Using the Malmquist Index in Evaluation Process to Enhance Mathematical Literacy in High School Students

Abstract

The study aimed to calculate the evaluation of 9^th grade female students and compare the development of the educational process in increasing mathematical literacy using the Malmquist Index at different time intervals. This educational process was accomplished by analysing and integrating realistic mathematical education and mathematical problem-solving. The populations of the study were 120 ninth grade female students. Each student was as a DMU whose inputs were the math test score and the outputs were math test score of December and June. The data analysis method was based on (DEA) technique to calculate efficiency. The output-driven (CCR) model was used to determine students' performance coefficient. Then, the Malmquist Index was used to compare productivity evaluation after the end of the training course in December and the end of the year in June. In general, the results from changes in productivity evaluation of students using the Malmquist Index showed that the students in the experimental group who learned problem-solving and realistic mathematics had an increase in the overall productivity evaluation factor after completing the training compared to the others.

Keywords

• Productivity Evaluation
• Mathematical Literacy
• The Malmquist Index
• Evaluation instrument GAMS

Using the Malmquist Index in Evaluation Process to Enhance Mathematical Literacy in High School Students

Öz

The study aimed to calculate the evaluation of 9th grade female students and compare the development of the educational process in increasing mathematical literacy using the Malmquist Index at different time intervals. This educational process was accomplished by analysing and integrating realistic mathematical education and mathematical problem-solving. The populations of the study were 120 ninth grade female students. Each student was as a DMU whose inputs were the math test score and the outputs were math test score of December and June. The data analysis method was based on (DEA) technique to calculate efficiency. The output-driven (CCR) model was used to determine students' performance coefficient. Then, the Malmquist Index was used to compare productivity evaluation after the end of the training course in December and the end of the year in June. In general, the results from changes in productivity evaluation of students using the Malmquist Index showed that the students in the experimental group who learned problem-solving and realistic mathematics had an increase in the overall productivity evaluation factor after completing the training compared to the others.

Anahtar Kelimeler

• Productivity Evaluation
• The Malmquist Index
• Mathematical Literacy
• Evaluation instrument GAMS

References

1. Adams, R., & Wu, M. (2000). Pisa 2000 Technical (OECD Organization for Economic Co-operation and Developmant). Paris: Publications 2 rue André-Pascal, 75775 Cedex 16, France.
2. Alimohammadlou, M., & Mohammadi, S. (2016). Evaluating the Productivity Using Malmquist Index Based on Double Frontiers Data. Procedia - Social and Behavioral Sciences, 230(May), 58–66. https://doi.org/10.1016/j.sbspro.2016.09.008.
3. Alvarez, R. (2018) ."A Focus on Mathematical Literacy to Increase Student Understanding and Performance". (Master's dissertation) . New York, USA. Retrieved May5 , 2019 , from https://digitalcommons.brockport.edu/ehd_theses/1169.
4. Andersen, P., & Petersen, N. C. (1993). A Procedure for Ranking Efficient Units in Data Envelopment Analysis process (DEA). Management Science, 39(10), 1261-1264. https://doi.org/10.2307/2632964.
5. Basic, T. H. E., & Model, C. C. R. (2005). The Basic CCR Model. In Data Envelopment Analysis (pp. 21–39). Boston: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47541-3_2.
6. Breen, S., Cleary, J., & Shea, A. O. (2009). An investigation of the Mathematical literacy of first year third-level students in the Republic of Ireland. International Journal of Mathematical Education, 40(2) , 229-246. https://doi.org/10.1080/00207390802566915.
7. Burnett, N. (2005). literacy for life. Education for All . France: Printed by Graphoprint, Paris ISBN 92-3-104008-1©UNESCO .https://unesdoc.unesco.org/ark:/48223/pf0000141639.
8. Chen, C., & Lin, M. (2006). Using DEA to Evaluate R & D Performance in the Integrated Semiconductor Firms - Case Study of Taiwan, International Journal of The Computer the Internet and Management, 14(3), 50–59.

9. Del Río, L. S., Sanz, C. V., & Búcari, N. D. (2019). Incidence of a hypermedia output material on the teaching and learning of mathematics. Journal of New Approaches in Educational Research, 8(1), 50–57. https://doi.org/10.7821/naer.2019.1.334.
10. Diewert, W. E., & Fox, K. J. (2010). Malmquist and Törnqvist productivity indexes: Returns to scale and technical progress with imperfect competition. Journal of Economics/ Zeitschrift Fur Nationalokonomie, 101(1), 73–95. https://doi.org/10.1007/s00712-010-0137-0.
11. Douglas, W., Caves ,E., Laurits, R., & Christensen, W. E. D. (2012). The Economic Theory of Index Numbers and the Measurement of Input , Output , and Productivity Author ( s ): Douglas W . Caves , Laurits R . Christensen , W . Erwin Diewert Reviewed work ( s ): Published by : 50(6), 1393–1414.
12. Esther, M., Pérez, M., Duque, A. P. G., & García, L. C. F. (2018). Game-Based Learning : Increasing the Logical-Mathematical , Naturalistic , and Linguistic Learning Levels of Primary School Students, 7(1), 31–39. https://doi.org/10.7821/naer.2018.1.248.
13. Fare, R., Grosskopf, S., Lindgren, B., Roos, P. (1992). A Non-Parametric Malmquist Approach. The Journal of Productivity Analysis, 3(1), 85–101. Retrieved from https://link.springer.com/content/pdf/10.1007%2FBF00158770.pdf.
14. Färe, R., Grosskopf, S., & Roos, P. (1995). Productivity and quality changes in Swedish pharmacies. International Journal of Production Economics, 39(1–2), 137–144. https://doi.org/10.1016/0925-5273(94)00063-G.
15. Freudenthal, H. (1973). Mathematics as an educational task, Reidel. Van den Heuvel-Panhuizen, M. (2000). Mathematics education in theNetherlands: A guided tour. Freudenthal Journal, Utrecht University.
16. Gatabi, A. R., Stacey, K., & Gooya, Z. (2012). Investigating grade nine textbook problems for characteristics related to mathematical. literacy Math Ed Res Journal, (2012) 24, 403–421. https://doi.org/10.1007/s13394-012-0052-5.
17. Gravemeijer, K. P. E. (1994). Developing realistic mathematics education. Journal of Curriculum Studies ,(1994) 11, 24-34. https://research.tue.nl/en/publications/developing-realistic-mathematics-education.
18. Gravemeijer, K., Terwel, J.(2000). Hans Freudenthal: a mathematician on didactics and curriculum theory. Journal of Curriculum Studies2000, VOL. 32, NO. 6, 777± 796.
19. Hosseinzadeh Lotfi, F., Jahanshahloo, G. R., Khodabakhshi, M., Rostamy-Malkhlifeh, M., Moghaddas, Z., & Vaez-Ghasemi, M. (2013). A Review of Ranking Models in Data Envelopment Analysis. Journal of Applied Mathematics, 2013 NO. (14), 1–20. https://doi.org/10.1155/2013/492421.
20. Kalvelagen, E. (2002). Data and Software Interoperability with Gams :A UserPerspectiveModelingLanguages, Solving Multi-Objective Models with GAMS Journal, http://citeseerx.ist.psu.edu/ doi=10.1.1.201.332&rep=rep1&type=pdf
21. Koçak, D., Türe, H., Atan, M. (2019). Efficiency Measurement with Network DEA : An Application to Sustainable Development Goals. International Journal of Assessment Tools in Educatio, 6(3), 415–435.
22. Koyuncu, İ., Guzeller, C. O., & Akyuz, D. (2016). The development of a self-efficacy scale for mathematical modeling competencies. International Journal of Assessment Tools in Education, 4(1), 19–35. https://doi.org/10.21449/ijate.256552
23. Lange, J. De. (1987). Mathematics, Insight and Meaning: Teaching, Learning and Testing of Mathematics for the Life and Social Sciences. Freudenthal Institute. Retrieved from https://books.google.com/books?id=wee5pwAACAAJ.
24. Maudos, J., & Pastor, J. M. (1998). Human capital in OECD countries : Technical change , efficincy and Joaquín Maudos , José Manuel Pastor and Lorenzo Serrano.
25. OECD. (2002). Reading for Change: Performance and Engagement across Countries. OECD. https://doi.org/10.1787/9789264099289-en.
26. Pintér, J. D. (2007). Nonlinear optimization with GAMS /LGO. Journal of Global Optimization, 38(1), 79–101. https://doi.org/10.1007/s10898-006-9084-2.
27. Polya, G. (1962). Mathematical discovery: On understanding, learning and teaching problem solving. New York: Wiley, (vol. 1).
28. Programme for International Student Assessment., & Organisation for Economic Co-operation and Development. (2009). Learning mathematics for life : a perspective from PISA. OECD.
29. Rosenthal, R. E. (2007). A GAMS Tutorial. GAMS - A User’s Guide, 5–26.
30. Sari, Y. M., & Valentino, E. (2016). An Analysis of Students Error In Solving PISA 2012 And Its Scaffolding, 1(2), 90–98.
31. Sinuany-Stern, Z., Mehrez, A., & Barboy, A. (1994). Academic departments efficiency via DEA. Computers & Operations Research, 21(5), 543–556. https://doi.org/10.1016/0305-0548(94)90103-1.
32. Stacey, K., Almuna, F., Caraballo, R. M., Lupia, L., Park, K. M., Perl, H., & Rafiepour, A. (2015). PISA’ s Influence on Thought and Action in Mathematics Education. https://doi.org/10.1007/978-3-319-10121-7.
33. Sumirattana, S., Makanong, A., & Thipkong, S. (2017). Using realistic mathematics education and the DAPIC problem-solving process to enhance secondary school students’ mathematical literacy. Kasetsart Journal of Social Sciences, 38(3), 307–315. https://doi.org/10.1016/j.kjss.2016.06.001.
34. The national curriculum in. (2014, December), https://www.gov.uk/dfe/nationalcurriculum .
35. Thomson, S., Hillman, K., & Bortoli, L. De. (2013). A Teacher’s Guide to PISA Mathematical Literacy. OECD Programme for International Student Assessment (PISA Australia). Retrieved from https://research.acer.edu.au/ozpisa/12.
36. Tohidi, G., & Razavyan, S. (2013). A circular global profit Malmquist productivity index in data envelopment analysis. Applied Mathematical Modelling, 37(1–2), 216–227. https://doi.org/10.1016/j.apm.2012.02.026.
37. Wang, Y. M., & Lan, Y. X. (2011). Measuring Malmquist productivity index: A new approach based on double frontiers data envelopment analysis. Mathematical and ComputerModelling, 54(11 12), 2760 2771. https://doi.org/10.1016/j.mcm.2011.06.064
38. Wei, Z., & Hao, R. (2011). The Role of Human Capital in China’s Total Factor Productivity Growth . The Developing Economies, 49(1), 1-35.