Türkiye Yüzyılı Maarif Modeli’nin K-12 Düzeyinde Tahmin Becerisi Açısından Karşılaştırılmalı Analizi

Öz

Bu çalışmanın amacı K-12 düzeyinde Türkiye Yüzyılı Maarif Modeli (TYMM) matematik öğrenme çıktıları ile Türkiye genelinde yürürlükte olan İlkokul, Ortaokul ve Ortaöğretim Matematik Dersi Öğretim Programları ve Okul Öncesi Eğitim Programları Matematik Alanı kazanımlarının tahmin becerisi çerçevesinde incelenmesi, farklılık gösterdikleri noktaların ortaya konulması, bu farklılıkların yorumlanması ve tartışılmasıdır. Doküman analizi tekniği kullanılarak incelenen programlarda işlemsel tahmin becerisine benzer şekilde yer verildiği gözlenmiştir. Ancak, TYMM’nin ölçmede tahmin ve yığın tahmini alanlarına yönelik daha fazla sayıda öğrenme çıktısı ve öğrenme-öğretme uygulaması içerdiği sonucuna ulaşılmıştır. Sayı doğrusuna dair tahmin becerisini içeren kazanım/öğrenme çıktılarına yürürlükte olan Matematik Dersi Öğretim Programlarında ve TYMM’de açıkça yer verilmediği fakat bazı kazanımların/öğrenme çıktılarının açıklamaları ve öğrenme-öğretme uygulamalarının bu tahmin türünü içerdiği sonucuna varılmıştır. Araştırma kapsamında incelenen ortaöğretim kademesine yönelik Matematik Dersi Öğretim Programlarında tahmin becerilerine yönelik herhangi bir öğrenme çıktısına rastlanmamıştır.

Anahtar Kelimeler

• Tahmin becerisi
• Türkiye Yüzyılı Maarif Modeli
• Matematik Dersi öğretim programı

A Comparative Analysis of the Türkiye Century Education Model at the K-12 Level in Terms of Estimation Skills

Öz

The aim of this study is to examine the mathematics learning outcomes of the Türkiye Century Education Model (TCEM) at the K–12 level within the framework of estimation skills, in comparison with the learning objectives of the mathematics domain of the currently implemented Preschool Education Curriculum and the Mathematics Curricula for Primary, Middle, and High School Education in Türkiye. The study seeks to identify and discuss the differences between these curricula and interpret their implications. Using document analysis, it was observed that computational estimation is similarly addressed in the programs. However, the TCEM was found to include a greater number of learning outcomes and learning-teaching practices related to measurement estimation and numerosity estimation. It was also concluded that while explicit learning outcomes related to number line estimation were not identified in either the current Mathematics Curricula or the TCEM, certain learning outcomes and associated instructional practices implicitly incorporate this type of estimation. Additionally, no learning outcomes related to estimation skills were found in the High School Mathematics Curricula examined within the scope of this research.

Anahtar Kelimeler

• Estimation skills
• Turkish Century Education Model
• Mathematics curriculum

Kaynakça

1. Andrews, P., Xenofontos, C., & Sayers, J. (2021). Estimation in the primary mathematics curricula of the United Kingdom: Ambivalent expectations of an essential competence. International Journal of Mathematical Education in Science and Technology, 53(8), 2199–2225. https://doi.org/10.1080/0020739X.2020.1868591
2. Barth, H., Starr, A., & Sullivan, J. (2009). Children’s mappings of large number words to numerosities. Cognitive Development, 24(3), 248–264. https://doi.org/10.1016/j.cogdev.2009.04.001
3. Bartelet, D., Vaessen, A., Blomert, L., & Ansari, D. (2014). What basic number processing measures in kindergarten explain unique variability in first-grade arithmetic proficiency? Journal of Experimental Child Psychology, 117, 12–28. https://doi.org/10.1016/j.jecp.2013.08.010
4. Best, J. W., & Khan, J, V. (2006). Research in education. (3rd Ed.). New York: Pearson
5. Bulut, S., Yavuz, F. D., & Yaman, B. (2017). Tahmin becerilerinin 1948’den 2015’e 1-5 sınıflar matematik dersi öğretim programlarındaki yeri. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 18(1), 19–39.
6. Common Core State Standards Initiative [CCSSI]. (2012). Common core state standards for mathematics. https://learning.ccsso.org/wp-content/uploads/2022/11/Math_Standards1.pdf
7. Desli, D., & Giakoumi, M. (2017). Children’s length estimation performance and strategies in standard and non-standard units of measurement. International Journal for Research in Mathematics Education, 7(3), 61–84.
8. Desli, D., & Lioliou, A. (2020). Relationship between computational estimation and problem solving. International Electronic Journal of Mathematics Education, 15(3). https://doi.org/10.29333/iejme/8435

9. DeWolf, M., Bassok, M., & Holyoak, K. (2015). From rational numbers to algebra: Separable contributions of decimal magnitude and relational understanding of fractions. Journal of Experimental Child Psychology, 133, 72–84. https://doi.org/10.1016/j.jecp.2015.01.013
10. Forster, N. (1995). The analysis of company documentation. C. Cassell & G. Symon (Eds). Qualitative methods in organizational research: A practical guide. London: Sage Publications.
11. Ganor-Stern, D. (2016). Solving math problems approximately: A developmental perspective. PLoSONE, 11(5), 1–16. https://doi.org/10.1371/journal.pone.0155515
12. Ganor-Stern, D. (2018). Do exact calculation and computation estimation reflect the same skills? Developmental and individual differences perspectives. Frontiers in Psychology, 9. https://doi.org/10.3389/fpsyg.2018.01316
13. Gliner, G. (1991). Factors contributing to success in mathematical estimation in preservice teachers: Types of problems and previous mathematical experience. Educational Studies in Mathematics, 22(6), 595–606. https://doi.org/10.1007/BF00312717
14. Gönen, S. (2008). A study on student teachers’ misconceptions and scientifically acceptable conceptions about mass and gravity. Journal of Science Education and Technology, 17, 70–81. https://doi.org/10.1007/s10956-007-9083-1
15. Hodzik, S., & Lemaire, P. (2011). Inhibition and shifting capacities mediate adults’ age-related differences in strategy selection and repertoire. Acta Psychologica, 137(3), 335–344. https://doi.org/10.1016/j.actpsy.2011.04.002
16. Hogan, T. P., & Brezinski, K. L. (2003). Quantitative estimation: One, two, or three abilities? Mathematical Thinking and Learning, 5(4), 259–280. https://doi.org/10.1207/S15327833MTL0504_02
17. Hong, D., Choi, K., Runnalls, C., & Hwang, J. (2018). Do textbooks address known learning challenges in area measurement? A comparative analysis. Mathematics Education Research Journal, 30(3), 325–354. https://doi.org/10.1007/s13394-018-0238-6
18. Hoth, J., Heinze, A., Weiher, D., Ruwisch, S., & Huang, H. (2019). Primary school students’ length estimation competence—A cross-country comparison between Taiwan and Germany. In J. Novotná, & H.Moraová (Eds.), Opportunities in learning and teaching Elementary mathematics (pp. 201–211). Charles University.
19. Huber, S., Sury, D., Moeller, K., Rubinsten, O., & Nuerk, H.-C. (2015). A general number-to-space mapping deficit in developmental dyscalculia. Research in Developmental Disabilities, 43–44, 32–42. https://doi.org/10.1016/j.ridd.2015.06.003
20. Jason, M. H. (Ed.). (2008). Evaluating programs to increase student achievement. Corwin Press.
21. Jones, M. G., & Taylor, A. R. (2009). Developing a sense of scale: Looking backward. Journal of Research in Science Teaching, 46(4), 460–475. https://doi.org/10.1002/tea.20288
22. Joram, E., Subrahmanyam, K., & Gelman, R. (1998). Measurement estimation: Learning to map the route from number to quantity and back. Review of Educational Research, 68, 413–419. https://doi.org/10.2307/1170734
23. Kayhan Altay, M., Alkaş Ulusoy, Ç., & Özer, A. (2024). Examining kindergarten children’s numerosity estimation skills. Early Childhood Educ J 52, 503–513. https://doi.org/10.1007/s10643-023-01449-z
24. Kramer, P., Bressan, P., & Grassi, M. (2018). The SNARC effect is associated with worse mathematical intelligence and poorer time estimation. Royal Society Open Science, 5(8), 172362. https://doi.org/10.1098/rsos.172362
25. Lemaire, P., & Arnaud, L. (2008). Young and older adults' strategies in complex arithmetic. The American Journal of Psychology, 121(1), 1–16. https://doi.org/10.2307/20445440
26. Lucas, K. K., & Son, J. W. (2012). Integrating Measurement and Computational Estimation in Geometry: classroom-ready activities. MatheMatics teaching in the Middle school, 18(5), 308–316. https://doi.org/10.5951/mathteacmiddscho.18.5.0308
27. Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. Jossey-Bass.
28. Milli Eğitim Bakanlığı [MEB]. (2013). Okul öncesi eğitimi programı. MEB. ttps://tegm. meb.gov.tr/dosya/okuloncesi/ooprogram.pdf
29. Milli Eğitim Bakanlığı [MEB]. (2018a). Matematik dersi öğretim programı İlkokul ve ortaokul 1,2,3,4,5, 6, 7 ve 8. sınıflar). MEB. http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329
30. Milli Eğitim Bakanlığı [MEB]. (2018b). Ortaöğretim matematik dersi (9, 10, 11 ve 12.sınıflar) öğretim programı. MEB. http://mufredat.meb.gov.tr/ProgramDetay.aspx?-PID=343
31. Milli Eğitim Bakanlığı [MEB]. (2018c). Matematik dersi öğretim programı tanıtım sunusu ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar. MEB. https://tegm.meb.gov.tr/meb_iys_dosyalar/2017_06/09163230_Matematik_Dersi_1-8_Ders_ProgramY_TanYtYm_Sunusu.pdf
32. Milli Eğitim Bakanlığı [MEB]. (2024a). Okul öncesi eğitim programı. MEB. https://tegm.meb.gov.tr/dosya/okuloncesi/guncellenenokuloncesiegitimprogrami.pdf
33. Milli Eğitim Bakanlığı [MEB]. (2024b). Okul öncesi eğitim programı Türkiye Yüzyılı Maarif Modeli. MEB. https://tymm.meb.gov.tr/upload/program/2024programokuloncesiOnayli.pdf
34. Milli Eğitim Bakanlığı [MEB]. (2024c). İlkokul matematik dersi öğretim programı (1, 2, 3, ve 4. sınıflar) Türkiye Yüzyılı Maarif Modeli. MEB. https://tymm.meb.gov.tr/upload/program/2024programmat1234Onayli.pdf
35. Milli Eğitim Bakanlığı [MEB]. (2024d). Ortaokul matematik dersi öğretim programı (5, 6, 7, ve 8. sınıflar) Türkiye Yüzyılı Maarif Modeli. MEB. https://tymm.meb.gov.tr/upload/program/2024programmat5678Onayli.pdf
36. Milli Eğitim Bakanlığı [MEB]. (2024e). Ortaöğretim matematik dersi öğretim programı (Hazırlık, 9, 10, 11, ve 12. sınıflar) Türkiye Yüzyılı Maarif Modeli. MEB. https://tymm.meb.gov.tr/upload/program/2024programmath9101112Onayli.pdf
37. Mitchell, J. H., Hawkins, E. F., Stancavage, F. B., & Dossey, J. A. (1999). Estimation skills, mathematics-in-context, and advanced skills in mathematics: Results from three studies of the National Assessment of Educational Progress 1996 mathematics assessment. National Center for Education Statistics.
38. National Council of Teachers of Mathematics [NCTM]. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence.NCTM
39. O’Leary. Z., (2004). The Essential Guide to Doing Research. Thousand Oaks, CA: Sage.
40. Pizarro, N., Gorgorió, N., & Albarracín, L. (2015). Primary teacher’ approach to measurement estimation activities. In K. Krainer, & N. Vondrová (Eds.), Proceedings of the Ninth Congress of the European Society for research in mathematics education (pp. 3227–3233). Charles University in Prague and ERME.
41. Reys, B. J. (1986). Teaching computational estimation: Concepts and strategies. In H. L. Shoen and W. J. Zweng (Eds.), Estimation and mental computation-1986 year book (pp. 31-44). National Council of Teachers of Mathematics.
42. Reys, R., & Bestgen, B. (1981). Teaching and assessing computational estimation skills. The Elementary School Journal, 82(2), 116–127. https://doi.org/10.1086/461246
43. Rouder, J., & Geary, D. (2014). Children’s cognitive representation of the mathematical number line. Developmental Science, 17(4), 525–536. https://doi.org/10.1111/desc.12166
44. Ruwisch, S., Heid, M., & Weiher, D. F. (2015). Measurement estimation in primary school: Which answer is adequate? InK. Beswick, T. Muir, & J. Fielding-Wells (Eds.), Proceedings of 39th Conference of the international group for the psychology of mathematics Education (Vol. 4, pp. 113–120). PME.
45. Seethaler, P., & Fuchs, L. (2006). The cognitive correlates of computational estimation skill among third-grade students. Learning Disabilities Research & Practice, 21(4), 233–243. https://doi.org/10.1111/j.1540-5826.2006.00220.x
46. Si, J., Li, H., Sun, Y., Xu, Y., & Sun, Y. (2016). Age-related differences of individuals’ arithmetic strategy utilization with different level of math anxiety. Frontiers in Psychology, 7, 1612–1612. PubMed. https://doi.org/10.3389/fpsyg.2016.01612
47. Siegler, R., & Booth, J. (2005). Development of numerical estimation: A review. In J. Campbell (Ed.), Handbook of mathematical cognition (s. 197–212). Psychology Press. https://doi.org/10.1111/j.1751228X.2009.01064.x
48. Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14(3), 237–250. https://doi.org/10.1111/1467-9280.02438
49. Siegler, R., Thompson, C., & Opfer, J. E. (2009). The logarithmic-to-linear shift: One learning sequence, many tasks, many time scales. Mind, Brain, and Education, 3(3), 143–150. https://doi.org/10.1111/j.1751-228X.2009.01064.x
50. Sowder, J. (1992). Estimation and number sense. In D.A. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning (s. 371–389). Macmillan.
51. Star, J. R., & Rittle-Johnson, B. (2009). It pays to compare: An experimental study on computational estimation. Journal of Experimental Child Psychology, 102(4), 408–426. https://doi.org/10.1016/j.jecp.2008.11.004
52. Sullivan, J., & Barner, D. (2014). The development of structural analogy in number-line estimation. Journal of Experimental Child Psychology, 128, 171–189. https://doi.org/10.1016/j.jecp.2014.07.004
53. Sunde, P. B., Petersson, J., Nosrati, M., Rosenqvist, E., & Andrews, P. (2021). Estimation in the Mathematics Curricula of Denmark, Norway and Sweden: Inadequate Conceptualisations of an Essential Competence. Scandinavian Journal of Educational Research, 66(4), 626–641. https://doi.org/10.1080/00313831.2021.1897881
54. Van de Walle, J., & Thompson, C. S. (1985). Let’s do it: Estimate how much. The Arithmetic Teacher, 32(9), 4–8. https://doi.org/10.5951/AT.32.9.0004
55. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2020). Elementary and middle school mathematics: Teaching developmentally. (10th ed.). Pearson.
56. Wong, T.-Y., Ho, S.-H., & Tang, J. (2016). Consistency of response patterns in different estimation tasks. Journal of Cognition and Development, 17(3), 526–547. https://doi.org/10.1080/15248372.2015.1072091