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Orantısal Akıl Yürütmeye İlk Adım: Birimleri Bağlama ve Yinelemedeki Temsiller

Year 2023, Volume: 24 Issue: 2, 1271 - 1300, 15.09.2023

Seçil Yemen Karpuzcu Rukiye Ayan Civak Mine Işıksal

https://doi.org/10.17679/inuefd.1226508

Abstract

Bu çalışmanın amacı orantısal akıl yürütme bağlamında, yedinci sınıf öğrencilerinin oran oluşturan çokluklara yönelik birleşik birimler oluşturmak, oluşturdukları birleşik birimleri birbirine bağlamak ve bu bağlı birleşik birimleri yinelemek için kullandıkları temsilleri incelemektir. Bu kapsamda, bu çalışmada birleşik birimleri bağlarken ve bağlı birleşik birimleri yinelerken, öğrencilerin temsilleri ne ölçüde kullandıkları ve informel temsillerden formel temsillere nasıl geçtikleri açıklanmıştır. Bu çalışma öğrencilerin orantısal akıl yürütmelerini desteklemek için varsayıma dayalı bir öğrenme rotasının geliştirildiği ve tasarı tabanlı araştırma modelinin kullanıldığı üç yıllık bir araştırma projesinin bir parçasıdır. Bu çalışmada amaçlı örneklem ile Ankara’da bir devlet okulunda çalışan bir ortaokul matematik öğretmeni ve onun yedinci sınıf öğrencileri katılımcılar olarak belirlenmiştir. Bu çalışmanın verileri, tasarlanan öğretim uygulaması sonunda elde edilmiştir. Veriler, uygulama sonrasında öğrencilere uygulanan açık uçlu sorular içeren teste verilen yazılı cevaplar ve öğrencilerle test sonrası yapılan yarı yapılandırılmış görüşmelerdir. Bu test bir ders saati süresince uygulanmıştır. Bulgular, bu öğrencilerin birleşik birimleri bağlama ve bağlı birleşik birimleri yineleme ile ilgili problemleri çözmek için çoğunlukla resimsel temsilleri kullandıklarını ortaya koymuştur. Ayrıca, öğrencilerin tablo ve sayısal temsilleri de kullandıklarını göstermiştir. Dahası, öğrenciler bu temsilleri kullanırken, iki temsil türünü bütünleşik olarak (ör. resimsel-sayısal) birlikte kullanabilmektedir. Bunlara ek olarak, bir soruya farklı yollardan çözümler sunduklarında öğrencilerin iki ayrı temsili de kullandıkları belirlenmiştir.

Keywords

orantısal akıl yürütme temsiller ortaokul öğrencileri durum çalışması

Supporting Institution

Tübitak

Project Number

217K430

Thanks

Bu çalışma, 217K430 kodlu Türkiye Bilimsel ve Teknolojik Araştırma Kurumu (TÜBİTAK) projesinden üretilmiştir.

References

  • Akkuş, O. & Duatepe Paksu, A. (2006). Orantısal akıl yürütme becerisi testi ve teste yönelik dereceli puanlama anahtarı geliştirilmesi. Eurasian Journal of Educational Research, 25, 1–10.
  • Arıcan, M. (2019). A diagnostic assessment to middle school students’ proportional reasoning. Turkish Journal of Education, 8(4), 237–257. https://doi.org/10.19128/turje.522839
  • Atabaş, Ş. & Öner, D. (2017). An examination of Turkish middle school students’ proportional reasoning. Boğaziçi Üniversitesi Eğitim Dergisi, 33(1), 63–85.
  • Battista, M. & Borrow, C. V. A. (1995). A proposed constructive itinerary from iterating composite units to ratio and proportion concepts. Paper presented at the Annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education: Columbus, OH.
  • Behr, M. J., Harel, G., Post, T. & Lesh, R. (1992). Rational number, ratio, and proportion. D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296–233). Macmillan.
  • Behr, M., Lesh, R., Post, T. & Silver E. (1983). Rational number concepts. R. Lesh ve M. Landau (Eds.), Acquisition of mathematics concepts and processes, (pp. 91–125). Academic Press.
  • Ben-Chaim, D., Fey, J. T., Fitzgerald, W. M., Benedetto, C., & Miller, J. (1998). Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics, 36(3), 247–273.
  • Cramer, K., Post, T. & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. D. Owens (Ed.), Research ideas for the classroom (pp. 159–178). Macmillan Publishing Company.
  • Çelik, A. & Yetkin-Özdemir, E. (2011). İlköğretim öğrencilerinin orantısal akıl yürütme becerileri ile problem kurma becerileri arasındaki ilişki. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30(1), 1–11.
  • Duatepe, A., Akkuş-Çıkla, O. & Kayhan, M. (2005). Orantısal akıl yürütme gerektiren sorularda öğrencilerin kullandıkları çözüm stratejilerinin soru türlerine göre değişiminin incelenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 28, 73–81.
  • Duval, R. (1999). Representation, vision and visualization: cognitive functions in mathematical thinking. Basic issues for learning. Proceedings of the annual meeting of the north american chapter of the International group fort he pschology of mathematics education (21st, Cuernavaca, Morelos, Mexico, October 23-26, 1999) (pp. 3–26).
  • Fernández, C., Llinares, S., Van Dooren, W., De Bock, D. & Verschaffel, L. (2012). The development of students’ use of additive and proportional methods along primary and secondary school. European Journal of Psychology of Education, 27(3), 421–438. http://dx.doi.org/10.1007/s10212-011-0087-0
  • Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Reserch in Mathematics Education, 16(1), 3–17. http://dx.doi.org/10.2307/748969
  • Goldin, G. (1997). Observing mathematical problem solving through task-based interviews. Journal for Research in Mathematics Education. Monograph, 9, 40–177. doi:10.2307/749946. http://dx.doi.org/10.2307/749946
  • Goldin, G.A. (2003). Representation in school mathematics: A unifying research perspective. In J. Kilpatrick, M. G. Martin, ve S. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 275–286). National Council of Teachers of Mathematics.
  • Gravemeijer, K. & Cobb, P. (2006). Design research from a learning design perspective. J. Van den Akker, K. Gravemeijer, S. McKenney ve N. Nieveen (Eds.), Educational design research (pp. 17–51). Routledge.
  • Harel, G., Behr, M., Lesh, R. & Post, T. (1994). Invariance of ratio: The case of children’s anticipatory scheme for constancy of taste. Journal for Research in Mathematics Education, 25(4), 324–345.
  • Inhelder, B. ve Piaget, J. (1958). The growth of logical thinking from childhood to adolescence. New York: Basic Books.
  • Kahraman, H., Kul, E. & Aydoğdu-İskenderoğlu, T. (2019). 7. ve 8. sınıf öğrencilerinin nicel karşılaştırma içeren orantısal akıl yürütme problemlerinde kullandıkları stratejiler. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 10(1), 195–216. https://doi.org/10.16949/turkbilmat.333046
  • Kaplan, A., İşleyen, T. & Öztürk, M. (2011). 6. sınıf oran orantı konusundaki kavram yanılgıları. Kastamonu Eğitim Dergisi, 19(3), 953–968.
  • Kaput, J. J. & West, M. M. (1994). Missing-value proportional problems: factors affecting informal reasoning patterns. G. Harel ve J. Confrey, (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 235–287). State University of New York Press.
  • Karplus, R., Pulos, S. & Stage, E. K. (1983). Early adolescents' proportional reasoning on ‘rate’ problems. Educational Studies in Mathematics, 14(3), 219–233.
  • Kayhan, M., Duatepe, A. & Akkuş-Çıkla, O. (2004, Eylül). İlköğretim ikinci kademe öğrencilerinin orantısal akıl yürütme gerektiren sorularda kullandıkları çözüm stratejileri. VI. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, 9-11 Eylül, İstanbul.
  • Lamon, S. J. (1994). Ratio and proportion: Cognitive foundations in unitizing and norming. G. Harel ve J. Confrey, (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 89–120). State University of New York Press.
  • Lamon, S. J. (1995). Ratio and proportion: Elementary didactical phenomenology. J. T. Sowder ve B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 167–198). State University of New York Press.
  • Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–668). Information Age Publishing.
  • Lesh, R., Behr, M. & Post, T. (1987a). Rational number relations and proportions. C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 41–58). Lawrence Erlbaum.
  • Lesh, R. & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. R. Lesh ve H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3–34). Lawrence Erlbaum Associates.
  • Lesh R., Post, T. & Behr, M. (1987b). Representations and translations among representations in mathematics learning and problem solving. C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 33–40). Lawrence Erlbaum Associates.
  • Lesh, R., Post, T. & Behr, M. (1988). Proportional reasoning. J. Hiebert, ve M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 93-118). Lawrence Erlbaum ve National Council of Teachers of Mathematics, Inc.
  • Martínez-Juste, S., Arıcan, M., Muñoz-Escolano, J. M., & Oller-Marcén, A. M. (2023). A diagnostic comparison of Spanish and Turkish middle school students’ proportional reasoning. Asian Journal for Mathematics Education, 2(1), 64-90. https://doi.org/10.1177/27527263231166
  • Mersin, N. (2018). İki aşamalı teşhis testine göre ortaokul 5, 6 ve 7. sınıf öğrencilerinin orantısal akıl yürütmelerinin değerlendirilmesi. Cumhuriyet Uluslararası Eğitim Dergisi, 7(4), 319–348. http://dx.doi.org/10.30703/cije.426627
  • Miles, M, B. & Huberman, A. M. (1994). Qualitative data analysis: An expanded Sourcebook. (2nd ed). Sage.
  • Misailidou, C. & Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. The Journal of Mathematical Behavior, 22(3), 335–368. https://doi.org/10.1016/S0732-3123(03)00025-7
  • Noelting, G. (1980a). The development of proportional reasoning and the ratio concept. Part I: The determination of stages. Educational Studies in Mathematics, 11(2), 217–253.
  • Noelting, G. (1980b). The development of proportional reasoning and the ratio concept Part II—problem-structure at successive stages; problem-solving strategies and the mechanism of adaptive restructuring. Educational Studies in Mathematics, 11(3), 331–363. https://doi.org/10.1007/BF00304357
  • Nunes, T., Bryant, P., Evans, D., & Bell, D. (2010). The scheme of correspondence and its role in children's mathematics. BJEP Monograph Series II, Number 7-Understanding number development and difficulties (Vol. 83, No. 99, pp. 83–99). British Psychological Society.
  • Özgün-Koca, S. A., & Altay, M. K. (2009). An investigation of proportional reasoning skills of middle school students. Investigations in Mathematics Learning, 2(1), 26–48. https://doi.org/10.1080/24727466.2009.11790289 Park, J. H. & Nunes, T. (2001). The development of the concept of multiplication. Cognitive Development, 16(3), 763–773. https://doi.org/10.1016/S0885-2014(01)00058-2
  • Patton, M. Q. (1990). Qualitative evaluation and research methods (2nd ed.). Sage Publications, Inc. Piaget, J. & Inhelder, B. (1975). The origin of idea of chance in children. Norton.
  • Post, T., Behr, M. & Lesh, R (1986). Research-based observations about children's learning of rational number concepts. Focus on Learning Problems in Mathematics. 8(1), 39–48.
  • Proulx, J. (2023). Relative proportional reasoning: transition from additive to multiplicative thinking through qualitative and quantitative enmeshments. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-023-10373-y
  • Resnick, L. B. & Singer, J. A. (1993). Protoquantitative origins of ratio reasoning. T. P. Carpenter, E. Fennema ve T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 107–130). Lawrence Erlbaum Associates, Inc.
  • Steffe, L. P. (1994). Children’s multiplying schemes. In G. Harel ve J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 3–39). State University of New York Press.
  • Supply, AS., Vanluydt, E., Van Dooren, W., & Onghena, P. (2023). Out of proportion or out of context? Comparing 8- to 9-year-olds’ proportional reasoning abilities across fair-sharing, mixtures, and probability contexts. Educational Studies in Mathematics, 113 (3), 371–388. https://doi.org/10.1007/s10649-023-10212-5
  • Tourniaire, F. (1986). Proportions in elementary school. Educational Studies in Mathematics, 17(4), 401–412. Tourniaire, F. & Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational Studies in Mathematics, 16(2), 181–204. https://doi.org/10.1007/PL00020739
  • van Dooren, W., De Bock, D. & Verschaffel, L. (2010). From addition to multiplication… and back: The development of students’ additive and multiplicative reasoning skills. Cognition and Instruction, 28(3), 360–381. https://doi.org/10.1080/07370008.2010.488306
  • Webb, D. C., Boswinkel, N., & Dekker, T. (2008). Beneath the tip of the iceberg: Using representations to support student understanding. Mathematics Teaching in the Middle School, 14(2), 110–113. https://doi.org/10.5951/MTMS.14.2.0110
  • Ayan-Civak, R., Işıksal-Bostan, M., & Yemen-Karpuzcu, S. (2022). Orantısal Akıl Yürütmenin Gelişimine Yönelik Varsayıma Dayalı Öğrenme Rotasının Geliştirilmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 37(1), 345–365. https://doi.org/10.16986/HUJE.2020063485
  • Ayan-Civak, R., Işıksal-Bostan, M., & Yemen-Karpuzcu, S. (2023). From informal to formal understandings: analysing the development of proportional reasoning and its retention. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2022.2160384
  • Yin, R. K. (2009). Case study research: design and methods (4th ed.). Sage Publications Inc.

Year 2023, Volume: 24 Issue: 2, 1271 - 1300, 15.09.2023

Seçil Yemen Karpuzcu Rukiye Ayan Civak Mine Işıksal

https://doi.org/10.17679/inuefd.1226508

Abstract

Project Number

217K430

References

  • Akkuş, O. & Duatepe Paksu, A. (2006). Orantısal akıl yürütme becerisi testi ve teste yönelik dereceli puanlama anahtarı geliştirilmesi. Eurasian Journal of Educational Research, 25, 1–10.
  • Arıcan, M. (2019). A diagnostic assessment to middle school students’ proportional reasoning. Turkish Journal of Education, 8(4), 237–257. https://doi.org/10.19128/turje.522839
  • Atabaş, Ş. & Öner, D. (2017). An examination of Turkish middle school students’ proportional reasoning. Boğaziçi Üniversitesi Eğitim Dergisi, 33(1), 63–85.
  • Battista, M. & Borrow, C. V. A. (1995). A proposed constructive itinerary from iterating composite units to ratio and proportion concepts. Paper presented at the Annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education: Columbus, OH.
  • Behr, M. J., Harel, G., Post, T. & Lesh, R. (1992). Rational number, ratio, and proportion. D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296–233). Macmillan.
  • Behr, M., Lesh, R., Post, T. & Silver E. (1983). Rational number concepts. R. Lesh ve M. Landau (Eds.), Acquisition of mathematics concepts and processes, (pp. 91–125). Academic Press.
  • Ben-Chaim, D., Fey, J. T., Fitzgerald, W. M., Benedetto, C., & Miller, J. (1998). Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics, 36(3), 247–273.
  • Cramer, K., Post, T. & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. D. Owens (Ed.), Research ideas for the classroom (pp. 159–178). Macmillan Publishing Company.
  • Çelik, A. & Yetkin-Özdemir, E. (2011). İlköğretim öğrencilerinin orantısal akıl yürütme becerileri ile problem kurma becerileri arasındaki ilişki. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30(1), 1–11.
  • Duatepe, A., Akkuş-Çıkla, O. & Kayhan, M. (2005). Orantısal akıl yürütme gerektiren sorularda öğrencilerin kullandıkları çözüm stratejilerinin soru türlerine göre değişiminin incelenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 28, 73–81.
  • Duval, R. (1999). Representation, vision and visualization: cognitive functions in mathematical thinking. Basic issues for learning. Proceedings of the annual meeting of the north american chapter of the International group fort he pschology of mathematics education (21st, Cuernavaca, Morelos, Mexico, October 23-26, 1999) (pp. 3–26).
  • Fernández, C., Llinares, S., Van Dooren, W., De Bock, D. & Verschaffel, L. (2012). The development of students’ use of additive and proportional methods along primary and secondary school. European Journal of Psychology of Education, 27(3), 421–438. http://dx.doi.org/10.1007/s10212-011-0087-0
  • Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Reserch in Mathematics Education, 16(1), 3–17. http://dx.doi.org/10.2307/748969
  • Goldin, G. (1997). Observing mathematical problem solving through task-based interviews. Journal for Research in Mathematics Education. Monograph, 9, 40–177. doi:10.2307/749946. http://dx.doi.org/10.2307/749946
  • Goldin, G.A. (2003). Representation in school mathematics: A unifying research perspective. In J. Kilpatrick, M. G. Martin, ve S. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 275–286). National Council of Teachers of Mathematics.
  • Gravemeijer, K. & Cobb, P. (2006). Design research from a learning design perspective. J. Van den Akker, K. Gravemeijer, S. McKenney ve N. Nieveen (Eds.), Educational design research (pp. 17–51). Routledge.
  • Harel, G., Behr, M., Lesh, R. & Post, T. (1994). Invariance of ratio: The case of children’s anticipatory scheme for constancy of taste. Journal for Research in Mathematics Education, 25(4), 324–345.
  • Inhelder, B. ve Piaget, J. (1958). The growth of logical thinking from childhood to adolescence. New York: Basic Books.
  • Kahraman, H., Kul, E. & Aydoğdu-İskenderoğlu, T. (2019). 7. ve 8. sınıf öğrencilerinin nicel karşılaştırma içeren orantısal akıl yürütme problemlerinde kullandıkları stratejiler. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 10(1), 195–216. https://doi.org/10.16949/turkbilmat.333046
  • Kaplan, A., İşleyen, T. & Öztürk, M. (2011). 6. sınıf oran orantı konusundaki kavram yanılgıları. Kastamonu Eğitim Dergisi, 19(3), 953–968.
  • Kaput, J. J. & West, M. M. (1994). Missing-value proportional problems: factors affecting informal reasoning patterns. G. Harel ve J. Confrey, (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 235–287). State University of New York Press.
  • Karplus, R., Pulos, S. & Stage, E. K. (1983). Early adolescents' proportional reasoning on ‘rate’ problems. Educational Studies in Mathematics, 14(3), 219–233.
  • Kayhan, M., Duatepe, A. & Akkuş-Çıkla, O. (2004, Eylül). İlköğretim ikinci kademe öğrencilerinin orantısal akıl yürütme gerektiren sorularda kullandıkları çözüm stratejileri. VI. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, 9-11 Eylül, İstanbul.
  • Lamon, S. J. (1994). Ratio and proportion: Cognitive foundations in unitizing and norming. G. Harel ve J. Confrey, (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 89–120). State University of New York Press.
  • Lamon, S. J. (1995). Ratio and proportion: Elementary didactical phenomenology. J. T. Sowder ve B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 167–198). State University of New York Press.
  • Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–668). Information Age Publishing.
  • Lesh, R., Behr, M. & Post, T. (1987a). Rational number relations and proportions. C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 41–58). Lawrence Erlbaum.
  • Lesh, R. & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. R. Lesh ve H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3–34). Lawrence Erlbaum Associates.
  • Lesh R., Post, T. & Behr, M. (1987b). Representations and translations among representations in mathematics learning and problem solving. C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 33–40). Lawrence Erlbaum Associates.
  • Lesh, R., Post, T. & Behr, M. (1988). Proportional reasoning. J. Hiebert, ve M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 93-118). Lawrence Erlbaum ve National Council of Teachers of Mathematics, Inc.
  • Martínez-Juste, S., Arıcan, M., Muñoz-Escolano, J. M., & Oller-Marcén, A. M. (2023). A diagnostic comparison of Spanish and Turkish middle school students’ proportional reasoning. Asian Journal for Mathematics Education, 2(1), 64-90. https://doi.org/10.1177/27527263231166
  • Mersin, N. (2018). İki aşamalı teşhis testine göre ortaokul 5, 6 ve 7. sınıf öğrencilerinin orantısal akıl yürütmelerinin değerlendirilmesi. Cumhuriyet Uluslararası Eğitim Dergisi, 7(4), 319–348. http://dx.doi.org/10.30703/cije.426627
  • Miles, M, B. & Huberman, A. M. (1994). Qualitative data analysis: An expanded Sourcebook. (2nd ed). Sage.
  • Misailidou, C. & Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. The Journal of Mathematical Behavior, 22(3), 335–368. https://doi.org/10.1016/S0732-3123(03)00025-7
  • Noelting, G. (1980a). The development of proportional reasoning and the ratio concept. Part I: The determination of stages. Educational Studies in Mathematics, 11(2), 217–253.
  • Noelting, G. (1980b). The development of proportional reasoning and the ratio concept Part II—problem-structure at successive stages; problem-solving strategies and the mechanism of adaptive restructuring. Educational Studies in Mathematics, 11(3), 331–363. https://doi.org/10.1007/BF00304357
  • Nunes, T., Bryant, P., Evans, D., & Bell, D. (2010). The scheme of correspondence and its role in children's mathematics. BJEP Monograph Series II, Number 7-Understanding number development and difficulties (Vol. 83, No. 99, pp. 83–99). British Psychological Society.
  • Özgün-Koca, S. A., & Altay, M. K. (2009). An investigation of proportional reasoning skills of middle school students. Investigations in Mathematics Learning, 2(1), 26–48. https://doi.org/10.1080/24727466.2009.11790289 Park, J. H. & Nunes, T. (2001). The development of the concept of multiplication. Cognitive Development, 16(3), 763–773. https://doi.org/10.1016/S0885-2014(01)00058-2
  • Patton, M. Q. (1990). Qualitative evaluation and research methods (2nd ed.). Sage Publications, Inc. Piaget, J. & Inhelder, B. (1975). The origin of idea of chance in children. Norton.
  • Post, T., Behr, M. & Lesh, R (1986). Research-based observations about children's learning of rational number concepts. Focus on Learning Problems in Mathematics. 8(1), 39–48.
  • Proulx, J. (2023). Relative proportional reasoning: transition from additive to multiplicative thinking through qualitative and quantitative enmeshments. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-023-10373-y
  • Resnick, L. B. & Singer, J. A. (1993). Protoquantitative origins of ratio reasoning. T. P. Carpenter, E. Fennema ve T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 107–130). Lawrence Erlbaum Associates, Inc.
  • Steffe, L. P. (1994). Children’s multiplying schemes. In G. Harel ve J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 3–39). State University of New York Press.
  • Supply, AS., Vanluydt, E., Van Dooren, W., & Onghena, P. (2023). Out of proportion or out of context? Comparing 8- to 9-year-olds’ proportional reasoning abilities across fair-sharing, mixtures, and probability contexts. Educational Studies in Mathematics, 113 (3), 371–388. https://doi.org/10.1007/s10649-023-10212-5
  • Tourniaire, F. (1986). Proportions in elementary school. Educational Studies in Mathematics, 17(4), 401–412. Tourniaire, F. & Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational Studies in Mathematics, 16(2), 181–204. https://doi.org/10.1007/PL00020739
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There are 50 citations in total.

Details

Primary Language Turkish
Subjects Specialist Studies in Education (Other)
Journal Section Articles
Authors

Seçil Yemen Karpuzcu 0000-0002-2150-000X

Rukiye Ayan Civak 0000-0002-1278-0257

Mine Işıksal 0000-0001-7619-1390

Project Number 217K430
Publication Date September 15, 2023
Published in Issue Year 2023 Volume: 24 Issue: 2

Cite

APA Yemen Karpuzcu, S., Ayan Civak, R., & Işıksal, M. (2023). Orantısal Akıl Yürütmeye İlk Adım: Birimleri Bağlama ve Yinelemedeki Temsiller. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 24(2), 1271-1300. https://doi.org/10.17679/inuefd.1226508
AMA Yemen Karpuzcu S, Ayan Civak R, Işıksal M. Orantısal Akıl Yürütmeye İlk Adım: Birimleri Bağlama ve Yinelemedeki Temsiller. INUJFE. September 2023;24(2):1271-1300. doi:10.17679/inuefd.1226508
Chicago Yemen Karpuzcu, Seçil, Rukiye Ayan Civak, and Mine Işıksal. “Orantısal Akıl Yürütmeye İlk Adım: Birimleri Bağlama Ve Yinelemedeki Temsiller”. İnönü Üniversitesi Eğitim Fakültesi Dergisi 24, no. 2 (September 2023): 1271-1300. https://doi.org/10.17679/inuefd.1226508.
EndNote Yemen Karpuzcu S, Ayan Civak R, Işıksal M (September 1, 2023) Orantısal Akıl Yürütmeye İlk Adım: Birimleri Bağlama ve Yinelemedeki Temsiller. İnönü Üniversitesi Eğitim Fakültesi Dergisi 24 2 1271–1300.
IEEE S. Yemen Karpuzcu, R. Ayan Civak, and M. Işıksal, “Orantısal Akıl Yürütmeye İlk Adım: Birimleri Bağlama ve Yinelemedeki Temsiller”, INUJFE, vol. 24, no. 2, pp. 1271–1300, 2023, doi: 10.17679/inuefd.1226508.
ISNAD Yemen Karpuzcu, Seçil et al. “Orantısal Akıl Yürütmeye İlk Adım: Birimleri Bağlama Ve Yinelemedeki Temsiller”. İnönü Üniversitesi Eğitim Fakültesi Dergisi 24/2 (September 2023), 1271-1300. https://doi.org/10.17679/inuefd.1226508.
JAMA Yemen Karpuzcu S, Ayan Civak R, Işıksal M. Orantısal Akıl Yürütmeye İlk Adım: Birimleri Bağlama ve Yinelemedeki Temsiller. INUJFE. 2023;24:1271–1300.
MLA Yemen Karpuzcu, Seçil et al. “Orantısal Akıl Yürütmeye İlk Adım: Birimleri Bağlama Ve Yinelemedeki Temsiller”. İnönü Üniversitesi Eğitim Fakültesi Dergisi, vol. 24, no. 2, 2023, pp. 1271-00, doi:10.17679/inuefd.1226508.
Vancouver Yemen Karpuzcu S, Ayan Civak R, Işıksal M. Orantısal Akıl Yürütmeye İlk Adım: Birimleri Bağlama ve Yinelemedeki Temsiller. INUJFE. 2023;24(2):1271-300.
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