Araştırma Makalesi
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Altıncı Sınıf Öğrencilerinin Kesir İşlemlerinde Yer Verilen Farklı Temsillere Yönelik Tercihleri ve Tercih Ettikleri Temsillerdeki Başarı Durumları

Yıl 2018, , 2136 - 2150, 01.12.2018
https://doi.org/10.17051/ilkonline.2019.506984

Öz

Bu çalışmanın amacı altıncı sınıf öğrencilerinin kesirlerde toplama
çıkarma işlemine yönelik temsil (sayısal, alan modeli, sayı doğrusu ve sözel)
tercihlerini belirlemek ve kendi tercihlerindeki başarı durumlarını ortaya
koymaktır. Betimleyici doğaya sahip olan bu çalışma tarama çalışması olarak
yürütülmüştür. Çalışma grubu Kastamonu şehrinde MEB'e bağlı üç ortaokulun
altıncı sınıfında olan 31'i erkek ve 28'i kız olmak üzere 59 öğrenciden
oluşmaktadır. Katılımcıları seçmek için amaçlı örnekleme seçim yöntemi
kullanılmıştır. Veriler "Kesir işlemlerinde Çoklu Temsiller Testi"
ile toplanmış ve önceden tanımlanmış temsiller arası geçiş kriterlerine göre
analiz edilmiştir. Öğrencilerin temsil tercihleri ​​ve tercihlerindeki
başarılarının yorumlanması betimsel istatistikler (yüzde ve frekans) ile
sunulmuştur. Alan modeli temsilleri tercihlerde ilk sırada yer alırken, sözel
temsiller en az tercih edilen temsil tipidir. Öğrencilerin temsillere ait
performansları incelendiğinde, öğrencilerin kesirlerde toplama ve çıkarma
işlemlerinde en başarılı oldukları temsil türleri sayısal ve alan model
temsillerdir. Öte yandan, öğrencilerin sözel ve sayısal temsil türlerindeki
başarı durumlarının oldukça düşük olduğu görülmüştür.

Kaynakça

  • Ainsworth, S. (1999). The functions of multiple representations. Computers and Education, 33,131-152. Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183–198. Ainsworth, S. E., Bibby, P.A. & Wood, D. J. (1997). Information technology and multiple representations: New opportunities-new problems. Journal of Information Technology for Teacher Education, 6 (1), 93-105. Ainsworth, S. E., Bibby, P.A. & Wood, D. J. (2002). Examining the effects of different multiple representational systems in learning primary mathematics. The Journal of the Learning Sciences, 11(1), 25-61. Akkuş, O. & Çakıroğlu, E. (2006). Seventh grade students’ use of multiple representations in pattern related algebra tasks. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 31, 13-24. Akkoç, H. (2005). Fonksiyon kavramının anlaşılması: Tanımsal özellikler ve çoğul temsiller. Eğitim Araştırmaları, 20, 14-24. Akkoç, H. (2006). Bilgisayar destekli matematik öğretimi: Grafik analiz yaklaşimi: İlköğretim ikinci kademe ve liseler için. Toroslu Kitaplığı: İstanbul. Alacacı, C. (2010). Öğrencilerin kesirler konusundaki kavram yanılgıları. E. Bingölbali ve M.F. Özmantar (Ed.), Matematiksel Zorluklar ve Çözüm Önerileri. Ankara: PegemA Yayıncılık. Bayik, F., & Incikabi, L. (2019). Incorporating Representation-Based Instruction into Mathematics Teaching: Engaging Middle Schoolers with Multiple Representations of Adding Fractions. In J Keengwe (Ed.), Handbook of Research on Pedagogical Models for Next-Generation Teaching and Learning (pp. 311-336). Hersley, PA: IGI Global. Bezerra, F., Magina, S. & Spinillo, A. G. (2002). How to promote children’s understanding of fractions? An exploratory study. Proceedings of the 26th International Conference for the Psychology of Mathematics Education (PME), vol. 2, pp. 89-96, Norwich, UK, July. Büyüköztürk, Ş. (2001). Deneysel desenler. Ankara: PegemA Yayıncılık. Charalambous C. Y. & Pantazi, D. P. (2005). Revisiting a theoretical Area model on Fractions: Implications for teaching and Research. In Chick, H.L. ve Vincent, J. L. (Eds.), Proceedings of the29th Conference of the International Group for the Psychology of Mathematics Education, (vol2, pp.233 – 240). diSessa, A. A. & Sherin, B. (2000). Meta-representation: An introduction. Journal of Mathematical Behavior,19(4), 385-398. Doğan, M. ve Yeniterzi, B. (2011). İlköğretim 7. Sınıf Öğrencilerinin Rasyonel Sayılar Konusundaki Hazır Bulunuşlukları. Selçuk Üniversitesi Ahmet Keleşoğlu Eğitim Fakültesi Dergisi, 31,217-237. Eisner, E. W. (1997). The promise and perils of alternative forms of data representation. Educational Researcher, 26(6), 4-10. English, L. D. (1997). Mathematical reasoning: analogies, Metaphors, and Images. New Jersey: Lawrence Erlbaum Associates. Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (1993). How to design and evaluate research in education (Vol. 7). New York: McGraw-Hill. Gelman, R. & Meck, B. (1992). Early principles aid initial but not later conceptions of number. In J. Bideaud; C. Meljac & J-P. Fischer (Eds.), Pathways to number: children’s developing numerical abilities (pp.171-190). Hillsdale, NJ: Lawrence Erlbaum. Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. Journal of Mathematical Behavior, 17 (2), 137-165. Goldin, G. A., & Kaput, J. J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. In L. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 397–430). Hillsdale: Erlbaum. Hatfield, M. M., Edwards, N. T. & Bitter, G. G. (1993). Mathematics methods for the elementary and middle school (2nd edition). USA: Allyn and Bacon. Herman, M. F. (2002). Relationship of college students' visual preference to use of representations: Conceptual understanding of functions in algebra. Unpublished PhD dissertation, Columbus: Ohio State University. Işık, C. (2011). İlköğretim Matematik Öğretmeni Adaylarının Kesirlerde Çarpma ve Bölmeye Yönelik Kurdukları Problemlerin Kavramsal Analizi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41, 231-243. Işık, C. ve Kar, T. (2012). Matematik Dersinde Problem Kurmaya Yönelik Öğretmen Görüşleri Üzerine Nitel Bir Çalışma. Milli Eğitim Dergisi, 194, 199-215. Işıksal, M. (2006). A study on pre-service elementary mathematics teachers‟ subject matter knowledge and pedagogical content knowledge regarding the multiplicatıon and division of fractions (unpublished doctoral dissertation). Middle East Technical University, Turkey. İncikabi, L. Biber, A. C, Takıcak, M., & Bayam, S. B. (2015). An investigation of seventh grade students’ performances on conceptual, procedural and graphical problems regarding circles. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 6(1), 1-17. İncikabı, S. (2016). Ortaokul Matematik Ders Kitaplarının Farklı Temsilleri Kullanım Biçimlerinin Araştırılması. Yayımlanmamış yüksek lisans tezi, Kastamonu Üniversitesi, Fen Bilimleri Enstitüsü. İncikabı, S. (2017). Multiple representations and teaching mathematics: An analysis of the mathematics textbooks. Cumhuriyet International Journal of Education, 6(1), 66-81. Janvier, C. (1987). Representations and understanding: The notion of function as an example. In C. Janvier (Ed.), Problems of representations in the learning and teaching of mathematics (pp. 67-73). New Jersey: Lawrence Erlbaum Associates. Janvier, C., Girardon, C., & Morand, J. C. (1993). Mathematical symbols and representations. In P. S. Wilson (Ed.), Research ideas for the classroom: High school mathematics (pp. 79–102). Reston, VA: NCTM. Kaput, J. J. (1989). Linking representations in the symbol systems of algebra. In S. Wagner ve C. Kieran (Eds). Research issues in the learning and teaching of algebra (pp. 167-194). Hillsdale, NJ: LEA. Kaput, J. J. (1994). The representational roles of technology in connecting mathematics with authentic experience. In R. Biehler, R. W. Scholz, R. Strasser ve B. Winkelman (Eds.), Didactics in Mathematics as a ScientificDiscipline, 379-397. Netherlands: Kluwer Academic Publishers. Kara, F., & Incikabi, L. (2018). Sixth grade students' skills of using multiple representations in addition and subtraction operations in fractions. International Electronic Journal of Elementary Education, 10(4), 463-474. Kerslake, D. (1986). Fractions: children’s strategies and errors: a report of the strategies and errors in secondary mathematics project. Windsor: NFER-Nelson. Küçük, A. ve Demir, B. (2009). İlköğretim 6-8. sınıflarda matematik öğretiminde karşılaşılan bazı kavram yanılgıları üzerine bir çalışma. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 13, 97-112. Lamon, S.J. (1999). Teaching fractions and relations for understanding: essential content knowledge and instructional strategies for children. Mahwah, NJ.: Lawrence Erlbaum. Lesh, R., Post, T. & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics, (pp. 33-40). New Jersey: Lawrence Erlbaum Associates. Miles, M. B. & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage. Milli Eğitim Bakanlığı (MEB) (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim programı. Ankara. Milli Eğitim Bakanlığı (MEB) (2018). Matematik dersi öğretim programı (İlkolkul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara. Misquitta, R. (2011). A review of the literature: Fraction instruction for struggling learners in mathematics. Learning Disabilities Research ve Practice, 26(2), 109–119. National Council of Teachers of Mathematics (NCTM) (2000). Standarts for School Mathematics. Reston, VA: NCTM Özgül, İ., & İncikabı, L. (2017). Prospective teachers’ representations for teaching note values: An analysis in the context of mathematics and music. Journal of Education and Training Studies, 5(11), 129-140. Özgün-Koca, S. A. (2001a). Computer-based representations in mathematics classrooms: The effects of multiple-linked and semi-linked representations on students' learning of linear relationship. Published PhD dissertation. Ohio: Ohio State University. Özgün-Koca, S. A. (2001b). The graphing skills of students in mathematics and science education. ERIC Digest. Padalkar, S. & Hegarty, M. (2015). Models as feedback: Developing representational competence in chemistry. Journal of Educational Psychology, 107(2), 451. Pitkethly, A. & Hunting, R. (1996). A review of recent research in the area of initial fraction concepts. Educational Studies in Mathematics, 30, 5-38. Pitts, V. R. (2003). Representations of functions: An examination of pre-service mathematics teachers' knowledge of translations between algebraic and graphical representations. Unpublished PhD Dissertation. Pittsburg: University of Pittsburg Sophian, C., Garyants, D. & Chang, C. (1997). When three is less than two: early developments in children’s understanding of fractional quantities. Developmental Psychology, 33 (5), 731-744. Stylianou, D. A. (2010). Teachers’ conceptions of representation in middle school mathematics. Journal of Mathematics Teacher Education, 13(4), 325343 Şiap, İ. ve Duru (2004). A. Kesirlerde Geometrik Area modelleri Kullanabilme Becerisi. Kastamonu Eğitim Dergisi, 12(1), 89-96. Streefland, L. (1991). Fractions in realistic mathematics education: a paradigm of developmental research. Dordrecht: Kluwer Academic Publishers. Tirosh, D. (2000). Enhancing prospective teachers‟ knowledge of children‟s conception: The case of division of fraction. Journal for Research in Mathematics Education, 31(1), 5-25. Van der Meij, H. (2007). What research has to say about gender-linked differences in CMC and does elementary school children’s e-mail use fit this picture? Sex Roles, 57(5-6), 341-354. Zacharia, Z. C. & Olympiou, G. (2011). Physical versus virtual manipulative experimentation in physics learning. Learning and Instruction, 21, 317-331.
  • Zembat, İ.Ö. (2007). Sorun Aynı – Kavramlar; Kitle Aynı - Öğretmen Adayları. Elementer Education Online, 6(2), 305-312, [Online]: http://ilkogretim-online.org.tr. Erişim tarihi: 14.05.2015.

Sixth Grade Students’ Preferences on Multiple Representations Used in Fraction Operations and Their Performance in their Preferences

Yıl 2018, , 2136 - 2150, 01.12.2018
https://doi.org/10.17051/ilkonline.2019.506984

Öz

The aim of this study is to determine the
representation preferences (numerical, area model, number line and verbal) of
the sixth-year students for the addition and subtraction of fractions and to
reveal their successes in their preferences. Being descriptive in nature, this
research has been conducted as a survey study. The study group consists of 59
students, 31 of whom are boys and 28 of whom are girls, who are in the sixth
grade of three middle schools affiliated to MoNE in the city of Kastamonu. A
purposeful sampling selection method was used to select participants. The data
were collected by " Multiple Representations in Fraction Operations Test
" and analyzed in accordance with predefined transition criteria.
Representation preferences of students and interpretations of their success in
their preferences were presented through descriptive statistics (percentage and
frequency). While area model representations take the first place in
preferences, verbal representations are the least preferred type of
representation. When students’ performances in the representations are
examined, the most successful representations of students in addition and
subtraction of fractions are numerical and area model representations. On the
other hand, it has been seen that the achievement status of students in the
verbal and numerical representation types is considerably low.

Kaynakça

  • Ainsworth, S. (1999). The functions of multiple representations. Computers and Education, 33,131-152. Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183–198. Ainsworth, S. E., Bibby, P.A. & Wood, D. J. (1997). Information technology and multiple representations: New opportunities-new problems. Journal of Information Technology for Teacher Education, 6 (1), 93-105. Ainsworth, S. E., Bibby, P.A. & Wood, D. J. (2002). Examining the effects of different multiple representational systems in learning primary mathematics. The Journal of the Learning Sciences, 11(1), 25-61. Akkuş, O. & Çakıroğlu, E. (2006). Seventh grade students’ use of multiple representations in pattern related algebra tasks. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 31, 13-24. Akkoç, H. (2005). Fonksiyon kavramının anlaşılması: Tanımsal özellikler ve çoğul temsiller. Eğitim Araştırmaları, 20, 14-24. Akkoç, H. (2006). Bilgisayar destekli matematik öğretimi: Grafik analiz yaklaşimi: İlköğretim ikinci kademe ve liseler için. Toroslu Kitaplığı: İstanbul. Alacacı, C. (2010). Öğrencilerin kesirler konusundaki kavram yanılgıları. E. Bingölbali ve M.F. Özmantar (Ed.), Matematiksel Zorluklar ve Çözüm Önerileri. Ankara: PegemA Yayıncılık. Bayik, F., & Incikabi, L. (2019). Incorporating Representation-Based Instruction into Mathematics Teaching: Engaging Middle Schoolers with Multiple Representations of Adding Fractions. In J Keengwe (Ed.), Handbook of Research on Pedagogical Models for Next-Generation Teaching and Learning (pp. 311-336). Hersley, PA: IGI Global. Bezerra, F., Magina, S. & Spinillo, A. G. (2002). How to promote children’s understanding of fractions? An exploratory study. Proceedings of the 26th International Conference for the Psychology of Mathematics Education (PME), vol. 2, pp. 89-96, Norwich, UK, July. Büyüköztürk, Ş. (2001). Deneysel desenler. Ankara: PegemA Yayıncılık. Charalambous C. Y. & Pantazi, D. P. (2005). Revisiting a theoretical Area model on Fractions: Implications for teaching and Research. In Chick, H.L. ve Vincent, J. L. (Eds.), Proceedings of the29th Conference of the International Group for the Psychology of Mathematics Education, (vol2, pp.233 – 240). diSessa, A. A. & Sherin, B. (2000). Meta-representation: An introduction. Journal of Mathematical Behavior,19(4), 385-398. Doğan, M. ve Yeniterzi, B. (2011). İlköğretim 7. Sınıf Öğrencilerinin Rasyonel Sayılar Konusundaki Hazır Bulunuşlukları. Selçuk Üniversitesi Ahmet Keleşoğlu Eğitim Fakültesi Dergisi, 31,217-237. Eisner, E. W. (1997). The promise and perils of alternative forms of data representation. Educational Researcher, 26(6), 4-10. English, L. D. (1997). Mathematical reasoning: analogies, Metaphors, and Images. New Jersey: Lawrence Erlbaum Associates. Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (1993). How to design and evaluate research in education (Vol. 7). New York: McGraw-Hill. Gelman, R. & Meck, B. (1992). Early principles aid initial but not later conceptions of number. In J. Bideaud; C. Meljac & J-P. Fischer (Eds.), Pathways to number: children’s developing numerical abilities (pp.171-190). Hillsdale, NJ: Lawrence Erlbaum. Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. Journal of Mathematical Behavior, 17 (2), 137-165. Goldin, G. A., & Kaput, J. J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. In L. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 397–430). Hillsdale: Erlbaum. Hatfield, M. M., Edwards, N. T. & Bitter, G. G. (1993). Mathematics methods for the elementary and middle school (2nd edition). USA: Allyn and Bacon. Herman, M. F. (2002). Relationship of college students' visual preference to use of representations: Conceptual understanding of functions in algebra. Unpublished PhD dissertation, Columbus: Ohio State University. Işık, C. (2011). İlköğretim Matematik Öğretmeni Adaylarının Kesirlerde Çarpma ve Bölmeye Yönelik Kurdukları Problemlerin Kavramsal Analizi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41, 231-243. Işık, C. ve Kar, T. (2012). Matematik Dersinde Problem Kurmaya Yönelik Öğretmen Görüşleri Üzerine Nitel Bir Çalışma. Milli Eğitim Dergisi, 194, 199-215. Işıksal, M. (2006). A study on pre-service elementary mathematics teachers‟ subject matter knowledge and pedagogical content knowledge regarding the multiplicatıon and division of fractions (unpublished doctoral dissertation). Middle East Technical University, Turkey. İncikabi, L. Biber, A. C, Takıcak, M., & Bayam, S. B. (2015). An investigation of seventh grade students’ performances on conceptual, procedural and graphical problems regarding circles. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 6(1), 1-17. İncikabı, S. (2016). Ortaokul Matematik Ders Kitaplarının Farklı Temsilleri Kullanım Biçimlerinin Araştırılması. Yayımlanmamış yüksek lisans tezi, Kastamonu Üniversitesi, Fen Bilimleri Enstitüsü. İncikabı, S. (2017). Multiple representations and teaching mathematics: An analysis of the mathematics textbooks. Cumhuriyet International Journal of Education, 6(1), 66-81. Janvier, C. (1987). Representations and understanding: The notion of function as an example. In C. Janvier (Ed.), Problems of representations in the learning and teaching of mathematics (pp. 67-73). New Jersey: Lawrence Erlbaum Associates. Janvier, C., Girardon, C., & Morand, J. C. (1993). Mathematical symbols and representations. In P. S. Wilson (Ed.), Research ideas for the classroom: High school mathematics (pp. 79–102). Reston, VA: NCTM. Kaput, J. J. (1989). Linking representations in the symbol systems of algebra. In S. Wagner ve C. Kieran (Eds). Research issues in the learning and teaching of algebra (pp. 167-194). Hillsdale, NJ: LEA. Kaput, J. J. (1994). The representational roles of technology in connecting mathematics with authentic experience. In R. Biehler, R. W. Scholz, R. Strasser ve B. Winkelman (Eds.), Didactics in Mathematics as a ScientificDiscipline, 379-397. Netherlands: Kluwer Academic Publishers. Kara, F., & Incikabi, L. (2018). Sixth grade students' skills of using multiple representations in addition and subtraction operations in fractions. International Electronic Journal of Elementary Education, 10(4), 463-474. Kerslake, D. (1986). Fractions: children’s strategies and errors: a report of the strategies and errors in secondary mathematics project. Windsor: NFER-Nelson. Küçük, A. ve Demir, B. (2009). İlköğretim 6-8. sınıflarda matematik öğretiminde karşılaşılan bazı kavram yanılgıları üzerine bir çalışma. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 13, 97-112. Lamon, S.J. (1999). Teaching fractions and relations for understanding: essential content knowledge and instructional strategies for children. Mahwah, NJ.: Lawrence Erlbaum. Lesh, R., Post, T. & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics, (pp. 33-40). New Jersey: Lawrence Erlbaum Associates. Miles, M. B. & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage. Milli Eğitim Bakanlığı (MEB) (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim programı. Ankara. Milli Eğitim Bakanlığı (MEB) (2018). Matematik dersi öğretim programı (İlkolkul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara. Misquitta, R. (2011). A review of the literature: Fraction instruction for struggling learners in mathematics. Learning Disabilities Research ve Practice, 26(2), 109–119. National Council of Teachers of Mathematics (NCTM) (2000). Standarts for School Mathematics. Reston, VA: NCTM Özgül, İ., & İncikabı, L. (2017). Prospective teachers’ representations for teaching note values: An analysis in the context of mathematics and music. Journal of Education and Training Studies, 5(11), 129-140. Özgün-Koca, S. A. (2001a). Computer-based representations in mathematics classrooms: The effects of multiple-linked and semi-linked representations on students' learning of linear relationship. Published PhD dissertation. Ohio: Ohio State University. Özgün-Koca, S. A. (2001b). The graphing skills of students in mathematics and science education. ERIC Digest. Padalkar, S. & Hegarty, M. (2015). Models as feedback: Developing representational competence in chemistry. Journal of Educational Psychology, 107(2), 451. Pitkethly, A. & Hunting, R. (1996). A review of recent research in the area of initial fraction concepts. Educational Studies in Mathematics, 30, 5-38. Pitts, V. R. (2003). Representations of functions: An examination of pre-service mathematics teachers' knowledge of translations between algebraic and graphical representations. Unpublished PhD Dissertation. Pittsburg: University of Pittsburg Sophian, C., Garyants, D. & Chang, C. (1997). When three is less than two: early developments in children’s understanding of fractional quantities. Developmental Psychology, 33 (5), 731-744. Stylianou, D. A. (2010). Teachers’ conceptions of representation in middle school mathematics. Journal of Mathematics Teacher Education, 13(4), 325343 Şiap, İ. ve Duru (2004). A. Kesirlerde Geometrik Area modelleri Kullanabilme Becerisi. Kastamonu Eğitim Dergisi, 12(1), 89-96. Streefland, L. (1991). Fractions in realistic mathematics education: a paradigm of developmental research. Dordrecht: Kluwer Academic Publishers. Tirosh, D. (2000). Enhancing prospective teachers‟ knowledge of children‟s conception: The case of division of fraction. Journal for Research in Mathematics Education, 31(1), 5-25. Van der Meij, H. (2007). What research has to say about gender-linked differences in CMC and does elementary school children’s e-mail use fit this picture? Sex Roles, 57(5-6), 341-354. Zacharia, Z. C. & Olympiou, G. (2011). Physical versus virtual manipulative experimentation in physics learning. Learning and Instruction, 21, 317-331.
  • Zembat, İ.Ö. (2007). Sorun Aynı – Kavramlar; Kitle Aynı - Öğretmen Adayları. Elementer Education Online, 6(2), 305-312, [Online]: http://ilkogretim-online.org.tr. Erişim tarihi: 14.05.2015.
Toplam 2 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makaleleri
Yazarlar

Fatma Kara Bu kişi benim 0000-0003-2036-8382

Lütfi İncikabı 0000-0002-7912-780X

Yayımlanma Tarihi 1 Aralık 2018
Yayımlandığı Sayı Yıl 2018

Kaynak Göster

APA Kara, F., & İncikabı, L. (2018). Sixth Grade Students’ Preferences on Multiple Representations Used in Fraction Operations and Their Performance in their Preferences. İlköğretim Online, 17(4), 2136-2150. https://doi.org/10.17051/ilkonline.2019.506984
AMA Kara F, İncikabı L. Sixth Grade Students’ Preferences on Multiple Representations Used in Fraction Operations and Their Performance in their Preferences. İOO. Aralık 2018;17(4):2136-2150. doi:10.17051/ilkonline.2019.506984
Chicago Kara, Fatma, ve Lütfi İncikabı. “Sixth Grade Students’ Preferences on Multiple Representations Used in Fraction Operations and Their Performance in Their Preferences”. İlköğretim Online 17, sy. 4 (Aralık 2018): 2136-50. https://doi.org/10.17051/ilkonline.2019.506984.
EndNote Kara F, İncikabı L (01 Aralık 2018) Sixth Grade Students’ Preferences on Multiple Representations Used in Fraction Operations and Their Performance in their Preferences. İlköğretim Online 17 4 2136–2150.
IEEE F. Kara ve L. İncikabı, “Sixth Grade Students’ Preferences on Multiple Representations Used in Fraction Operations and Their Performance in their Preferences”, İOO, c. 17, sy. 4, ss. 2136–2150, 2018, doi: 10.17051/ilkonline.2019.506984.
ISNAD Kara, Fatma - İncikabı, Lütfi. “Sixth Grade Students’ Preferences on Multiple Representations Used in Fraction Operations and Their Performance in Their Preferences”. İlköğretim Online 17/4 (Aralık 2018), 2136-2150. https://doi.org/10.17051/ilkonline.2019.506984.
JAMA Kara F, İncikabı L. Sixth Grade Students’ Preferences on Multiple Representations Used in Fraction Operations and Their Performance in their Preferences. İOO. 2018;17:2136–2150.
MLA Kara, Fatma ve Lütfi İncikabı. “Sixth Grade Students’ Preferences on Multiple Representations Used in Fraction Operations and Their Performance in Their Preferences”. İlköğretim Online, c. 17, sy. 4, 2018, ss. 2136-50, doi:10.17051/ilkonline.2019.506984.
Vancouver Kara F, İncikabı L. Sixth Grade Students’ Preferences on Multiple Representations Used in Fraction Operations and Their Performance in their Preferences. İOO. 2018;17(4):2136-50.