İLKOKUL 4. SINIF ÖĞRENCİLERİNİN MODELLEME SÜREÇLERİNİN İNCELENMESİNE YÖNELİK BİR ODAK GRUP ÇALIŞMASI: ALIŞ-VERİŞ PROBLEMİ

Bu çalışmanın amacı ilkokul öğrencilerinin model oluşturma sürecindeki düşünme süreçlerini ve eğer varsa bu süreçte karşılaştıkları zorlukları belirlemektir. Araştırma 2016/2017 eğitim öğretim yılında Kütahya ili Dumlupınar Kolejinde gerçekleştirilmiş nitel bir araştırmadır. Araştırmanın çalışma grubunu amaçlı örnekleme yöntemlerinden ölçüt örnekleme yöntemi kullanılarak seçilen 4 ilkokul 4. sınıf öğrencisi oluşturmaktadır. Veri toplama aracı olarak bir adet gerçek hayat durumlarını içeren alış-veriş problemi kullanılmıştır. Problemde verilenler açık bir şekilde sunulmamış öğrencilerden problem durumunu gerçek hayat koşullarına indirgeyerek problemin içindeki gizli problemleri ortaya çıkarmaları ve gizli problemlerin çözümü için veri toplamaları beklenmiştir. Çalışma verileri odak grup görüşmesi yöntemiyle toplanmış, betimsel analiz yapılarak raporlaştırılmıştır. Çalışma soncunda öğrencilerin grup içi etkileşim sayesinde yeni ve farklı fikirler ortaya atabildikleri, ortaya attıkları fikirleri kanıtlandırarak diğer grup üyelerini ikna etmeye çabaladıkları, arkadaşlarının görüşlerinden hareketle kendi fikirlerini yeniden geliştirebildikleri görülmüştür. Çalışma sonucunda öğrencilerin problem metnine eleştirel gözle bakarak çıkarımlarda bulunabildikleri, gerçekçi bir model kurabilmek için yeni problemler kurabildikleri, araştırma yaparak ihtiyaçları olan ekstra bilgilere ulaşabildikleri, kurdukları problemleri çözüm stratejilerini kullanarak matematiksel ifadelere dönüştürebildikleri, buldukları birden fazla sonucu göz önünde bulundurarak önerilerde bulunabildikleri, buldukları sonuçları değerlendirerek tespit ettikleri tutarsızlıkları giderebildikleri görülmüştür. Çalışma sonucunda elde edilen bir diğer bulgu ise modelleme çalışmalarının doğrusal olmayıp döngüsel olduğu, gerektiğinde bir önceki basamaklara geri dönüşlerin gerçekleşebildiği bulgusudur

A FOCUS GROUP STUDY FOR EXAMINING PRIMARY SCHOOL 4TH-GRADE STUDENTS’ MODELING PROCESS: THE SHOPPING PROBLEM

The purpose of this study is to identify primary school students’ thinking processes within the modeling process and the challenges they encounter, if any. This is a qualitative research study conducted in Dumlupınar college associated with a state university in the city center of Kütahya in the academic year of 2015-2016. The study group of the research was composed of 4 primary school 4th-grade students who were selected with criterion sampling which is a purposive sampling method. The data of the study was collected with the focus group interview method and reported with descriptive analysis. It was seen in the study that the students could suggest new and different ideas, testify these ideas to try to convince other group members and improve their own ideas based on their friends’ opinions. It was concluded that the students could look at the problem text from a critical perspective, create new problems to be able to set a realistic model, access extra information by investigating, mathematize the problems they created by using solution strategies, make recommendations in consideration of multiple results they achieved and evaluate these results and eliminate the inconsistencies they identified

PDF

___

Aşilioğlu, B. (2008). Bilişsel öğrenmeler için eleştirel okumanın önemi ve onu geliştirme yolları. Dicle University Journal of Ziya Gokalp Education Faculty, 11.
Barbey, A. K., Barsalou, L. W. (2009). Reasoning and problem solving: Models. In L. Squire (Ed.), Encyclopedia of neuroscience (pp. 35-43). Oxford: Academic Press.
Basaraba, D., Yovanoff, P., Alonzo, J., ve Tindal, G. (2013). Examining the structure of reading comprehension: do literal, inferential, and evaluative comprehension truly exist?. Reading and Writing, 26(3), 349-379.
Blum ,W. (2015) Quality Teaching of Mathematical Modelling: What Do We Know, What Can We Do? S.J. Cho (ed.), The Proceedings of the 12th International Congress on Mathematical Education, DOI 10.1007/978-3-319-12688-3_9
Blum, W. veve Leiß, D. (2006). “Filling up”– The problem of independence-preserving teacher interventions in lessons with demanding modelling tasks. In: Bosch, M. (Ed.), CERME-4– Proceedings of the Fourth Conference of the European Society for Research in Mathematics Education. Guixol.
Blum, W. veve Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects – state, trends and issues in mathematics instruction. In: Educational Studies in Mathematics 22(1), 37-68.
Boaler, J. (2001) Mathematical modelling and new theories of learning. Teaching Mathematics and its Applications, 20(3), 121–128
Bowling, A. (2002). Research Methods in Health: Investigating Health and Health Services. Philadelphia, PA: McGraw-Hill House.
Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86-95.
Borromeo Ferri, R. (2007). Modelling problems from a cognitive perspective. In: Haines, C. et al. (Eds), Mathematical Modelling: Education, Engineering and Economics. Chichester: Horwood, 260-270.
Borromeo Ferri, R. ve Blum, W. (2009). Insight into Teachers’ Unconscious Behaviour in Modeling Contexts. In: Lesh, R. et al. (Eds), Modeling Students’ Mathematical Modeling Competencies. New York: Springer, 423-432.
Borromeo Ferri, R. ve Blum, W. (2010). Mathematical Modelling in Teacher Education – Experiences from a Modelling Seminar. In: Durand-Guerrier, V., Soury-Lavergne, S. veArzarello, F.(Eds),CERME-6–Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. INRP, Lyon 2010, 2046-2055.
Chamberlin, M. T. (2004). Design principles for teacher investigations of student work. Mathematics Teacher Education and Development, 6, 61–72.
Chikalanga, I. (1992). A Suggested Taxanomy of Inferences for Reading Teacher, Reading in a Foreign Language, 8 (2), 697-709
Çelik, D., Güler, M. (2013) İlköğretim 6. Sınıf Öğrencilerinin Gerçek Yaşam Problemlerini Çözme Becerilerinin İncelenmesi. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 20 180- 195
Çelik, A. ve Özdemir, E. Y. (2011). İlköğretim öğrencilerinin orantısal akıl yürütme becerileri ile oran-orantı problemi kurma becerileri arasındaki ilişki. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30(1), 1-11.
Çetin, H., ve Ertekin, E. (2011). Te relationship between eighth grade primary school students’ proportional reasoning skills and success in solving equations. International Journal of Instruction, 4(1), 47-62.
English, L. D., ve Watters, J. J. (2005). Mathematical modeling in third-grade classrooms. Mathematics Education Research Journal, 16, 59–80.
English, L. D., ve Watters, J. (2004). Mathematical modeling in the early school years. Mathematics Education Research Journal, 16(3), 59–80.
Eraslan, A. ve Kant, S. (2015). Modeling processes of 4th-year middle-school students and the difficulties encountered. Educational Sciences: Theory and Practice, 15(3), 809-824.
Hegarty, M., Mayer, R. E., ve Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87, 18–32.
Hite, S. (2009). Improving Problem Solving by Improving Reading Skills. Math in the Middle Institute Partnership Summative Projects for MA Degree. University of Nebraska – Lincoln
Jitendra, A. K., ve Hoff, K. (1996). The effects of schema-based instruction on the mathematical wordproblem solving performance of students with learning disabilities. Journal of Learning Disabilities, 29, 422– 432.
Keene, E. O. ve Zimmermann, S. (1997). Mosaic of thought: Teaching comprehension in a reader’s workshop. Portsmouth, NH: Heinemann.
Kintsch, W., ve Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92 (1), 109-129
Kintsch, W. (1988). The role of knowledge in discourse comprehension: A construction integration model. Psychological Review, 95, 163-182.
Kispal, A. (2008). Effective Teaching of Inference Skills for Reading. Literature Review. Research Report, DCSF-RR031, 2008. ED501868
Krueger, R.A. (1994). Focus Groups: A Practical Guide For Applied Research. London: SAGE.
Lapp, D., ve Flood, J. (1983). Teaching reading to every child. New York: MacMillan
Lesh, R.A. ve Doerr, H.M. (2003). Beyond constructivism: A models and modelling perspective on teaching, learning, and problem solving in mathematics education. Mahwah: Lawrence Erlbaum.
Liang, X. (2010). Assessmentuse, self-efficacy and mathematics achievement: Comparative analysis of PISA 2003. Data of Finland, Canada and the USA. Evaluation & Research in Education, 23(3), 213-229.
Maass, K. (2010). Classification scheme for modelling tasks. Journal für Mathematik-Didaktik, 31(2), 285-311.
McCormick, S. (1992). Disabled readers’ erroneous responses to inferential comprehension questions Description and analyses. Reading Research Quarterly, 27(1), 54–77.MEB (2005). İlköğretim 1–5. Sınıflar Matematik Dersi Öğretim Programı. Ankara: Talim ve Terbiye Kurulu Başkanlığı.
Merriam, S. (2009).Qualitative research: A guide to design and implementation. San Francisco, CA: Jossey-Bass.
Merriam, S.B. (1998). Qualitative research and case study applications in education. San Francisco: Jossey-Bass.
Niss, M. (2003). Mathematical Competencies and the Learning of Mathematics: The Danish KOM Project. In: Gagatsis, A. ve Papastavridis, S. (Eds), 3rd Mediterranean Conference on Mathematical Education. Athens: The Hellenic Mathematical Society, 115-124.
Leighton, J. P., ve Sternberg, R. J. (2003). Reasoning and problem solving. In A. F. Healy ve R. W. Proctor (Eds.), Experimental Psychology (pp. 623-648). Volume 4 in I. B. Weiner (Editor-inChief) Handbook of psychology. New York: Wiley.
Maass, K. (2007). Modelling tasks for low achieving students. First results of an empirical study. In D. PittaPantazi ve G. Philippou (Eds.), CERME 5 – Proceedings of the Fiſth Congress of the European Society for Research in Mathematics Education (pp. 2120–2129). Larnaca: University of Cyprus.
Odabaş, H., Odabaş, Y., ve Polat, C. (2008). Üniversite öğrencilerinin okuma alışkanlığı: Ankara Üniversitesi örneği. Bilgi Dünyası, 9(2), 431-465.
Özensoy, A. U. (2011). Eleştirel okumaya göre düzenlenmiş sosyal bilgiler dersinin eleştirel düşünme becerisine etkisi. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 7(2).
Özsoy, G.( 2007). İlköğretim 5. Sınıfta Problem Çözme Becerisi ile Matematik başarısı arasındaki ilişki. Yayınlanmamış doktora tezi. Gazi üniversitesi. Ankara.
Pape, S. J. (2004). Middle school children's problem-solving behavior: A cognitive analysis from a reading comprehension perspective. Journal for Research in Mathematics Education, 35 , pp. 187-219.
Perfetti, C. A., Landi, N., ve Oakhill, J. (2005). The acquisition of reading comprehension skill. In M. J. Snowling ve C. Hulme (Eds.), The science of reading: A handbook (pp. 227–247). Malden, MA: Blackwell.
Pressley, M. (2000). What should comprehension Instruction be the Instruction of?. In: Kamil, M. L., Mosenthal, P. B., Pearson, P. D., Ban, R. (Ed.), Handbook of Reading Research, (ss.545-562), Mahwah, NJ: LEA.
Reusser, K. (1985). From situation to equation. On formulation, understanding and solving "situation problems". Institute of Cognitive Science, University of Colorado at Boulder. Technical Report No. l43.
Schapp, S., Vos, P., ve Goedhart, M. (2011). Students overcoming blockages while building a mathematical model: Exploring a framework. In G. Kaiser, W. Blum, R. B. Ferri, ve G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: Te 14. ICMTA Study (pp. 137–146). New York, NY: Springer.
Schleicher, A. (2007). Can competencies assessed by PISA be considered the fundamental school knowledge 15-year-olds shouldpossess? Educational Change, 8(4), 349-357. Smith, G.G., Gerretson, H., Olkun, S. ve Joutsenlahti, J. (2010). Effect of causal stories in solving mathematical story Problems. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi (H. U. Journal of Education), 39: 284-295
Soylu, Y. ve Soylu, C. (2006). Matematik derslerinde başarıya giden yolda problem çözmenin rolü. İnönü Eğitim Fakültesi Dergisi, 7(11), 97–111.
Staub, F.C. ve Reusser, K. (1995). The role of presentational structures in understanding and solving mathematical word problems. In C.A. Weaver, S. Mannes ve C.R. Fletcher (eds.), Discourse comprehension. Essays in honor of Walter Kintsch (pp. 285-305). Hillsdale, NJ: Lawrence Erlbaum.
Steele, D.F ve Johanning, D.I. (2004). A schematic–theoretic view of problem solving and development of algebraic thinking. Educational Studies in Mathematics, 57, 65–90.
Suk, H.J. (1997). The effects of language ability, text presentation style and the nature of questions inference, Doktora tezi, Chong-buk Üniversitesi. Kore
Van Dijk, T. A., ve Kintsch, W. (1983). Strategies of discourse comprehension. New York: Academic Press.
Verschaffel, L., De Corte, E., ve Vierstraete, H. (1999). Upper elementary school pupils’ difficulties in modeling and solving nonstandard additive word problems involving ordinal numbers. Journal for Research in Mathematics Education, 30(3), 265-285.
Verschaffel, L., Greer, B., ve De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets and Zietlinger.
Viennot, D.C., Moreau, S.(2007). Arithmetic problems at school: When there is an apparent contradiction between the situation model and the problem model. British Journal of Educational Psychology (2007), 77, 69–80
Teong. K.S.(2002). Metacognitive Intervention Strategy and Word Problem Solving in a CognitiveApprenticeship-Computer-Based Environment. National Institute of Education, Nanyang Technological University.
Umay, A. (2003). Matematiksel muhakeme yeteneği. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24(3), 234-243.
Ulu, M. (2011). İlköğretim 5. Sınıf öğrencilerinin rutin olmayan problemlerde yaptıkları hataların belirlenmesi ve giderilmesine yönelik bir uygulama. Gazi Üniversitesi, Yayınlanmamış Doktora tezi. Ankara.
Xin, Z., Lin,C.,Zhang.L ve Yan, R.(2007). The Performance of Chinese Primary School Students on Realistic Arithmetic Word Problems. Educational Psychology in Practice, 23, 2, 145–159
Wijaya, A., Van den Heuvel-Panhuizen, M., Doorman, M., ve Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors. The Mathematics Enthusiast, 11(3), 555–584
Yıldırım, A. ve Şimşek, H. (2006). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. 6. Baskı. Ankara: Seçkin Yayıncılık.
Yore, L. D., Anderson, J. O., & Hung Chiu, M. (2010). Moving PISA results into the policy arena: Perspectives on knowledge transfer for future considerations and preparations. International Journal of Science and Mathematics Education, 8(3), 593-603.
Yurt, E. ve Sünbül, A. M. (2014). A Structural Equation Model Explaining the Mathematics Achievements of the 8th Grade Students, Educational Sciences: Theory ve Practice, 14(4), 1629-1653
Zwiers, J. (2004). Making inferences and predictions. In: Money,M.M. (Ed.), Building Reading Comprehension Habits in Grades 6-12: a Toolkit of Classroom Activities, 2.Edt.,Chapter 5, (ss.99-122) , Newark DE: International Reading Assoc.