Journal of Research in Science, Mathematics and Technology Education

The Role of Representations in the Understanding of Mathematical Concepts in Higher Education: The case of Function for Economics Students

Eleni Deliyianni 1 * ,
Athanasios Gagatsis 2,
Areti Panaoura 3,
Styliana Nicolaou 2,
Iliada Elia 2,
Stylianos Stamatakis 4
1 Cyprus Ministry of Education2 University of Cyprus3 Frederick University4 Aristotle University of Thessaloniki* Corresponding Author
Download PDF
Journal of Research in Science, Mathematics and Technology Education, Volume 5, Issue 1, January 2022, pp. 69-92
OPEN ACCESS VIEWS: 870 DOWNLOADS: 552 Publication date: 01 Jan 2022
ABSTRACT
There are numerous studies about the teaching and learning of mathematics at different educational levels. In the case of higher education most studies were conducted at pedagogical departments for prospective teachers and mathematical departments. The present study concentrates on university students who attend a course on mathematics as part of a program at the Faculty of Economics and Management. It examines aspects of students’ affective and cognitive behavior in solving representation tasks concerning their understanding of exponential and logarithmic functions. Results confirmed the existence of a comprehensive model with significant interrelations among general beliefs, self-efficacy beliefs and cognitive behaviour about the use of representations in general and, in the case of the specific concept. Regression analysis indicated the predominant role the self-efficacy beliefs play in the use of representations in defining the concept of function and solving recognition and translation tasks. Implications about the teaching of mathematics in higher education are discussed.
KEYWORDS
Self-efficacy beliefs, Function, General beliefs, Representations.
CITATION (APA)
Deliyianni, E., Gagatsis, A., Panaoura, A., Nicolaou, S., Elia, I., & Stamatakis, S. (2022). The Role of Representations in the Understanding of Mathematical Concepts in Higher Education: The case of Function for Economics Students. Journal of Research in Science, Mathematics and Technology Education, 5(1), 69-92. https://doi.org/10.31756/jrsmte.513
REFERENCES
  1. Abdulwahed, M., Jaworski, B., & Crowford, A. R. (2012). Innovative approaches to teaching mathematics in higher education: a review and critique. Nordic Studies in Mathematics Education, 17(2), 49-68.
  2. Alkhateeb, M. (2019). Multiple representations in 8th grade mathematics textbook ant the extent to which teachers implement them. International Electronic Journal of Mathematics Education, 14(1), 137-145. https://doi.org/10.12973/iejme/3982
  3. Bandura, A. (1997). Self-efficacy: The exercise of control. N.H. Freeman.
  4. Ballard, J.W. (2000). Students’ use of multiple representations in mathematical problem solving (Doctoral dissertation). Retrieved from https://scholarworks.montana.edu/xmlui/handle/1/8054
  5. Barnett, L. (2009). Key aspects of teaching and learning in economics. In H. Fry, S. Ketteridge & S. Marshall (Eds.).
  6. A handbook for teaching and learning in higher education (pp. 405-423). Routledge.
  7. Beltran-Pellicer, P., & Godino, J. (2019). An onto-semiotic approach to the analysis of the affective domain in mathematics education. Cambridge Journal of Education. doi. 10.1080/0305764X.2019.1623175
  8. Berthiaume, D. (2009). Teaching in the disciplines. In H. Fry, S. Ketteridge & S. Marshall (Eds.). A handbook for teaching and learning in higher education (pp. 215-225). Routledge.
  9. Borromeo – Ferri, R. (2015). To deny conventions? University students demand of concrete examples and less mathematical formalization. In R. Goller, R. Biehler, R. Hochmuth & H. Ruck (Eds.) Didactics of mathematics in higher education as a scientific discipline (pp. 260-263). Universitätsbibliothek Kassel.
  10. Bosse, M., Adu-Gyamfi, K., & Cheetham, C. (2011). Translations among mathematical representations: Teacher beliefs and practices. International Journal for Mathematics Teaching and Learning. Retrieved from www.cim.t.org.uk/journal.
  11. Cai, J., Perry, B., Wong, N.Y., & Wang, T. (2009). What is effective teaching? In J. Cai, G. Kaiser, B., Perry &
  12. N.Y. Wong (Eds.). Effective mathematics teaching from teachers’ perspectives: National and cross-national studies (pp. 1-36). Sense Publishers.
  13. Carson, M., Oehrtman, M., & Engelke, N. (2010). The precalculus concept assessment: a tool for assessing students reasoning abilities and understandings. Cognition and Instruction, 28(2), 113-145. https://doi.org/10.1080/07370001003676587
  14. Clement, L. (2001). What do students really know about functions? Mathematics Teacher, 94(9), 745-748.
  15. Daryaee, A., Shahvarani, A., Tehranian, A., Lotfi, F. H., & Rostamy-Malkhalifeh, M. (2018). Executable functions of the representations in learning the algebraic concepts. PNA 13(1), 1- 18.
  16. Deliyianni, E., Gagatsis, A., Elia, I. & Panaoura, A. (2010). Representational flexibility and problem-solving ability in function and decima number addition, a structural model. International Journal of Science and Mathematics Education, 14 (2), 397-417. https://doi.org/10.1007/s10763-015-9625-6
  17. Ding, L., Wei, X. & Mollohan, K. (2016). Does higher education improve student scientific reasoning skills?
  18. International Journal of Science and Mathematics Education, 14(4), 619–634. https://doi.org/10.1007/s10763014-9597-y
  19. Dorfler, W. (2015). Reducing math anxiety. In R. Goller, R. Biehler, R. Hochmuth & H. Ruck (Eds.) Didactics of mathematics in higher education as a scientific discipline -Conference proceedings (pp. 268-270). Kassel: Universität Kassel
  20. Dreyfus, T., & Eisenberg, T. (1982). Intuitive functional concepts: A baseline study on intuitions. Journal for Research in Mathematics Education, 13, 360-380.
  21. Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational
  22. Studies in Mathematics, 61, 103-131. https://doi.org/10.1007/s10649-006-0400-z
  23. Elia, I., Panaoura, A., Eracleous, A., & Gagatsis, A. (2007). Relations between secondary pupils’ conceptions about functions and problem solving in different representations. International Journal of Science and Mathematics Education, 5(3), 533-556. https://doi.org/10.1007/s10763-006-9054-7
  24. Fry, H., Ketteridge, S., & Marshall, S. (2009). Understanding student learning. In H. Fry, S. Ketteridge & S.
  25. Marshall (Eds.). A handbook for teaching and learning in higher education (pp. 8-26). Routledge.
  26. Ignacio, N., Nieto, L., & Barona, E. (2006). The affective domain in mathematics learning. International Electronic Journal of Mathematics Education, 1(1), 16-32.
  27. Gagatsis, A., Elia, I., & Mougi, A. (2002). The nature of multiple representations in developing mathematical relations. Scientia Paedagogica Experimentalis, 39(1), 9-24.
  28. Gagasis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational Psychology, 24(5), 645-657. https://doi.org/10.1080/0144341042000262953
  29. Gagatsis, A., Deliyianni, E., Elia, I., & Panaoura, A. (2017). Representational flexibility in fractions and decimals: A synthesis of research studies. Communication and Cognition, 50 (3-4), 93-120.
  30. Godino, J. & Font, B. (2010). The theory of representations as viewed from the onto-semiotic approach to mathematics education. Mediterranean Journal for Research in Mathematics Education, 9(1), 189-210.
  31. Goldin, G. (2008). Perspectives on representations in mathematical learning and problem solving. In L.D. English (Ed.), Handbook of international research in mathematics education (pp. 176-201). Routledge.
  32. Gouya, Z., & Sereshti, H. (2006). Teaching calculus: Existing problems and the role of technology. Journal of Developments in Mathematics Education, 83, 30-31.
  33. Grootenboer, P., & Hemmings, B. (2007). Mathematics performance and the role played by affective and background factors. Mathematics Education Research Journal, 19(3), 3-20. https://doi.org/10.1007/BF03217459
  34. Kastberg, S. (2002). Understanding mathematical concepts: the case of the logarithmic function (Doctoral dissertation). Retrieved from http://jwilson.coe.uga.edu/Pers/Dissertations/kastberg_signe_e_200205_phd.pdf
  35. Kyle, J., & Kahn, P. (2009). Key aspects of teaching and learning in mathematics and statistics. In H. Fry, S.
  36. Ketteridge & S. Marshall (Eds.). A handbook for teaching and learning in higher education (pp. 246-263).
  37. Routledge.
  38. Mardanov, R., & Khasanova, A. (2014). Current issues of teaching mathematics in economic faculties of universities. Procedia – Social and Behavioral Sciences, 152, 1062-1065.
  39. Maron, A. (2016). Priorities of teaching mathematics in universities. IEJME-Mathematics Education, 11(9), 33393350.
  40. Marsh, H. W., Trautwein, U., Ludtke, O., Koller, O., & Bumert, J. (2005). Academic self-concept, interest grades and standardized test scores. Reciprocal effects models of causal ordering. Child Development, 76(2), 397-416. https://doi.org/10.1111/j.1467-8624.2005.00853.x
  41. Moru, E. K. (2009). Epistemological obstacles in coming to understand the limit of a function at undergraduate level: A case from the national university of Lesotho. International Journal of Science and Mathematics
  42. Education, 7, 431–454. https://doi.org/10.1007/s10763-008-9143-x
  43. O’Shea, A., Breen, S., & Jaworski, B. (2016). The development of a function concept inventory. International
  44. Journal of Research Undergraduate Mathematics Education, 2, 279-296. https://doi.org/10.1007/s40753-0160030-5
  45. Panaoura, A., Gagatsis, A., Deliyianni, E., & Elia, I. (2009a). The structure of students’ beliefs about the use of representations and their performance on the learning of fractions. Educational Psychology, 29, 713-728. https://doi.org/10.1080/01443410903229437
  46. Panaoura, A., Elia, I., Stamboulides, N., & Spyrou, P. (2009b). Students’ structure for the understanding of the axis of reflective symmetry in mathematics. Acta Didactica Universitatis Comenianae Mathematics, 9, 41-62.
  47. Panaoura, A., Gagatsis, A., Deliyianni, E., & Elia, I. (2010). A model of the cognitive and affective factors for the use of representations at the learning of decimals. Educational Psychology, 30 (6), 713-734. https://doi.org/10.1080/01443410.2010.501103
  48. Panaoura, A., Michael, P., Gagatsis, A., Elia, I., & Philippou, A. (2017). Teaching the concept of function: Definition and problem solving. International Journal of Science and Mathematics Education, 15, 723-740. https://doi.org/10.1007/s10763-016-9714-1
  49. Petocz, P., Reid, A., Wood, L. N., Smith, G. H., Mather, G., Harding, A., Engelbrecht, J., Houston, K., Hillel, J., &
  50. Perrett, G. (2007). Undergraduate students’ conceptions of mathematics: An international study. International Journal of Science and Mathematics Education, 5(3), 439–459. https://doi.org/10.1007/s10763-006-9059-2
  51. Pettersson, K. (2012). The threshold concept of function – A case study of a student’s development of her understanding. In C. Bergsten, E. Jablonka, & M. Raman (Eds.), Evaluation and comparison of mathematical achievement: Dimensions and perspectives. Proceedings of MADIF 8, the eight Swedish mathematics education research seminar (pp. 171-180). SMDF
  52. Sajka, M. (2003). A secondary school students’ understanding of the concept of function – a case study. Educational
  53. Studies in Mathematics, 53, 229-254. https://doi.org/10.1023/A:1026033415747
  54. Shreider, J.B. (2002). Institutional and student factors and their influence on advanced mathematics achievement.
  55. The Journal of Educational Research, 95(5). 274-286.
  56. Siti, A. (2010). Comprehending the concept of functions. Procedia Social Behavioral Sciences, 8, 281-287.
  57. Sterner, G., Wolff, U., & Helenius, O. (2020). Reasoning about representations: Effects of an early math intervention, Scandinavian Journal of Educational Research, 64(5), 782-800. https://doi.org/10.1080/00313831.2019.1600579
  58. You, Z., & Quinn, R. (2010). Prospective elementary and middle school teachers’ knowledge of linear functions: A quantitative approach. Journal of Mathematics Education, 3(1), 66-76.
  59. Viirman, O. (2014). The function concept and university mathematics teaching. (Doctoral dissertation). Retrieved from https://www.divaportal.org/smash/get/diva2:693890/FULLTEXT01.pdf
  60. Voßkamp, R. (2017). Mathematics in economics study programmes in Germany: structures and challenges. In R. Göller, R. Biehler, R. Hochmuth & H.-G. Rück (Eds.). Didactics of mathematics in higher education as a scientific discipline – Conference Proceedings (pp. 184-189). Universität Kassel
LICENSE
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.