BibTex RIS Kaynak Göster

FIFTH GRADE STUDENTS USED REPRESENTATIONS WHILE SOLVING PROBLEMS WHICH REQUIRE COMPARISON AND ORDERING IN FRACTIONS

Yıl 2010, Cilt: 18 Sayı: 2, 513 - 530, 01.05.2010

Öz

The purpose of the study was to investigate elementary fifth grade students used representations while solving problems which require comparison and ordering in fractions. Nine students participated and three problems requiring comparison and ordering in fractions were asked to each. In research data was collected via clinical interview technique and in data analysis classification determined by Miles and Huberman 1994 was used. The results obtained from the research showed that students used spoken language, symbolic and pictural drawing and figure representations. Moreover, some of the students encountered issues like not construct ing appropriate representation for problem or not associating representation that they used with the problems.

Kaynakça

  • 1. Cathcart, W. G., et al (2003). Learning Mathematics in Elementary and Middle Schools. (3rd Ed.). N.J. : Merrill/Prentice Hall.
  • 2. Reys, R. M., Suydam, M. Lindquist & N. Smith. (1998). Helping Children Learn Mathematics. USA: A Viacom Company.
  • 3. Lesh, R., Post, T., ve Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. C. Janvier, (Ed.), Problems of Representations in the Teaching and Learning of Mathematics (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum.
  • 4. Olkun S. ve Toluk-Uçar Z. (2007). İlköğretimde Etkinlik Temelli Matematik Öğretimi (3. Baskı). Ankara: Maya Akademi Yayın Dağıtım.
  • 5. Van de Walle J. A. (2004). Elementary and Middle School Mathematics. Teaching Developmentally (5 th Ed.). Boston: Allyn &Bacon.
  • 6. Haser, Ç. ve Ubuz, B. (2003). Students’ Conception of Fractions: A Study of 5th Grade Students. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 64-69.
  • 7. Soylu, Y&Soylu, C. (2005). İlköğretim Beşinci Sınıf Öğrencilerinin Kesirler Konusundaki Öğrenme Güçlükleri: Kesirlerde Sıralama, Toplama, Çıkarma, Çarpma ve Kesirlerle ilgi-li Problemler. Erzincan Eğitim Fakültesi Dergisi 7 (2), 101-117.
  • 8. Holmes, E. E. (1995). Directions in Elementary School Mathematics: Interactive Teaching and Learning. Englewood Cliffs: Merrill.
  • 9. Watanabe, T. (2002). Representations in Teaching and Learning Fractions. Teaching Children Mathematics, 8 (8), 457-463.
  • 10. Gould, P. (2005). “Year 6 Students’ Methods of Comparing the Size of Fractions”. In P Clarkson, A. Downtown, D. Gronn, M. Horne, A. McDonough, R. Pierce&A. Roche (Eds.), Building Connections: Research, Theory and Practice. Paper prsented annual meeting of the Annual Conference Mathematics Education Research Group of Australia, (pp. 393-400).Sydney: MERGA.
  • 11. MEB (2005). İlköğretim Matematik Dersi Öğretim Programı (1-5. sınıflar). Ankara: Devlet Kitapları Müdürlüğü.
  • 12. NCTM (2000). Principles and Standards for School Mathematics. İndirilme tarihi: (2005, Eylül).
  • 13. Goldin, G. (2002). Representation in mathematical learning and problem solving. Lyn D. English. (Ed.), Handbook of International Research in Mathematics. Lawrence Erlbaum Associates Publishers.
  • 14. Lubinski, C. A. ve Otto A. D. (2002). Meaningful Mathematical Representations and Early Algebraic Reasoning Teaching Children Mathematics, 9 (2), 76-80.
  • 15. Cai, J. (2005). US and Chinese Teachers’ Constructing, Knowing and Evaluating Representations to Teach Mathematics. Mathematical Thinking and Learning, 7 (2), 135-169.
  • 16. Clement, L. (2004). A Model for Understanding, Using, and Connecting Representations. Teaching Children Mathematics, 11(2), 97-102.
  • 17. Wong, M.&Evans, D. (2007). Students’ Conceptual Understanding of Equivalent Fractions. Mathematics: Essential Research, Essential Practice, 2, 824-833.
  • 18. Dewindt-King A. M. ve Goldin G. A. (2003). Children’s Visual Imagery: Aspects of Cognitive Representation in Solving Problems with Fractions. Mediterranean Journal for Research in Mathematics Education, 2 (1),1-42.
  • 19. Empson, S. B. (2001). Equal Sharing and the Roots of Fraction Equivalence. Teaching Children Mathematics, 7 (7), 421-425.
  • 20. Heritage, M. ve Niemi, D. (2006). Toward a Framework for Using Student Mathematical Representations As Formative Assessments. Educational Asssessment 11(3 & 4), 265–282.
  • 21. Patton, M. Q. (1990). Qualitative Evaluation and Research Methods. (2nd Ed.). California: Sage Publication. 22. Patton, M. Q. (2002). Qualitative Research and Evaluation Methods. (3rd ed.). California:Sage Publication.
  • 23. Goldin, G. (1998). Observing mathematical problem solving through task based interviews. A. Teppo. (Ed.), Qualitative Research Methods in Mathematics Education (pp. 40–62).Reston, Virginia:National Council of Teachers of Mathematics.
  • 24. Miles, M. B. ve Huberman A. M. (1994). An Expanded Sourcebook Qualitative Data Analysis. (2nd Ed.). California: Sage Publications.

İLKÖĞRETİM 5. SINIF ÖĞRENCİLERİNİN KESİRLERDE KARŞILAŞTIRMA VE SIRALAMA YAPMAYI GEREKTİREN PROBLEMLERİN ÇÖZÜMLERİNDE KULLANDIKLARI TEMSİLLER

Yıl 2010, Cilt: 18 Sayı: 2, 513 - 530, 01.05.2010

Öz

Bu çalışmanın amacı, ilköğretim beşinci sınıf öğrencilerinin, kesirlerde karşılaştırma ve sıralama yapmayı gerektiren problemlerin çözümleri sırasında, ne tür temsil kullandıkları ve bu kullandıkları temsillerle ilgili sorunlar yaşayıp yaşamadıklarını araştırmaktır. Araştırmaya toplam dokuz öğrenci katılmış ve her bir öğrenciye ttoplam üç tane problem sorulmuştur. Araştırmada veriler klinik görüşme tekniği ile toplanmış olup, veri analizinde Miles ve Huberman 1994 tarafından belirlenen sınıflama kullanılmıştır. Araştırmadan elde edilen sonuçlara bakıldığında, öğrencilerin problemlerin çözümleri sırasında konuşma dili, sembolik ve resimle çizim ve şekil temsil türlerini kullandıkları belirlenmiştir. Bunun yanı sıra, öğrencilerden bazılarının probleme uygun temsil oluşturamama ya da kullanılan temsili problemle ilişkilendirememe sorunlarını yaşadıkları görülmüştür.

Kaynakça

  • 1. Cathcart, W. G., et al (2003). Learning Mathematics in Elementary and Middle Schools. (3rd Ed.). N.J. : Merrill/Prentice Hall.
  • 2. Reys, R. M., Suydam, M. Lindquist & N. Smith. (1998). Helping Children Learn Mathematics. USA: A Viacom Company.
  • 3. Lesh, R., Post, T., ve Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. C. Janvier, (Ed.), Problems of Representations in the Teaching and Learning of Mathematics (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum.
  • 4. Olkun S. ve Toluk-Uçar Z. (2007). İlköğretimde Etkinlik Temelli Matematik Öğretimi (3. Baskı). Ankara: Maya Akademi Yayın Dağıtım.
  • 5. Van de Walle J. A. (2004). Elementary and Middle School Mathematics. Teaching Developmentally (5 th Ed.). Boston: Allyn &Bacon.
  • 6. Haser, Ç. ve Ubuz, B. (2003). Students’ Conception of Fractions: A Study of 5th Grade Students. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 64-69.
  • 7. Soylu, Y&Soylu, C. (2005). İlköğretim Beşinci Sınıf Öğrencilerinin Kesirler Konusundaki Öğrenme Güçlükleri: Kesirlerde Sıralama, Toplama, Çıkarma, Çarpma ve Kesirlerle ilgi-li Problemler. Erzincan Eğitim Fakültesi Dergisi 7 (2), 101-117.
  • 8. Holmes, E. E. (1995). Directions in Elementary School Mathematics: Interactive Teaching and Learning. Englewood Cliffs: Merrill.
  • 9. Watanabe, T. (2002). Representations in Teaching and Learning Fractions. Teaching Children Mathematics, 8 (8), 457-463.
  • 10. Gould, P. (2005). “Year 6 Students’ Methods of Comparing the Size of Fractions”. In P Clarkson, A. Downtown, D. Gronn, M. Horne, A. McDonough, R. Pierce&A. Roche (Eds.), Building Connections: Research, Theory and Practice. Paper prsented annual meeting of the Annual Conference Mathematics Education Research Group of Australia, (pp. 393-400).Sydney: MERGA.
  • 11. MEB (2005). İlköğretim Matematik Dersi Öğretim Programı (1-5. sınıflar). Ankara: Devlet Kitapları Müdürlüğü.
  • 12. NCTM (2000). Principles and Standards for School Mathematics. İndirilme tarihi: (2005, Eylül).
  • 13. Goldin, G. (2002). Representation in mathematical learning and problem solving. Lyn D. English. (Ed.), Handbook of International Research in Mathematics. Lawrence Erlbaum Associates Publishers.
  • 14. Lubinski, C. A. ve Otto A. D. (2002). Meaningful Mathematical Representations and Early Algebraic Reasoning Teaching Children Mathematics, 9 (2), 76-80.
  • 15. Cai, J. (2005). US and Chinese Teachers’ Constructing, Knowing and Evaluating Representations to Teach Mathematics. Mathematical Thinking and Learning, 7 (2), 135-169.
  • 16. Clement, L. (2004). A Model for Understanding, Using, and Connecting Representations. Teaching Children Mathematics, 11(2), 97-102.
  • 17. Wong, M.&Evans, D. (2007). Students’ Conceptual Understanding of Equivalent Fractions. Mathematics: Essential Research, Essential Practice, 2, 824-833.
  • 18. Dewindt-King A. M. ve Goldin G. A. (2003). Children’s Visual Imagery: Aspects of Cognitive Representation in Solving Problems with Fractions. Mediterranean Journal for Research in Mathematics Education, 2 (1),1-42.
  • 19. Empson, S. B. (2001). Equal Sharing and the Roots of Fraction Equivalence. Teaching Children Mathematics, 7 (7), 421-425.
  • 20. Heritage, M. ve Niemi, D. (2006). Toward a Framework for Using Student Mathematical Representations As Formative Assessments. Educational Asssessment 11(3 & 4), 265–282.
  • 21. Patton, M. Q. (1990). Qualitative Evaluation and Research Methods. (2nd Ed.). California: Sage Publication. 22. Patton, M. Q. (2002). Qualitative Research and Evaluation Methods. (3rd ed.). California:Sage Publication.
  • 23. Goldin, G. (1998). Observing mathematical problem solving through task based interviews. A. Teppo. (Ed.), Qualitative Research Methods in Mathematics Education (pp. 40–62).Reston, Virginia:National Council of Teachers of Mathematics.
  • 24. Miles, M. B. ve Huberman A. M. (1994). An Expanded Sourcebook Qualitative Data Analysis. (2nd Ed.). California: Sage Publications.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Research Article
Yazarlar

Çiğdem Kılıç Bu kişi benim

Aynur Özdaş Bu kişi benim

Yayımlanma Tarihi 1 Mayıs 2010
Yayımlandığı Sayı Yıl 2010 Cilt: 18 Sayı: 2

Kaynak Göster

APA Kılıç, Ç., & Özdaş, A. (2010). İLKÖĞRETİM 5. SINIF ÖĞRENCİLERİNİN KESİRLERDE KARŞILAŞTIRMA VE SIRALAMA YAPMAYI GEREKTİREN PROBLEMLERİN ÇÖZÜMLERİNDE KULLANDIKLARI TEMSİLLER. Kastamonu Education Journal, 18(2), 513-530.