Cumhuriyet Dönemi İlkokul Matematik Dersi Öğretim Programlarında Problem Çözme Becerisi
Year 2017,
Volume: 4 Issue: 7 - JUNE, 120 - 146, 15.06.2017
Mehmet Fatih Özmantar
,
Ayşe Öztürk
Abstract
Bu
çalışma kapsamında, Cumhuriyet tarihi boyunca uygulamaya konulan ilkokul
matematik dersi öğretim programlarının, problem çözme becerisine dönük
düzenlemeler bağlamında karşılaştırmalı olarak incelenmesi amaçlanmıştır.
Araştırmada doküman incelemesi yöntemi kullanılmıştır. Çalışmanın verilerini
ise Cumhuriyet döneminde uygulamaya konulan öğretim programlarının yazılı
metinleri oluşturmuştur. Dokümanlar içerik analizine tabi tutularak
incelenmiştir. Analizler sonucunda problem çözme konusunda dört ana tema
belirlenmiştir: (1) matematiksel problem kavramı, (2) önerilen problem çözme
adımları, (3) öğrenme-öğretme sürecine ilişkin eğitsel düzenlemeler ve (4)
problem çözmeye ilişkin rol tanımlamaları. Cumhuriyet tarihi boyunca uygulamaya
konulan dokuz öğretim programının bu temalara dayalı olarak karşılaştırmalı
analizleri gerçekleştirilmiştir. Elde edilen sonuçlar matematiksel problemin ve
problem çözme kavramının ele alınış şekli, öğrencilerin problem çözme
becerilerinin gelişimi için benimsenin yaklaşımlar ile öğretmenlere bu süreçte
tayin edilen roller konusunda aydınlatıcı bilgiler sunmaktadır. Bulgular
tarihsel bağlamda karşılaştırmalı olarak irdelenmekte ve gelecekte yapılacak
program geliştirme çalışmalarına ilişkin bir takım önerilerde bulunulmaktadır.
References
- Baş, S. (2016) İlkokul matematik dersi öğretim programlarının matematiksel modelleme bağlamında incelenmesi. İçinde M.F.Özmantar, A.Öztürk, & E.Bay (Eds.), Reform ve değişim bağlamında ilkokul matematik öğretim programları (ss. 425-454). Ankara: PegemAkademi Publication
- Begle, E. G. (1979). Critical variable in mathematics education: Findings from a survey of the empirical literature. Washington, DC: Mathematical Association of America:
- Bowen, G.A. (2009). Document Analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27-40
Bransford, J. & Stein, B. (1984). The IDEAL problem solver: A guide for improving thinking, learning, and creativity. New York: W.H. Freeman.
- Bransford, J.D., Brown, A.L. & Cocking, R.R. (1999). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press
- Burkhardt, H. (1988). Teaching problem solving. In H. Burkhardt, S. Groves, A. Schoenfeld & K. Stacey (Eds.), Problem solving -A world view (pp 17-42), Nottingham, England: The Shell Centre for Mathematical Education, University of Nottingham.
- Burton, L. (1984). Thinking things through. problem solving in mathematics. Oxford: Basil Blackwell
- Cai, J. & Nie, B. (2007). Problem solving in Chinese mathematics education: Research and practice. ZDM: Mathematics Education, 39, 459–473
- Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2001). Learning mathematics in elementary and middle schools, (2nd ed.). Upper Saddle River, NH: Merrill Prentice Hall.
- Cobb, P., Yackel, E., & Wood, T. (1989). Young children’s emotional acts while engaged in mathematical problem solving. In Affect and mathematical problem solving (pp. 117-148). New York: Springer
- Cooper, B. & Harries, A.V. (2005). Making sense of realistic word problems: portraying working class 'failure' on a division with remainder problem. International Journal of Research & Method in Education 28(2), 147-169.
- de Lange, J. (1996). Using and applying mathematics in education. In A.J. Bishop, et al. (Eds). 1996. International handbook of mathematics education (pp. 49-97). Kluwer academic publisher.
- DeBellis, V. and Goldin, G. (1997).The affective domain in mathematical problem solving. In E. Pehkonen (Ed.), Proceedings of the twenty-first Annual Meeting of PME (Vol 2, pp.209-216). Lahti, Finland: Univ. of Helsinki
- DeCaro, M. S., & Rittle-Johnson, B. (2012). Exploring mathematics problems prepares children to learn from instruction. Journal of experimental child psychology, 113(4), 552-568.
- Demirel, O. (1999). Kuramdan uygulamaya eğitimde program geliştirme. Ankara: PegemAkademi Publication.
- Dinç-Artut, P., & Tarım, K. (2016). İlkokul matematik programlarının problem çözme açısından incelenmesi. İçinde M.F. Özmantar, A. Öztürk, & E.Bay (Ed.). Reform ve değişim bağlamında ilkokul matematik öğretim programları (293-315). Ankara: Pegem Akademi,
Dolan, D. T., & Williamson, J. (1983). Teaching problem-solving strategies. Menlo Park, CA: Addison-Wesley.
- English, L. D. (1997). The development of fifth-grade children’s problem posing abilities. Educational Studies in Mathematics, 34, 183-217.
- Ergün, M., Özmantar, M. F., Bay, E., & Agaç, G. (2015). Cumhuriyetin ilanından günümüze eğitimde, program geliştirmede ve matematik programlarında yaşanan değişim ve gelişimler. In M. F. Özmantar, A. Öztürk & E, Bay (Eds.), Reform ve değişim bağlamında ilkokul matematik öğretim programları (p. 407-424). Ankara: PegemAkademi Publication
- Gözütok, F. D. (2003). Türkiye’de program geliştirme çalışmaları [Curriculum development studies in Turkey]. Milli Eğitim Dergisi [Journal of National Education], 160.
- Hannula, M. S. (2014). Affect in mathematics education. In S.Lerman (Ed) Encyclopedia of mathematics education (pp. 23-27). Dortrecht: Springer Netherlands.
- Hardiman, P. T., Pollatsek, A., & Well, A. D. (1986). Learning to understand the balance beam. Cognition and Instruction, 3(1), 63-86.
Hiebert, J. Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1997). Making mathematics problematic: A rejoinder to Prawat and Smith. Educational Researcher, 26 (2). 24-26.
- Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371-404). Charlotte, NC: Information Age
- Holth, P. (2008). What is a problem? Theoretical conceptions and methodological approaches to the study of problem solving. European Journal of Behavior Analysis, 9(2), 157-172
- Kamii, C. (1982). Number in preschool and kindergarten: Educational implications of Piaget’s theory. Washington, DC: National Association for the Education of Young Children
- Kapur, M. (2014). Productive failure in math learning. Cognitive Science, 38, 1008-1022.
- Karakaya, S. (2004). Eğitimde program geliştirme çalışmaları ve yeni yönelimler. Ankara: Asil Release Distribution
- Karp, A., & Vogeli, B. R. (2010). Russian mathematics education: History and world significance. Singapore: World Scientific.
- Kennedy, L. M., Tipps, S., & Johnson, A. (2008). Guiding children’s learning of mathematics (11th ed.). Clifton Park, NY: Wadsworth Cengage Learning.
- Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75-86.
- Krulik, S., & Rudnick, J. A. (1987). Problem solving: A handbook for teachers (2nd Ed.). Boston: Allyn and Bacon.
- Krulik, S., & Rudnick, J. A. (2000). Teaching middle school mathematics: Activities, materials, and problems. Needham Heights, MA: Allyn & Bacon.
- Maccini, P. & Hughes, C. A. (2000). Effects of a problem-solving strategy on the introductory algebra performance of secondary students with learning disabilities. Learning Disabilities Research and Practice, 15, 10-21.
- Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı (MEB-TTKB). (1990). İlköğretim matematik dersi programı. Ankara: MEB.
- Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı (MEB-TTKB). (1998). İlköğretim okulu matematik dersi öğretim programı. Ankara: MEB.
- Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı (MEB-TTKB). (2005). İlköğretim matematik programı. Ankara: MEB.
- Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı (MEB-TTKB). (2015). İlköğretim matematik dersi (1, 2, 3 ve 4. Sınıflar) öğretim programı. Ankara: MEB.
- Milli Eğitim Bakanlığı. (1948). İlkokul programı. İstanbul: Milli Eğitim Basımevi.
- Milli Eğitim Gençlik ve Spor Bakanlığı (MEB). (1968). İlkokul matematik programı. Ankara: MEB.
- Milli Eğitim Gençlik ve Spor Bakanlığı (MEB). (1983). İlkokul matematik programı. Ankara: MEB.
- National Council of Teachers of Mathematics. (1980). An agenda for action: directions for school mathematics for the 1980s. Reston, VA: Author.
- National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
- Neuman W L (1991) Social research methods: Qualitative and quantitative approaches. Boston: Allyn and Bacon
- Polya, G. (1945). How to solve it: a new aspect of mathematical method. Princeton University Press, Princeton.
- Santos-Trigo M (2007) Mathematical problem solving: an evolving research and practice domain. ZDM Int J Math Educ 39(5, 6), 523–536.
- Santos-Trigo, M. (2014). Problem solving in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 496–501). New York: Springer.
- Schoenfeld, A. (1992). Learning think to matematically: Problem solving, metacognition and sense making in mathematics. In D. A. Grouws (Ed), Handbook of research on mathematics teaching and learning (334-370). Newyork: Macmillan
- Schoenfeld, A. H. (1985). Making sense of “out loud” problem-solving protocols. The Journal of Mathematical Behavior, 4(2), 171-191.
- Siegler, R. S. (2002). Microgenetic studies of self-explanation. In N. Garnott & J. Parziale (Eds.), Microdevelopment: A process-oriented perspective for studying development and learning (pp. 31–58). Cambridge, UK: Cambridge University Press.
- Silver E. A. & Cai, J. (1996). An analysis of arithmetic problem posing by middle school. Journal for Research in Mathematics Education, 27 (5), 521-539
- Sriraman, B., & English, L. (2010). Surveying theories and philosophies of mathematics education. In Theories of mathematics education (pp. 7-32). Springer Berlin Heidelberg.
- Stephan, M. (2014). Learner-centered teaching in mathematics education. In S. Lerman (Ed), Encyclopedia of mathematics education (pp. 338-343). Springer Netherlands.
- Suydam, M. (1987). Indications from research on problem solving. In F. R. Curcio (Ed.), Teaching and learning: A problem solving focus. Reston, VA: National Council of Teachers of Mathematics.
- Sweller, J., & Chandler, P. (1991). Evidence for cognitive load theory. Cognition and instruction, 8(4), 351-362.
- Türkiye Cumhuriyeti Maarif Vekaleti. (1930). İlk mektep müfredat programı. İstanbul: Devlet Matbaası.
- Türkiye Cumuriyeti Kültür Bakanlığı. (1936). İlkokul programı. İstanbul: Devlet Basımevi.
- van de Walle, J., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: teaching developmentally (7th ed.). Boston: Allyn & Bacon.
- Wilson, J W , Fernandez, M L , & Hadaway, N (1993). Mathematical problem solving In P S Wilson (Ed), Research ideas for the classroom: High school mathematics (pp 57-78). New York: Macmillan.
Problem Solving Skill in Primary Mathematics Curricula Documents of the Republican Period
Year 2017,
Volume: 4 Issue: 7 - JUNE, 120 - 146, 15.06.2017
Mehmet Fatih Özmantar
,
Ayşe Öztürk
Abstract
The aim of this study is to examine problem solving skill
attended to in primary mathematics curricula put into practice during Turkish
Republican period. The study employs a document analysis method and the
official curricula documents constitute the data. The documents are examined
via content analysis technique. There emerge four main themes of mathematical
problem solving through the analysis: (1) the notion of mathematical problem,
(2) prescribed problem solving steps, (3) instructional arrangements for
teaching-learning process and (4) role definitions regarding problem solving.
These themes are comparatively analysed along nine different primary
mathematics curricula that have been put into effect since 1926. The findings
shed some light on the conceptualisation of mathematical problem and problem
solving as well as approaches adopted to enhance students’ problem solving
skills and the expected duties of teachers. The findings are discussed in a
historical context and suggestions are made for future program development
efforts.
References
- Baş, S. (2016) İlkokul matematik dersi öğretim programlarının matematiksel modelleme bağlamında incelenmesi. İçinde M.F.Özmantar, A.Öztürk, & E.Bay (Eds.), Reform ve değişim bağlamında ilkokul matematik öğretim programları (ss. 425-454). Ankara: PegemAkademi Publication
- Begle, E. G. (1979). Critical variable in mathematics education: Findings from a survey of the empirical literature. Washington, DC: Mathematical Association of America:
- Bowen, G.A. (2009). Document Analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27-40
Bransford, J. & Stein, B. (1984). The IDEAL problem solver: A guide for improving thinking, learning, and creativity. New York: W.H. Freeman.
- Bransford, J.D., Brown, A.L. & Cocking, R.R. (1999). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press
- Burkhardt, H. (1988). Teaching problem solving. In H. Burkhardt, S. Groves, A. Schoenfeld & K. Stacey (Eds.), Problem solving -A world view (pp 17-42), Nottingham, England: The Shell Centre for Mathematical Education, University of Nottingham.
- Burton, L. (1984). Thinking things through. problem solving in mathematics. Oxford: Basil Blackwell
- Cai, J. & Nie, B. (2007). Problem solving in Chinese mathematics education: Research and practice. ZDM: Mathematics Education, 39, 459–473
- Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2001). Learning mathematics in elementary and middle schools, (2nd ed.). Upper Saddle River, NH: Merrill Prentice Hall.
- Cobb, P., Yackel, E., & Wood, T. (1989). Young children’s emotional acts while engaged in mathematical problem solving. In Affect and mathematical problem solving (pp. 117-148). New York: Springer
- Cooper, B. & Harries, A.V. (2005). Making sense of realistic word problems: portraying working class 'failure' on a division with remainder problem. International Journal of Research & Method in Education 28(2), 147-169.
- de Lange, J. (1996). Using and applying mathematics in education. In A.J. Bishop, et al. (Eds). 1996. International handbook of mathematics education (pp. 49-97). Kluwer academic publisher.
- DeBellis, V. and Goldin, G. (1997).The affective domain in mathematical problem solving. In E. Pehkonen (Ed.), Proceedings of the twenty-first Annual Meeting of PME (Vol 2, pp.209-216). Lahti, Finland: Univ. of Helsinki
- DeCaro, M. S., & Rittle-Johnson, B. (2012). Exploring mathematics problems prepares children to learn from instruction. Journal of experimental child psychology, 113(4), 552-568.
- Demirel, O. (1999). Kuramdan uygulamaya eğitimde program geliştirme. Ankara: PegemAkademi Publication.
- Dinç-Artut, P., & Tarım, K. (2016). İlkokul matematik programlarının problem çözme açısından incelenmesi. İçinde M.F. Özmantar, A. Öztürk, & E.Bay (Ed.). Reform ve değişim bağlamında ilkokul matematik öğretim programları (293-315). Ankara: Pegem Akademi,
Dolan, D. T., & Williamson, J. (1983). Teaching problem-solving strategies. Menlo Park, CA: Addison-Wesley.
- English, L. D. (1997). The development of fifth-grade children’s problem posing abilities. Educational Studies in Mathematics, 34, 183-217.
- Ergün, M., Özmantar, M. F., Bay, E., & Agaç, G. (2015). Cumhuriyetin ilanından günümüze eğitimde, program geliştirmede ve matematik programlarında yaşanan değişim ve gelişimler. In M. F. Özmantar, A. Öztürk & E, Bay (Eds.), Reform ve değişim bağlamında ilkokul matematik öğretim programları (p. 407-424). Ankara: PegemAkademi Publication
- Gözütok, F. D. (2003). Türkiye’de program geliştirme çalışmaları [Curriculum development studies in Turkey]. Milli Eğitim Dergisi [Journal of National Education], 160.
- Hannula, M. S. (2014). Affect in mathematics education. In S.Lerman (Ed) Encyclopedia of mathematics education (pp. 23-27). Dortrecht: Springer Netherlands.
- Hardiman, P. T., Pollatsek, A., & Well, A. D. (1986). Learning to understand the balance beam. Cognition and Instruction, 3(1), 63-86.
Hiebert, J. Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1997). Making mathematics problematic: A rejoinder to Prawat and Smith. Educational Researcher, 26 (2). 24-26.
- Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371-404). Charlotte, NC: Information Age
- Holth, P. (2008). What is a problem? Theoretical conceptions and methodological approaches to the study of problem solving. European Journal of Behavior Analysis, 9(2), 157-172
- Kamii, C. (1982). Number in preschool and kindergarten: Educational implications of Piaget’s theory. Washington, DC: National Association for the Education of Young Children
- Kapur, M. (2014). Productive failure in math learning. Cognitive Science, 38, 1008-1022.
- Karakaya, S. (2004). Eğitimde program geliştirme çalışmaları ve yeni yönelimler. Ankara: Asil Release Distribution
- Karp, A., & Vogeli, B. R. (2010). Russian mathematics education: History and world significance. Singapore: World Scientific.
- Kennedy, L. M., Tipps, S., & Johnson, A. (2008). Guiding children’s learning of mathematics (11th ed.). Clifton Park, NY: Wadsworth Cengage Learning.
- Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75-86.
- Krulik, S., & Rudnick, J. A. (1987). Problem solving: A handbook for teachers (2nd Ed.). Boston: Allyn and Bacon.
- Krulik, S., & Rudnick, J. A. (2000). Teaching middle school mathematics: Activities, materials, and problems. Needham Heights, MA: Allyn & Bacon.
- Maccini, P. & Hughes, C. A. (2000). Effects of a problem-solving strategy on the introductory algebra performance of secondary students with learning disabilities. Learning Disabilities Research and Practice, 15, 10-21.
- Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı (MEB-TTKB). (1990). İlköğretim matematik dersi programı. Ankara: MEB.
- Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı (MEB-TTKB). (1998). İlköğretim okulu matematik dersi öğretim programı. Ankara: MEB.
- Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı (MEB-TTKB). (2005). İlköğretim matematik programı. Ankara: MEB.
- Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı (MEB-TTKB). (2015). İlköğretim matematik dersi (1, 2, 3 ve 4. Sınıflar) öğretim programı. Ankara: MEB.
- Milli Eğitim Bakanlığı. (1948). İlkokul programı. İstanbul: Milli Eğitim Basımevi.
- Milli Eğitim Gençlik ve Spor Bakanlığı (MEB). (1968). İlkokul matematik programı. Ankara: MEB.
- Milli Eğitim Gençlik ve Spor Bakanlığı (MEB). (1983). İlkokul matematik programı. Ankara: MEB.
- National Council of Teachers of Mathematics. (1980). An agenda for action: directions for school mathematics for the 1980s. Reston, VA: Author.
- National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
- Neuman W L (1991) Social research methods: Qualitative and quantitative approaches. Boston: Allyn and Bacon
- Polya, G. (1945). How to solve it: a new aspect of mathematical method. Princeton University Press, Princeton.
- Santos-Trigo M (2007) Mathematical problem solving: an evolving research and practice domain. ZDM Int J Math Educ 39(5, 6), 523–536.
- Santos-Trigo, M. (2014). Problem solving in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 496–501). New York: Springer.
- Schoenfeld, A. (1992). Learning think to matematically: Problem solving, metacognition and sense making in mathematics. In D. A. Grouws (Ed), Handbook of research on mathematics teaching and learning (334-370). Newyork: Macmillan
- Schoenfeld, A. H. (1985). Making sense of “out loud” problem-solving protocols. The Journal of Mathematical Behavior, 4(2), 171-191.
- Siegler, R. S. (2002). Microgenetic studies of self-explanation. In N. Garnott & J. Parziale (Eds.), Microdevelopment: A process-oriented perspective for studying development and learning (pp. 31–58). Cambridge, UK: Cambridge University Press.
- Silver E. A. & Cai, J. (1996). An analysis of arithmetic problem posing by middle school. Journal for Research in Mathematics Education, 27 (5), 521-539
- Sriraman, B., & English, L. (2010). Surveying theories and philosophies of mathematics education. In Theories of mathematics education (pp. 7-32). Springer Berlin Heidelberg.
- Stephan, M. (2014). Learner-centered teaching in mathematics education. In S. Lerman (Ed), Encyclopedia of mathematics education (pp. 338-343). Springer Netherlands.
- Suydam, M. (1987). Indications from research on problem solving. In F. R. Curcio (Ed.), Teaching and learning: A problem solving focus. Reston, VA: National Council of Teachers of Mathematics.
- Sweller, J., & Chandler, P. (1991). Evidence for cognitive load theory. Cognition and instruction, 8(4), 351-362.
- Türkiye Cumhuriyeti Maarif Vekaleti. (1930). İlk mektep müfredat programı. İstanbul: Devlet Matbaası.
- Türkiye Cumuriyeti Kültür Bakanlığı. (1936). İlkokul programı. İstanbul: Devlet Basımevi.
- van de Walle, J., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: teaching developmentally (7th ed.). Boston: Allyn & Bacon.
- Wilson, J W , Fernandez, M L , & Hadaway, N (1993). Mathematical problem solving In P S Wilson (Ed), Research ideas for the classroom: High school mathematics (pp 57-78). New York: Macmillan.