Article Sidebar

Download
PDF
Statistic
Read Counter : 1932 Download : 880

Downloads

Download data is not yet available.

Main Article Content

Abstract

Physical distancing, which is widely practiced limiting the spread of COVID-19, is recognized to contain mathematical thoughts that can be harnessed as a context for prospective teachers’ practices of mathematical problem posing. The goal of this study is to investigate the profile of mathematical tasks posed by prospective mathematics teachers using the context of physical distancing that meets the criteria of numeracy tasks. Data were collected from 66 mathematical tasks posed by thirty-three prospective teachers at a public university in Surabaya, Indonesia, attending an assessment course of numeracy based on a problem-posing task. To analyze, the posed tasks were first identified as solvable or unsolvable tasks and then further categorized into the domains of the level of context use and the level of cognitive processes. Results show that the level of context use embedded in the posed tasks varies from zero to first order, with only a few of the posed tasks being coded as having second-order context. Regarding the levels of cognitive processes, most of the posed tasks reach the level of understanding, with only a small number of reasoning tasks identified. Interestingly, all the tasks coded to contain second-order context are classified as reasoning tasks. Some implications regarding designing numeracy tasks using physical distancing and interventions in teacher education related to numeracy task design are discussed.

Keywords

COVID-19 Numeracy Task Physical Distancing Prospective Teacher

Article Details

Creative Commons License

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

How to Cite
Kohar, A. W., Rahaju, E. B., & Rohim, A. (2022). Prospective teachers’ design of numeracy tasks using a physical distancing context. Journal on Mathematics Education, 13(2), 191–210. https://doi.org/10.22342/jme.v13i2.pp191-210
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX

References

  1. Anderson, L. W., & Krathwohl, D. R. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom's taxonomy of educational objectives. New York: Addison Wesley Longman, Inc.
  2. Baumanns, L., & Rott, B. (2021). Developing a framework for characterising problem-posing activities: A review. Research in Mathematics Education, 1-23. https://doi.org/10.1080/14794802.2021.1897036
  3. Bortolete, J. C., Bueno, L. F., Butkeraites, R., Chaves, A. A., Collaço, G., Magueta, M., ... & Yanasse, H. H. (2022). A support tool for planning classrooms considering social distancing between students. Computational and Applied Mathematics, 41(1), 1-23. https://doi.org/10.1007/s40314-021-01718-w
  4. Boaler, J. (1993). The role of contexts in the mathematics classroom: Do they make mathematics more" real"?. For the learning of mathematics, 13(2), 12-17. https://www.jstor.org/stable/40248079
  5. Bonotto, C. (2007). How to replace word problems with activities of realistic mathematical modelling. In Modelling and applications in mathematics education (pp. 185-192). Springer, Boston, MA. https://link.springer.com/chapter/10.1007/978-0-387-29822-1_18
  6. Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects—State, trends, and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37-68. https://doi.org/10.1007/BF00302716
  7. Centre of Assessment and Learning (CAL). (2020). AKM dan Implikasinya dalam Pembelajaran (Minimum Competency Assessment and its Implications for Learning). Ministry of Education. https://hasilun.puspendik.kemdikbud.go.id/akm/file_akm2_202101_1.pdf
  8. Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395-415. https://doi.org/10.1007/s10857-008-9081-0
  9. Crespo, S. (2020). Learning to pose collaborative mathematics problems with secondary prospective teachers. International Journal of Educational Research, 102, 101430. https://doi.org/10.1016/j.ijer.2019.05.003
  10. Dogan, M. F. (2020). Evaluating pre-service teachers’ design of mathematical modelling tasks. International Journal of Innovation in Science and Mathematics Education, 28(1), 44-59. https://doi.org/10.30722/IJISME.28.01.004
  11. de Lange, J. (1987). Mathematics—Insight and meaning. Utrecht: Rijksuniversiteit Utrecht.
  12. Ekawati, R., Kohar, A. W., & Hartono, S. (2017). Experts’ notion and students’ responses on context-based mathematics problem. Journal of Engineering Science and Technology (JESTEC), 53-64.
  13. Fitriana, L. D., Ekawati, R., & Kovács, Z. (2022). Perspectives on the problem-posing activity by prospective teachers: A cross-national study. Journal on Mathematics Education, 13(1),149-172. http://doi.org/10.22342/jme.v13i1.pp149-172
  14. Felton, M. (2010). Is math politically neutral? Teaching Children Mathematics, 17(2), 60-63. https://doi.org/10.5951/TCM.17.2.0060
  15. Ferri, R. B. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer International Publishing. https://doi.org/10.1007/978-3-319-68072-9
  16. Geiger, V., Forgasz, H., Goos, M., & Bennison, A. (2014). Devising Principles of Design for Numeracy Tasks. In J. Anderson, M. Cavanagh & A. Prescott (Eds.). Curriculum in Focus: Research Guided Practice (Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia) (Vol 1, pp. 239–246). https://acuresearchbank.acu.edu.au/item/88vz0/devising-principles-of-design-for-numeracy-tasks
  17. Geiger, V., Forgasz, H., & Goos, M. (2015). A critical orientation to numeracy across the curriculum. ZDM, 47(4), 611–624. https://doi.org/10.1007/s11858-014-0648-1
  18. Guo, M., Leung, F. K., & Hu, X. (2020). Affective determinants of mathematical problem posing: the case of Chinese Miao students. Educational Studies in Mathematics, 105(3), 367-387. https://doi.org/10.1007/s10649-020-09972-1
  19. Goos, M., Geiger, V., & Dole, S. (2013). Designing rich numeracy tasks. In C. Margolinas (Ed.), Task design in mathematics education. Proceedings of ICMI Study 22 (vol.1). London, UK: Oxford.
  20. Islam, M. T., Jain, S., Chen, Y., Chowdhury, B. D. B., & Son, Y. J. (2021). An agent-based simulation model to evaluate contacts, layout, and policies in entrance, exit, and seating in indoor activities under a pandemic situation. IEEE Transactions on Automation Science and Engineering. https://doi.org/10.1109/TASE.2021.3118008
  21. Jones, N. R., Qureshi, Z. U., Temple, R. J., Larwood, J. P., Greenhalgh, T., & Bourouiba, L. (2020). Two meters or one: What is the evidence for physical distancing in COVID-19?. BMJ, 370, 1-6 https://doi.org/10.1136/bmj.m3223
  22. Kılıç, Ç. (2013). Pre-service primary teachers’ free problem-posing performances in the context of fractions: An example from Turkey. The Asia-Pacific Education Researcher, 22(4), 677–686. https://doi.org/10.1007/s40299-013-0073-1
  23. Kohar, A. W., Wardani, A. K., & Fachrudin, A. D. (2019). Profiling context-based mathematics tasks developed by novice PISA-like task designers. Journal of Physics: Conference Series, 1200(1), 012014. http://dx.doi.org/10.1088/1742-6596/1200/1/012014
  24. Kwek, M. L. (2015). Using problem posing as a formative assessment tool. In Mathematical problem posing (pp. 273-292). Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6258-3_13
  25. Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33(1), 159-174. https://doi.org/10.2307/2529310
  26. Leavy, A., & Hourigan, M. (2020). Posing mathematically worthwhile problems: Developing the problem-posing skills of prospective teachers. Journal of Mathematics Teacher Education, 23, 341–361. https://doi.org/10.1007/s10857-018-09425-w.
  27. Lee, Y., Capraro, R. M., & Capraro, M. M. (2018). Mathematics teachers’ subject matter knowledge and pedagogical content knowledge in problem posing. International Electronic Journal of Mathematics Education, 13(2), 75-90. https://doi.org/10.12973/iejme/2698
  28. Limin, C. H. E. N., Van Dooren, W., & Verschaffel, L. (2013). The relationship between students’ problem posing and problem solving abilities and beliefs: A small-scale study with Chinese elementary school children. Frontiers of Education in China, 8(1), 147-161. https://doi.org/10.3868/110-002-013-0010-5
  29. Liljedahl, P. (2015). Numeracy task design: A case of changing mathematics teaching practice. ZDM, 47(4), 625-637. https://doi.org/10.1007/s11858-015-0703-6
  30. Liu, F., Luo, Z., Li, Y., Zheng, X., Zhang, C., & Qian, H. (2021). Revisiting physical distancing threshold in indoor environment using infection-risk-based modeling. Environment international, 153, 106542. https://doi.org/10.1016/j.envint.2021.106542
  31. Maaß, K. (2010). Classification scheme for modelling tasks. Journal für Mathematik-Didaktik, 31(2), 285-311. https://doi.org/10.1007/s13138-010-0010-2
  32. Ministry of Education (MoE) (2017). Materi Pendukung Literasi Numerasi [Numerical Literacy Support Material]. Ministry of Education. http://gln.kemdikbud.go.id/glnsite/wp-content/uploads/2017/10/materi-pendukung-literasi-numerasi-rev.pdf
  33. Murray, A. T. (2020). Planning for classroom physical distancing to minimize the threat of COVID-19 disease spread. PloS one, 15(12), e0243345. https://doi.org/10.6084/m9.figshare.13247687.v1
  34. Niss, M. (2015). Mathematical competencies and PISA. In Assessing mathematical literacy (pp. 35-55). Springer, Cham. https://doi.org/10.1007/978-3-319-10121-7_2
  35. Niss, M., & Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102(1), 9-28. https://doi.org/10.1007/s10649-019-09903-9
  36. Nusantara, D. S., & Putri, R. I. I. (2020). Designing PISA-like mathematics problem in COVID-19 pandemic (PISAComat). Journal of Physics: Conference Series, 1657(1), 012057. https://doi.org/10.1088/1742-6596/1657/1/012057
  37. Nusantara, D. S., Zulkardi, & Putri, R. I. I. (2021). Designing PISA-like mathematics task using a COVID-19 context (PISAComat). Journal on Mathematics Education, 12(2), 349-364. http://dx.doi.org/10.22342/jme.12.2.13181.349-364
  38. OECD. (2010). Learning mathematics for life: A perspective from PISA. OECD Publishing. http://hdl.voced.edu.au/10707/21273
  39. OECD. (2013). PISA 2012 Assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy. OECD Publishing. http://dx.doi.org/10.1787/9789264190511-en
  40. OECD. (2018). PISA 2022 Mathematics Framework. https://pisa2022-maths.oecd.org/ca/index.html
  41. Palm, T. (2006). Word problems as simulations of real-world situations: A proposed framework. For the Learning of Mathematics, 26(1), 42–47. https://www.jstor.org/stable/40248523
  42. Paolucci, C., & Wessels, H. (2017). An examination of preservice teachers’ capacity to create mathematical modeling problems for children. Journal of Teacher Education, 68(3), 330-344. https://doi.org/10.1177%2F0022487117697636
  43. Park, J., Choi, M., & Kang, J. Y. (2021). Spatial optimization of indoor sports stadium seats under social distancing practice during the COVID-19 pandemic. Journal of the Korean Geographical Society, 56(1), 53-66. https://doi.org/10.22776/kgs.2021.56.1.53
  44. Pettersen, A., & Nortvedt, G. A. (2018). Identifying competency demands in mathematical tasks: Recognising what matters. International Journal of Science and Mathematics Education, 16(5), 949-965. http://dx.doi.org/10.1007/s10763-017-9807-5
  45. Salgado, F. J. A. (2016). Developing a theoretical framework for classifying levels of context use for mathematical problems. Mathematics Education Research Group of Australasia. https://files.eric.ed.gov/fulltext/ED572410.pdf
  46. Salgado, F. J. A. (2017). The role of context and context familiarity on mathematics problems. Revista latinoamericana de investigación en matemática educativa, 20(3), 265-292. https://doi.org/10.12802/relime.17.2031
  47. Sari, S. P., Zulkardi, & Darmawijoyo. (2021). Students' numeracy skills relating to algebra topic using COVID-19 Context. JTAM (Jurnal Teori dan Aplikasi Matematika), 5(1), 182-192. https://doi.org/10.31764/jtam.v5i1.3881
  48. Sevinc, S., & Lesh, R. (2021). Preservice mathematics teachers’ conceptions of mathematically rich and contextually realistic problems. Journal of Mathematics Teacher Education, 1-29. https://link.springer.com/article/10.1007%2Fs10857-021-09512-5
  49. Siswono, T. Y. E., Kohar, A. W., & Hartono, S. (2018). An innovative training model for supporting in-service teachers’ understanding on problem-solving knowledge for teaching. In Hsieh, F.-J. (Ed.), Proceeding of ICMI‐East Asia Regional Conference on Mathematics Education (EARCOME8), (Vol. 2, pp 321-332).
  50. Siswono, T. Y. E., Kohar, A. W., Rosyidi, A. H., & Hartono, S. (2018). Searching for authentic context in designing PISA-like mathematics problem: From indoor to outdoor field experience. Journal of Physics: Conference Series, 953(1), 012197. https://doi.org/10.1088/1742-6596/953/1/012197
  51. Stacey, K., & Turner, R. (2015). The evolution and key concepts of the PISA mathematics frameworks. In K. Stacey & R. Turner (Eds.), Assessing Mathematical Literacy (pp. 5-33): Springer International Publishing. https://doi.org/10.1007/978-3-319-10121-7_1
  52. Stillman, G. A., Brown, J. P., & Geiger, V. (2015). Facilitating mathematisation in modelling by beginning modellers in secondary school. In Mathematical modelling in education research and practice (pp. 93-104). Springer, Cham. https://doi.org/10.1007/978-3-319-18272-8_7
  53. Stoll, M. S. (2022). Solutions to the distance constrained cinema seating problem (Master's thesis). Utrecht University. https://studenttheses.uu.nl/bitstream/handle/20.500.12932/589/master_thesis_cinema_seating_problem_final.pdf?sequence=1
  54. Tout, D., & Spithill, J. (2015). The challenges and complexities of writing items to test mathematical literacy. In Assessing Mathematical Literacy (pp. 145-171). Springer, Cham. https://doi.org/10.1007/978-3-319-10121-7_7
  55. Turner, R., Blum, W., & Niss, M. (2015). Using competencies to explain mathematical item demand: A work in progress. In Assessing mathematical literacy (pp. 85-115). Springer, Cham. https://doi.org/10.1007/978-3-319-10121-7_4
  56. Utami, I. Q., & Hwang, W. Y. (2021). The impact of collaborative problem posing and solving with ubiquitous-decimal app in authentic contexts on math learning. Journal of Computers in Education, 1-28. https://doi.org/10.1007/s40692-021-00209-5
  57. Ulger, T. K., Bozkurt, I., & Altun, M. (2022). Analyzing in-service teachers’ process of mathematical literacy problem posing. International Electronic Journal of Mathematics Education, 17(3), 1-19. https://doi.org/10.29333/iejme/11985
  58. Van Harpen, X. Y., & Presmeg, N. C. (2013). An investigation of relationships between students’ mathematical problem-posing abilities and their mathematical content knowledge. Educational Studies in Mathematics, 83(1), 117-132. https://doi.org/10.1007/s10649-012-9456-0
  59. Zulkardi, & Kohar, A. W. (2018). Designing PISA-like mathematics tasks in Indonesia: Experiences and challenges. Journal of Physics: Conference Series, 947(1), 012015. https://doi.org/10.1088/1742-6596/947/1/012015
  60. Zulkardi, Meryansumayeka, Putri, R. I. I., Alwi, Z., Nusantara, D. S., Ambarita, S. M., Maharani, Y., & Puspitasari, L. (2020). How students work with PISA-like mathematical tasks using COVID-19 context. Journal on Mathematics Education, 11(3), 405-416. https://doi.org/10.22342/jme.11.3.12915.405-416