MATEMATİK BAŞARISINI ETKİLEYEN BAZI FAKTÖRLERİN YORDAMA GÜCÜNÜN YAPAY SİNİR AĞLARI İLE BELİRLENMESİ

Öz

Bu çalışmada PISA 2012’ye katılan 15 yaş grubu Türk öğrencilere ilişkin veriler ışığında; öğrencilerin matematik başarılarını etkileyen bazı faktörlerin yordama gücünün belirlenmesi amaçlanmaktadır. Bu amaçla, “fen bilimleri başarısı”, “okuma başarısı”, “matematik kaygısı”, “evdeki eğitimsel olanaklar”, “evdeki olanaklar”, “matematiğe yönelik ilgi”, “matematiğe yönelik tutum” ve “matematik öğretmeninin desteği” değişken olarak ele alınmıştır. Bu değişkenlerin, öğrencilerin matematik başarısını yordayıcılık düzeyini belirlemede Yapay Sinir Ağlarından (YSA) yararlanılmıştır. Çalışmadan elde edilen bulgularda, yapay sinir ağları modelinde matematik başarısını doğru sınıflama yüzdesi %89,1 olarak hesaplanmıştır. Ayrıca matematik başarısı üzerinde istatistiksel olarak diğer değişkenlere göre; en çok anlamlı etkiye sahip olan değişken “fen bilimleri başarısı”, en az anlamlı etkiye sahip olan değişken ise “evdeki olanaklar” olarak belirlenmiştir.

Anahtar Kelimeler

• PISA 2012,yapay sinir ağları,matematik başarısı

Kaynakça

1. Abazaoğlu, İ., Yatağan, M., Yıldızhan, Y., Arifoğlu, A., ve Umurhan, H. (2015). Öğrencilerin matematik başarısının uluslararası fen ve matematik eğilimleri araştırması sonuçlarına göre değerlendirilmesi. Turkish Studies, 10(7), 33-50
2. Aiken, L. R. (1970). Attitudes toward mathematics. Review of educational research, 40(4), 551-596.
3. Akyüz, G. (2014). The effects of student and school factors on mathematics achievement in TIMSS 2011. Egitim ve Bilim, 39(172), 150-162.
4. Al Mutawah, M. A. (2015). The Influence of Mathematics Anxiety in Middle and High School Students Math Achievement. International Education Studies,8(11), 239.
5. Allport, G. W. 1935. Attitudes. C. Murchison (Ed.)Handbook of social psychology içinde (s.798–844). Worcester, MA: Clark Univ. Press.
6. Andrews, A. ve Brown, J. (2015). The effects of math anxiety. Education,135(3), 362-370.
7. Andrews, P. (2007). The curricular importance of mathematics: a comparison of English and Hungarian teachers’ espoused beliefs. Journal of Curriculum Studies, 39(3), 317-338.
8. Angateeah, K. S., Gonpot, P. ve Sukon, K. S. (2014, Haziran). Mathematics achievement: Impact of affective variables and socio-economic status. International Conference on Advanced Education and Management, Pekin, Çin kongresinde bildiri olarak sunulmuştur. Bildiri özeti http://apps.webofknowledge.com/Search.do?product=UA&SID=T2yASUuwi5bOqLJCIFV&search_mode=GeneralSearch&prID=45bbef77-b8ae-4974-a69a-df4bc1f2bfb6 adresinden alınmıştır.

9. Anıl, D., Özer - Özkan, Y. ve Demir, E. (2015). PISA 2012 Araştırması Ulusal Nihai Rapor. Ankara: T.C. Milli Eğitim Bakanlığı.
10. Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current directions in psychological science, 11(5), 181-185.
11. Aypay, A. (2010). Information and communication technology (ICT) usage and achievement of Turkish students in PISA 2006. The Turkish Online Journal of Educational Technology-TOJET, 9(2), 116-124.
12. Baldwin, D. ve Henderson, P. B. (2002). The Importance of mathematics to the software practitioner. IEEE Software, 19(2) , Pages: 111-112. http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=991383 adresinden alınmıştır.
13. Bekdemir, M. (2009). Meslek yüksekokulu öğrencilerinin matematik kaygı düzeylerinin ve başarılarının değerlendirilmesi. Erzincan University Journal of Science and Technology, 2(2), 169-189.
14. Billstein, R., Libeskind, S. ve Lott, J. (2014). A problem solving approach to mathematics for elementary school teachers (11. Baskı). Pearson.
15. Breslich, E. R. (1966). Importance of Mathematics in General Education. The Mathematics Teacher,59(5), 464-469.
16. Caponera, E., ve Russo, P. M. (2014). Student characteristics and mathematics achievement in Timss. Cadmo, 22(2).
17. Chen, J. J. L. (2005). Relation of academic support from parents, teachers, and peers to Hong Kong adolescents' academic achievement: The mediating role of academic engagement. Genetic, Social, And General Psychology Monographs, 131(2), 77-127.
18. Chen, J. J. L. (2008). Grade-level differences relations of parental, teacher and peer support to academic engagement and achievement among Hong Kong students. School Psychology International, 29(2), 183-198.
19. Christou, C., Mousoulides, N., Pittalis, M. ve Pitta-Pantazi, D. (2005, Ağustos). Student, classroom, and school variables' effects on mathematical achievement. International Symposium on Elementary Mathematics Teaching, Prag, Çek Cumhuriyeti sempozyumunda bildiri olarak sunulmuştur. Bildiri özeti http://apps.webofknowledge.com/Search.do?product=UA&SID=N219VpBnZqU4XAcUAVG&search_mode=GeneralSearch&prID=15e63b74-b5d4-49b1-88ef-f6b4b6df51f6 adresinden alınmıştır.
20. Coleman, J. S., Campbelli E. Q, Hobson C., McPartland, J., Mood, A. M., Weinfield, F. D. ve York, R. L. (1966). Equality of educational opportunity. (Rapor numarası: 0E-36001). Washington: National Center for Educational Statistics.
21. Corfield, D. (2001). The importance of mathematical conceptualisation. Studies in History and Philosophy of Science Part A, 32(3), 507-533.
22. Çırak, G. ve Çokluk, Ö. (2013). Yükseköğretimde öğrenci başarılarının sınıflandırılmasında yapay sinirağları ve lojistik regresyon yöntemlerinin kullanılması.Mediterranean Journal of Humanities, 3(2), 71-79.
23. D’Ambrosio, U. (1990). The role of mathematics in building up a democratic society and the civilizatory mission of the European powers since the discoveries. R. Noss; A. Brown; P. Dowling; P. Drake; M. Harris; C. Hoyles; S. Mellin-Olsen (Ed.), Political dimensions of mathematics education: Action and critique içerisinde. Proceedings of the First International Conference. London: Institute of Education, University of London, p. 13– 21.
24. Demir, İ. ve Kılıç, S. (2010). Using PISA 2003, Examining the factors affecting students’ mathematics achievement, H. Ü. Eğitim Fakültesi Dergisi, 38, 44-54.
25. Demir, İ. Ünal, H. ve Kılıç, S. (2010). The effect of quality of educational resources on mathematics achievement: Turkish case from PISA-2006. Procedia Social and Behavioral Sciences, 2, 1855-1859.
26. Demir, İ. Kılıç, S. ve Ünal, H. (2010). Effects of students’ and schools’ characteristics on mathematics achievement: findings from PISA 2006. Procedia-Social and Behavioral Sciences, 2(2), 3099-3103.
27. Dewey, J. (1913). İnterest and effort in education. Boston: Riverside.
28. Dewey, J. (1933). How we think? Lexington, MA: Heath.
29. Dewey, J. (1938). Experience and education. New York: Maxmillian.
30. Dinçer, M. A. Ve Uysal - Kolaşin, G. (2009). Türkiye’de öğrenci başar›s›nda eşitsizliğin belirleyicileri. Eğitim Reformu Girişimi.
31. EARGED. (2005). PISA 2003 Projesi Ulusal Nihai Rapor. Ankara: MEB. http://pisa.meb.gov.tr/wp-content/uploads/2013/07/PISA-2003-Ulusal-Nihai-Rapor.pdf adresinden alınmıştır.
32. Eun, Y. J. (2007). The influence of students' backgroud, classroom practice, and schools' environmental factors on mathematics achievement. The journal of Yeolin Education, 15(3), 263-280.
33. Fisher, P. H., Dobbs-Oates, J., Doctoroff, G. L. ve Arnold, D. H. (2012). Early math interest and the development of math skills. Journal of Educational Psychology, 104(3), 673 - 681.
34. Gilleece, L., Cosgrove, J. ve Sofroniou, N. (2010). Equity in mathematics and science outcomes: Characteristics associated with high and low achievement on PISA 2006 in Ireland. International Journal of Science and Mathematics Education, 8(3), 475-496.
35. Goforth, K., Noltemeyer, A., Patton, J., Bush, K. R., ve Bergen, D. (2014). Understanding mathematics achievement: an analysis of the effects of student and family factors. Educational Studies, 40(2), 196-214.
36. Gürsakal, S. (2012). PISA 2009 öğrenci başarı düzeylerini etkileyen faktörlerin değerlendirilmesi. Süleyman Demirel University Journal of Faculty of Economics & Administrative Sciences, 17(1), 441-452.
37. Güzel, I.Ç., ve Berberoğlu, G. (2005). An analysis of the programme for international student assessment 2000 (PISA 2000) mathematical literacy data for Brazilian, Japanese, and Norwegian students. Studies In Educational Evaluation, 31(4), 283-314.
38. Güzeller, C.O., ve Akın, A. (2011). An examination of the programme for international student assessment (PISA) 2003 Turkish database with the aim of exploring the relationship between homework variables and mathematics achievement. Educational Research and Reviews, 6(13), 793-803.
39. Hammouri, H. (2004). Attitudinal and motivational variables related to mathematics achievement in Jordan: findings from the Third International Mathematics and Science Study (TIMSS). Educational Research, 46(3), 241-257.
40. Hamzaçebi, C. (2011). Yapay sinir ağları. Bursa: Ekin.
41. Hannaford, C. (1998). Mathematics teaching is democratic education. ZentralblattfürDidaktik der Mathematik, 30(6), p.181-187.
42. Hart, S. A., Logan, J. A., Thompson, L., Kovas, Y., McLoughlin, G. ve Petrill, S. A. (2016). A latent profile analysis of math achievement, numerosity, and math anxiety in twins. Journal of educational psychology, 108(2), 181.
43. Hidi, S. (1990). Interest and its contribution as a mental resource for learning. Review Of Educational Research, 60(4), 549-571.
44. http://pisa.meb.gov.tr/?page_id=18
45. http://www.oecd.org/pisa/aboutpisa/
46. Ilhyuk, K. ve Sang-Jin, K. (2005). Structural relations between high school students' family background factors and mathematics achievement. The Journal of Korean Education, 32(4), 193-221.
47. Ismail, N.A. ve Awang, H. (2012) Student Factors and Mathematics Achievement: Evidence from TIMSS 2007. Eurasia Journal of Mathematics, Science & Technology Education, 8(4), 249-255.
48. Işık, A., Çiltaş, A., ve Bekdemir, M. (2008). Matematik eğitiminin gerekliliği ve önemi.Atatürk Üniversitesi Kazım Karabekir Eğitim Fakültesi Dergisi, (17).
49. İlhan, M. ve Sünkür, M. Ö. (2013). Matematik kaygısının matematik başarısını yordama gücünün cinsiyet ve sınıf değişkenleri açısından incelenmesi. University of Gaziantep Journal of Social Sciences, 12(3), 427-441.
50. Jiban, C. L., ve Deno, S. L. (2007). Using math and reading curriculumbased measurements to predict state mathematics test performance: Are simple one-minute measures technically adequate? Assessment for Effective Intervention, 32, 78–89.
51. Kalender, Ö. M. (2010). The roles of affective, socioeconomic status and school factors on mathematics achievement: A structural equation modeling study. (Yayımlanmamış doktora tezi). Middle East Technical University, Ankara.
52. Katz, I., Assor, A., Kanat-Maymon, Y. ve Bereby-Meyer, Y. (2006). Interest as a motivational resource: Feedback and gender matter, but interest makes the difference. Social Psychology of Education, 9(1), 27-42.
53. Kıray, S. A., Gök, B., ve Bozkır, A. S. (2015). Identifying the factors affecting science and mathematics achievement using data mining methods. Journal of Education in Science, Environment and Health, 1(1), 28-48.
54. Kiwanuka, H. N., Van Damme, J., Van Den Noortgate, W., Anumendem, D. N. ve Namusisi, S. (2015). Factors affecting Mathematics achievement of first-year secondary school students in Central Uganda. South African Journal of Education, 35(3), 1-16.
55. Koğar, H, (2015). Examination of factors affecting PISA 2012 mathematical literacy through mediation model. Eğitim ve Bilim, 40(179), 45-55.
56. Köller, O., Baumert, J. ve Schnabel, K. (2001). Does interest matter? The relationship between academic interest and achievement in mathematics. Journal for Research in Mathematics Education 32(5), 448-470.
57. Krapp, A. (1999). Interest, motivation and learning: An educational-psychological perspective. European Journal Of Psychology Of Education, 14(1), 23-40.
58. Krech D., Crutchfield R. S., Ballacy E. L. (1962): Individual in Society: A textbook of social psychology. New York, NY, US: McGraw-Hill.
59. Larwin, K. H. (2010). Reading is fundamental in predicting math achievement in 10 th graders. International Electronic Journal of Mathematics Education, 5(3), 131-145.
60. Liu, T., Holmes, K., ve Albright, J. (2015). Predictors of mathematics achievement of migrant children in Chinese urban schools: A comparative study. International Journal of Educational Development, 42, 35-42.
61. Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal for research in mathematics education, 520-540.
62. Ma, X. ve Xu, J. (2004). The causal ordering of mathematics anxiety and mathematics achievement: a longitudinal panel analysis. Journal of Adolescence, 27(2), 165-179.
63. Martins, L. ve Veiga, P. (2010). Do inequalities in parents’ education play an important role in PISA students’ mathematics achievement test score disparities? Economics of Education Review, 29(6), 1016-1033.
64. MEB (2010). Uluslararası öğrenci değerlendirme programı pısa 2009 ulusal ön raporu. Eğitimi Araştırma ve Geliştirme Dairesi Başkanlığı.
65. McConney, A. ve Perry, L. B. (2010). Science and mathematics achievement in Australia: The role of school socioeconomic composition in educational equity and effectiveness. International Journal of Science and Mathematics Education, 8(3), 429-452.
66. Mullis, I. V. S., Martin, M. O.ve Foy, P. (2013). The impact of reading ability on TIMSS Mathematics and Science Achievement at the Fourth Grade: An analysis by item reading demands. M. O. Martin ve I. V. S. Mullis (Ed.), Relationships among reading, mathematics and science achievement at the fourth grade-Implications for early learningiçinde. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College.
67. Núñez-Peña, M. I., Suárez-Pellicioni, M. ve Bono, R. (2013). Effects of math anxiety on student success in higher education. International Journal of Educational Research, 58, 36-43.
68. OECD, (1999). Measuring student knowledge and skills http://www.oecd.org/edu/school/programmeforinternationalstudentassessmentpisa/33693997.pdf adresinden alınmıştır.
69. OECD, (2001). Knowledge and skills for life: First results from the OECD programme for international student assesment (PISA) 2000. https://www.oecd.org/edu/school/programmeforinternationalstudentassessmentpisa/33691620.pdf adresinden alınmıştır.
70. 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 adresinden alınmıştır.
71. OECD, (2014). PISA 2012 Technical report. https://www.oecd.org/pisa/pisaproducts/PISA-2012-technical-report-final.pdf adresinden alınmıştır.
72. Opdenakker, M. C., Van Damme, J., De Fraine, D. F., Van Landeghem, G., ve Onghena, P. (2002). The effect of schools and classes on mathematics achievement. School effectiveness and school improvement, 13(4), 399-427.
73. Oral, I. ve McGivney, E. (2013). Türkiye’de matematik ve fen bilimleri alanlarında öğrenci performansı ve başarının belirleyicileri. Eğitim Reformu Girişimi Analiz Raporu. http://www.egitimreformugirisimi.org/sites/www.egitimreformugirisimi.org/files/ERG%20-TIMSS%202011%20Analiz%20Raporu-03.09.2013.pdf adresinden alınmıştır.
74. Osgood, C.E., Suci, G., ve Tannenbaum, P. (1957) The measurement of meaning. Urbana, IL: University of Illinois Press.
75. Ovayolu, Ö., ve Kutlu, Ö.(2011). The range of scores in competency clusters of Turkish students in mathematics sub-test according to PISA2006. Procedia Social and Behavioral Sciences, 15, 17–26.
76. Öztemel, E. (2003). Yapay sinir ağları. İstanbul: Papatya.
77. Prechelt, L. (1998). Early stopping-but when? G. Montavon, G. B. Orr ve K. R. Müller (Ed.),Neural Networks: Tricks of the trade içinde (s. 55-69). Berlin Heidelberg: Springer.
78. Priddy, K. L. ve Keller, P. E. (2005). Artificial neural networks: An introduction, Washington: SPIE Press.
79. Polya, G. (1973). How to solve it: A new aspect of mathematical method (2. baskı) Princeton: Princeton university press.
80. Ramirez, G.,Gunderson, E. A., Levine, S. C. ve Beilock, S. L. (2013). Math anxiety, working memory, and math achievement in early elementary school. Journal of Cognition and Development, 14(2), 187-202.
81. Renninger, K. ve Hidi, S. (2002). Student interest and achievement: Developmental issues raised by a case study. Wigfield, A. ve Eccles, J. S. (Ed), (2002). Development of achievement motivation. A volume in the educational psychology series içinde (pp. 173-195). San Diego, CA, US: Academic Press.http://dx.doi.org/10.1016/B978-012750053-9/50009-7
82. Renninger, A., Hidi, S. ve Krapp, A. (Ed.) (1992). The role of interest in learning and development. New York: Psychology Press.
83. Reyna, V. F. ve Brainerd, C. J. (2007). The importance of mathematics in health and human judgment: Numeracy, risk communication, and medical decision making. Learning and Individual Differences, 17(2), 147-159.
84. Roe, A. ve Taube, K. (2006). How can reading abilities explain differences in math performances? Mejding, J. ve Roe, A. (Ed.), Northern lights on PISA 2003: A reflection from Nordic countries içinde (s. 129-141).
85. Ruff, S. E. ve Boes, S. R. (2014). The sum of all fears: The effects of math anxiety on math achievement in fifth grade students and the implications for school counselors. Georgia School Counselors Association Journal, 21(1).
86. Sarnoff, I. (1960). Psychoanalytic theory and social attitudes. Public opinion quarterly, 24(2), 251-279.
87. Savaş, E. (2003).Matematik eğitimi ile demokrasi arasındaki ilişki üzerine bir çalışma. Eğitim Araştırmaları Dergisi, 11.
88. Savaş, E., Taş, S. ve Duru, A. (2010). Factors affecting students’ achievement in mathematics. Mathematics learning, 11(1).
89. Schiefele, U. (1991). Interest, learning, and motivation. Educational Psychologist, 26(3-4), 299-323.
90. Schiefele, U., Krapp, A. ve Winteler, A. (1992). Interest as a predictor of academic achievement: A meta-analysis of research. Renninger, A., Hidi, S., ve Krapp, A. (Ed.), The role of interest in learning and development içinde (s. 183-196). New York: Psychology Press.
91. Schreiber, J. B. (2002). Institutional and student factors and their influence on advanced mathematics achievement. The Journal of Educational Research,95(5), 274-286.
92. Shelley, M. ve Yıldırım, A. (2013). Transfer of learning in mathematics, science, and reading among students in Turkey: A study using 2009 PISA data. International Journal of Education in Mathematics, Science and Technology, 1(2), 83-95
93. Smith, M. B., Bruner, J. S. ve White, R. W. (1956). Opinions and personality. New York: John Wiley
94. Sirin, S. R. (2005). Socioeconomic status and academic achievement: A meta-analytic review of research. Review of educational research, 75(3), 417-453.
95. Skovsmose, O. (1990). Mathematical education and democracy. Educational Studies in Mathematics, 21.
96. Skovsmose, O. (1998). Linking mathematics education and democracy: Citizenship, mathematical archaeology, mathemacy and deliberative interaction. Zentralblattfür Didaktik der Mathematik, 30(6), p. 195-203.
97. Strecker, J ve Noack, P (2002). Importance and usefulness of mathematics from the viewpoint of the student. Zeitschrift Fur Padagogik, 45, 359-372.
98. Su, Y.J. ve Lian, G. H. (2011). Reading activity effects on reading achievement and mathematic achievement in post-secondary education. Education and Education Management, 2, 130-134.
99. Şad, S.N., Kış, A., Demir, M. ve Özer, N. (2016). Meta-analysis of the relationship between mathematics anxiety and mathematics achievement. Pegem Eğitim ve Öğretim Dergisi, 6(3), 371-392, http://dx.doi.org/10.14527/pegegog.2016.019
100. Tang Z. ve Fishwick, P.A. (1993). Feedforward Neural nets as models for time series forecasting. ORSA Journal on Computing, 5(4), 374-385.
101. Tennant, J. E., Demaray, M. K., Malecki, C. K., Terry, M. N., Clary, M. ve Elzinga, N. (2015). Students’ ratings of teacher support and academic and social–emotional well-being. School Psychology Quarterly, 30(4), 494.
102. Tepehan, T. (2011). Türk öğrencilerinin PISA başarılarının yordanmasında yapay sinir ağı ve lojistik regresyon modeli performanslarının karşılaştırılması (Yayımlanmamış doktora tezi). Hacettepe Üniversitesi, Ankara.
103. Thurber, R. S., Shinn, M. R., ve Smolkowski, K. (2002). What is measured in mathematics tests? Construct validity of curriculum-based mathematics measures. School Psychology Review, 31, 498–513.
104. Tobias, S. (1994). Interest, prior knowledge, and learning. Review of Educational Research, 64(1), 37-54.
105. Tosun, S. (2007). Sınıflandırmada yapay sinir ağları ve karar ağaçları karşılaştırması: Öğrenci başarıları üzerine bir uygulama (Yayımlanmamış doktora tezi). İstanbul Teknik Üniversitesi, İstanbul.
106. Ünal, H., ve Demir, I. (2009). Divergent thinking and mathematics achievement in Turkey: Findings from the programme for international student achievement (PISA-2003). Procedia Social and Behavioral Sciences,1(1), 1767-1770.
107. Visser, M., Juan, A., ve Feza, N. (2015). Home and school resources as predictors of mathematics performance in South Africa. South African Journal of Education, 35(1), 1-10.
108. Wang, Z., Lukowski, S.L., Hart, S.A., Lyons, I.M., Thompson, L.A., Kovas, Y., Mazzocco, M.M.M., Plomin, R. ve Petrill, S.A. (2015). Is math anxiety always bad for math learning? The role of math motivation
109. Psychological Science, 26(12), 1863–1876.
110. White, K. R. (1982). The relation between socioeconomic status and academic achievement.Psychological Bulletin, 91(3), 461.
111. Wu, S. S., Willcutt, E. G., Escovar, E., ve Menon, V. (2014). Mathematics achievement and anxiety and their relation to internalizing and externalizing behaviors. Journal of learning disabilities, 47(6), 503-514.
112. Zhang, G., Patuwo, B. E., ve Hu, M. Y. (1998). Forecasting with artificial neural networks: The state of the art. International journal of forecasting, 14(1), 35-62.
113. Ziya, E., Doğan, N., ve Kelecioğlu, H. (2010). What is the predicted level of which computer using skills measured in PISA for achievement in mathematics. The Turkish Online Journal of Educational Technology-TOJET, 9(4), 185-191.