https://doi.org/10.1080/14780887.2013.801543
  • Roble, D.B. (2017). Communicating and valuing students’ productive struggles and creativity in calculus. Turkish Online Journal of Design Art and Communication, 7(22), 255–263, https://doi.org/10.7456/10702100/009.
  • Sadler, P., & Sonnert, G. (2018). The path to college calculus: The impact of high school mathematics coursework. Journal for Research in Mathematics Education, 49(3), 292–329.
  • Sebsibe, A.S., & Feza, N.N. (2019). Assessment of students’ conceptual knowledge in limit functions. International Electronic Journal of Mathematics Education, 15(2), https://doi.org/10.29333/iejme/6294
  • Sebsibe, A. S., Bekana, T., & Dorra, B. T. (2019). Effect of Error Analysis and Concept Change Strategy on Students Understanding of Calculus Concepts. IEEE-SEM7, (7), July-2019 ISSN 2320-9151.
  • Siyepu, S.W. (2015). Analysis of errors in derivatives of trigonometric functions. International Journal of STEM Education, 2(1), 1–16, https://doi.org/10.1186/s40594-015-0029-5
  • Smith, J.P., diSessa, A. A., & Rochelle, J. (1993). Misconceptions reconceived: A constructivist analysis of knowledge in transition. The Journal of the Learning Sciences, 3(2), 115–163.
  • Suganthan, M. A., & Raju, R. L. N. The English Teacher’s Competence in Error Analysis and Its Application in the Classroom. Strength for Today and Bright Hope for Tomorrow Volume 19: 9 September 2019 ISSN 1930-2940, 110.
  • Schnepper, L. C., & McCoy, L. P. (2013). Analysis of misconceptions in high school mathematics. Networks: An Online Journal for Teacher Research, 15(1), 625–625.
  • Sebsibe, A. S., & Feza, N. N. (2020). Assessment of students’ conceptual knowledge in limit of functions. International Electronic Journal of Mathematics Education, 15(2), em0574. https://doi.org/10.29333/iejme/6294
  • Schnepper, L. C., & McCoy, L. P. (2013). Analysis of misconceptions in high school mathematics. Networks: An Online Journal for Teacher Research, 15(1), 625–625.
  • Usman, A. I. (2017). Geometric Error Analysis in Applied Calculus Problem Solving. European Journal of Science and Mathematics Education, 5(2), 119–133.
  • Wahyuni, A. (2017). Analisis Hambatan Belajar Mahasiswa Pada Mata Kuliah Kalkulus Dasar. JNPM (Jurnal Nasional Pendidikan Matematika), 1(1), 10–23.
  • Wiens, A. (2007). An Investigation into careless errors made by 7th Grade mathematics students. Masters dissertation. Department of Mathematics, University of Nebraska – Lincoln.

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