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A COGNITIVE GAP BETWEEN FORMAL ARITHMETIC AND VISUAL REPRESENTATION IN FRACTIONAL OPERATIONS

Year 2007, Volume 8, Issue 13, 99 - 111, 01.02.2007

Abstract

The purpose of this study was to investigate the achievement of fourth grade students on fractions via formal aritmetics and visual representation according to gender variable and to obtain the relationship between formal arithmetics and visual representation of fractional operations According to the findings it was observed that boys were more successful in fractions in terms of formal arithmetic whereas no significant difference was observed in girls? success in fractions in terms of formal arithmetics and visual representation The analysis of the findings revealed a cognitive deficiency between formal aritmetics and visual representation about fraction It was seen that the level of achievement by boys and girls on fractions is extremely low and there is no significant difference between their achievement levels

References

  • Aksu,M. (1997). Student Performance in dealing with fractions. The Journal of Educational Research, 90(6),375-380.
  • Arcavi, A. (2003). A role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215-241.
  • Behr, M.J., Wachsmuth, I., Post, R.T. (1985). Construct a sum: A measure of children’s understanding of fraction size. Journal for Research in Mathematics Education, 16(2), 120-131.
  • Bezuk, N.S.& Bieck, M. (1993). Current research on rational numbers and common fractions: Summary and implications for teachers. In D.T. Owens (Ed.), Research ideas for the classroom-Middle grades mathematics 118-136. New York:Macmillan.
  • Booker,G. (1998). Children’s construction of initial fraction concepts. In Proceedings of the 22ndConference of the International Group for the Psychology of Mathematics Education, Stellenbosh, South Africa, 2, 128-135.
  • Bright, W.G.,Behr,J.M., Post, R.T., Wachsmuth, I.(1988). Identifying fractions on number lines. Journal for Research in Mathematics Education, 19 (3), 215-232.
  • Carraher, D.W.&Schliemann, A.D. (1991). Children’s understanding of fractions as expressions of relative magnitude. In F. Furinghetti (Ed.), Proceedings of the Fifteenth PME Conference, Asisi, Italy, Vol I, 184-191.
  • Davis, E.G.(2003). Teaching and classroom experiments dealing with fractions and proportional reasoning. Journal of Mathematical Behavior, 22, 107-111.
  • Filep, L., Bereznai, Gy., (1999). History of numerals. Budapest, Filum. (2nd ed., in Hungarian, also in Bulgarian: Sophia, Technika.)
  • Garofalo, J., Sharp, B., (2003, April). Teaching fractions using simulated sharing activity. Learning and Learning with Technology, 30, 41, 36-39.
  • Hart, K.M. (1987). Practical work and formalisation, too great a gap. In J.C.Bergeron, N. Herscovics, C. Kieran. Proceedings of the Eleventh International Conference Psychology of Mathematics Education (PME-XI) Vol II, 408-415. Montreal.
  • Hasemann, K. (1981). On difficulties with fractions. Educational Studies in Mathematics, 12(1), 71-87.
  • Howard, A.C. (1991). Addition of fractions. The unrecognized problem. Mathematics Teacher, December, 710-713.
  • Keijzer, R., Terwel, J., (2003). Learning for mathematical insight: a longitudinal comparative study on modelling. Learning and Instruction, 13, 285-304.
  • Kieren,T.E.(1993). Rational and fractional numbers:From quotient field to recursive understanding. In T.P.Carperten,E.Fennema&T.A.Romberg(Eds.), Rational numbers:An integration of research 49-84.Hillsdade,NJ:Erlbaum
  • Lamon,S.L. (1999). Teaching Fractions and Ratios for Understanding, Lawrence Erlbaum Associates, New Jersey.
  • Lehrer, R., Strom, D.&Confrey, J. (2002).Grounding metaphors and inscriptional resonance: Children’s emerging understanding of mathematical similarity. Cognition and Instruction, 20(3), 359-398.
  • Mack,N.K. (1990). Learning fraction with understanding, building on informal knowledge. Journal for Research in Mathematics Education, 21, 16-32.
  • Mayer, R.W., (1989). Models for understanding. Review of Educational Research, 59(1), 4364.
  • Milli Eğitim Bakanlığı ( MEB) (1997). İlköğretim Matematik Programı.
  • Nowlin, D. (1996). Division with fractions. Mathematics Teaching in the Middle School, 2(2), 116-119.
  • Oklun, S. (2004). When does the volume formula make sense to students. Hacettepe Univesity Journal of Faculty of Education, 25, 160–165.
  • Olive, J. (1999). From fractions to rational numbers of arithmetic:a reorganization hypothesis. Mathematical Thinking and Learning, 1(4), 279-314.
  • Perkins, D.N.& Unger, Chr. (1999). Teaching and Learning for understanding. In C.M. Reigeluth (Ed.), Instructional desing theories and models. Vol II. A new paradingm of instructional theory. Mahwah, NJ:Erlbaum.
  • Saenz-Ludlow, A. (1995). Ann’s fraction schemes. Educational Studies in Mathematics, 28(2), 101-132.
  • Sharp, J., Adams, B., (2002, August). Children’s contructions of knowledge for fraction division after solving realistic problems. The Journal of Educational Research. Washington, D.C., 333-347.
  • Şiap,İ., Duru, A.(2004). Skills of using geometrical models in fractions. Kastamonu Eğitim Dergisi, 12(1), 89-96.
  • Steencken, E.P., Maher, A. C. (2003). Tracing fourth graders’ learning of fractions: early episodes from a year-long teaching experiment. Journal of Mathematical Behavior, 22, 113-132.
  • Steffe, P.L. (2002). A new hypothesis concerning children’s fractional knowledge. Journal of Mathematical Behavior, 20, 267-307.
  • Streefland, L., (1982). Subtracting fractions with different denominators. Educational Studies in Mathematics, 13(3), 233-255.
  • Streefland, L. (1990). Fractions in realistic mathematics education, a paradigm of developmental research. Dordrecht: Kluver Academic.
  • Steiner,F.G., Stoecklin,M.(1997). Fraction calculation. Adidactic approach to constructing mathematical Networks. Learning and Instruction, 7(3), 211-233.
  • Tzur, R. (1999). An integrated study of children’s construction of improper fractions and the teacher’s role in promoting that learning. Journal for Research in Mathematics, 30(4), 390–416.
  • Wright, R. J., Martland, J., Stafford, A.K.&Stanger, G. (2002). Teaching number.Advancing children’s skills and strategies. London: Paul Chapman.

KESİR İŞLEMLERİNDE FORMAL ARİTMETİK VE GÖRSELLEŞTİRME ARASINDAKİ BİLİŞSEL BOŞLUK

Year 2007, Volume 8, Issue 13, 99 - 111, 01.02.2007

Abstract

Bu çalışmanın amacı 4 sınıf öğrencilerinin kesir konusundaki başarılarını formal aritmetik ve görselleştirme açısından cinsiyete göre incelemek ve kesir işlemlerinde formal aritmetik ve görselleştirme arasındaki ilişkiyi ortaya koymaktır Elde edilen bulgulara göre erkek öğrencilerin kesir konusunda formal aritmetik açısından daha başarılı olduğu kız öğrencilerin ise kesir konusunda formal aritmetik ve görselleştirme açısından başarılarında istatistiksel olarak anlamlı bir fark olmadığı görülmüştür Yapılan incelemeye göre kesirler konusunda formal aritmetik ve görselleştirme arasında bir bilişsel eksiklik olduğu bulunmuştur Genel olarak tüm örneklem içerisinde kız ve erkek öğrencilerin kesir konusundaki başarılarında anlamlı bir fark olmadığı her iki grupta da başarının düşük olduğu görülmüştür

References

  • Aksu,M. (1997). Student Performance in dealing with fractions. The Journal of Educational Research, 90(6),375-380.
  • Arcavi, A. (2003). A role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215-241.
  • Behr, M.J., Wachsmuth, I., Post, R.T. (1985). Construct a sum: A measure of children’s understanding of fraction size. Journal for Research in Mathematics Education, 16(2), 120-131.
  • Bezuk, N.S.& Bieck, M. (1993). Current research on rational numbers and common fractions: Summary and implications for teachers. In D.T. Owens (Ed.), Research ideas for the classroom-Middle grades mathematics 118-136. New York:Macmillan.
  • Booker,G. (1998). Children’s construction of initial fraction concepts. In Proceedings of the 22ndConference of the International Group for the Psychology of Mathematics Education, Stellenbosh, South Africa, 2, 128-135.
  • Bright, W.G.,Behr,J.M., Post, R.T., Wachsmuth, I.(1988). Identifying fractions on number lines. Journal for Research in Mathematics Education, 19 (3), 215-232.
  • Carraher, D.W.&Schliemann, A.D. (1991). Children’s understanding of fractions as expressions of relative magnitude. In F. Furinghetti (Ed.), Proceedings of the Fifteenth PME Conference, Asisi, Italy, Vol I, 184-191.
  • Davis, E.G.(2003). Teaching and classroom experiments dealing with fractions and proportional reasoning. Journal of Mathematical Behavior, 22, 107-111.
  • Filep, L., Bereznai, Gy., (1999). History of numerals. Budapest, Filum. (2nd ed., in Hungarian, also in Bulgarian: Sophia, Technika.)
  • Garofalo, J., Sharp, B., (2003, April). Teaching fractions using simulated sharing activity. Learning and Learning with Technology, 30, 41, 36-39.
  • Hart, K.M. (1987). Practical work and formalisation, too great a gap. In J.C.Bergeron, N. Herscovics, C. Kieran. Proceedings of the Eleventh International Conference Psychology of Mathematics Education (PME-XI) Vol II, 408-415. Montreal.
  • Hasemann, K. (1981). On difficulties with fractions. Educational Studies in Mathematics, 12(1), 71-87.
  • Howard, A.C. (1991). Addition of fractions. The unrecognized problem. Mathematics Teacher, December, 710-713.
  • Keijzer, R., Terwel, J., (2003). Learning for mathematical insight: a longitudinal comparative study on modelling. Learning and Instruction, 13, 285-304.
  • Kieren,T.E.(1993). Rational and fractional numbers:From quotient field to recursive understanding. In T.P.Carperten,E.Fennema&T.A.Romberg(Eds.), Rational numbers:An integration of research 49-84.Hillsdade,NJ:Erlbaum
  • Lamon,S.L. (1999). Teaching Fractions and Ratios for Understanding, Lawrence Erlbaum Associates, New Jersey.
  • Lehrer, R., Strom, D.&Confrey, J. (2002).Grounding metaphors and inscriptional resonance: Children’s emerging understanding of mathematical similarity. Cognition and Instruction, 20(3), 359-398.
  • Mack,N.K. (1990). Learning fraction with understanding, building on informal knowledge. Journal for Research in Mathematics Education, 21, 16-32.
  • Mayer, R.W., (1989). Models for understanding. Review of Educational Research, 59(1), 4364.
  • Milli Eğitim Bakanlığı ( MEB) (1997). İlköğretim Matematik Programı.
  • Nowlin, D. (1996). Division with fractions. Mathematics Teaching in the Middle School, 2(2), 116-119.
  • Oklun, S. (2004). When does the volume formula make sense to students. Hacettepe Univesity Journal of Faculty of Education, 25, 160–165.
  • Olive, J. (1999). From fractions to rational numbers of arithmetic:a reorganization hypothesis. Mathematical Thinking and Learning, 1(4), 279-314.
  • Perkins, D.N.& Unger, Chr. (1999). Teaching and Learning for understanding. In C.M. Reigeluth (Ed.), Instructional desing theories and models. Vol II. A new paradingm of instructional theory. Mahwah, NJ:Erlbaum.
  • Saenz-Ludlow, A. (1995). Ann’s fraction schemes. Educational Studies in Mathematics, 28(2), 101-132.
  • Sharp, J., Adams, B., (2002, August). Children’s contructions of knowledge for fraction division after solving realistic problems. The Journal of Educational Research. Washington, D.C., 333-347.
  • Şiap,İ., Duru, A.(2004). Skills of using geometrical models in fractions. Kastamonu Eğitim Dergisi, 12(1), 89-96.
  • Steencken, E.P., Maher, A. C. (2003). Tracing fourth graders’ learning of fractions: early episodes from a year-long teaching experiment. Journal of Mathematical Behavior, 22, 113-132.
  • Steffe, P.L. (2002). A new hypothesis concerning children’s fractional knowledge. Journal of Mathematical Behavior, 20, 267-307.
  • Streefland, L., (1982). Subtracting fractions with different denominators. Educational Studies in Mathematics, 13(3), 233-255.
  • Streefland, L. (1990). Fractions in realistic mathematics education, a paradigm of developmental research. Dordrecht: Kluver Academic.
  • Steiner,F.G., Stoecklin,M.(1997). Fraction calculation. Adidactic approach to constructing mathematical Networks. Learning and Instruction, 7(3), 211-233.
  • Tzur, R. (1999). An integrated study of children’s construction of improper fractions and the teacher’s role in promoting that learning. Journal for Research in Mathematics, 30(4), 390–416.
  • Wright, R. J., Martland, J., Stafford, A.K.&Stanger, G. (2002). Teaching number.Advancing children’s skills and strategies. London: Paul Chapman.

Details

Primary Language Turkish
Journal Section Articles
Authors

Nevin ORHUN This is me

Publication Date February 1, 2007
Published in Issue Year 2007, Volume 8, Issue 13

Cite

Bibtex @ { inuefd108731, journal = {İnönü Üniversitesi Eğitim Fakültesi Dergisi}, issn = {1300-2899}, eissn = {2149-9683}, address = {}, publisher = {Inonu University}, year = {2007}, volume = {8}, number = {13}, pages = {99 - 111}, title = {KESİR İŞLEMLERİNDE FORMAL ARİTMETİK VE GÖRSELLEŞTİRME ARASINDAKİ BİLİŞSEL BOŞLUK}, key = {cite}, author = {Orhun, Nevin} }
APA Orhun, N. (2007). KESİR İŞLEMLERİNDE FORMAL ARİTMETİK VE GÖRSELLEŞTİRME ARASINDAKİ BİLİŞSEL BOŞLUK . İnönü Üniversitesi Eğitim Fakültesi Dergisi , 8 (13) , 99-111 . Retrieved from https://dergipark.org.tr/en/pub/inuefd/issue/8709/108731
MLA Orhun, N. "KESİR İŞLEMLERİNDE FORMAL ARİTMETİK VE GÖRSELLEŞTİRME ARASINDAKİ BİLİŞSEL BOŞLUK" . İnönü Üniversitesi Eğitim Fakültesi Dergisi 8 (2007 ): 99-111 <https://dergipark.org.tr/en/pub/inuefd/issue/8709/108731>
Chicago Orhun, N. "KESİR İŞLEMLERİNDE FORMAL ARİTMETİK VE GÖRSELLEŞTİRME ARASINDAKİ BİLİŞSEL BOŞLUK". İnönü Üniversitesi Eğitim Fakültesi Dergisi 8 (2007 ): 99-111
RIS TY - JOUR T1 - A COGNITIVE GAP BETWEEN FORMAL ARITHMETIC AND VISUAL REPRESENTATION IN FRACTIONAL OPERATIONS AU - NevinOrhun Y1 - 2007 PY - 2007 N1 - DO - T2 - İnönü Üniversitesi Eğitim Fakültesi Dergisi JF - Journal JO - JOR SP - 99 EP - 111 VL - 8 IS - 13 SN - 1300-2899-2149-9683 M3 - UR - Y2 - 2022 ER -
EndNote %0 Inonu University Journal of the Faculty of Education KESİR İŞLEMLERİNDE FORMAL ARİTMETİK VE GÖRSELLEŞTİRME ARASINDAKİ BİLİŞSEL BOŞLUK %A Nevin Orhun %T KESİR İŞLEMLERİNDE FORMAL ARİTMETİK VE GÖRSELLEŞTİRME ARASINDAKİ BİLİŞSEL BOŞLUK %D 2007 %J İnönü Üniversitesi Eğitim Fakültesi Dergisi %P 1300-2899-2149-9683 %V 8 %N 13 %R %U
ISNAD Orhun, Nevin . "KESİR İŞLEMLERİNDE FORMAL ARİTMETİK VE GÖRSELLEŞTİRME ARASINDAKİ BİLİŞSEL BOŞLUK". İnönü Üniversitesi Eğitim Fakültesi Dergisi 8 / 13 (February 2007): 99-111 .
AMA Orhun N. KESİR İŞLEMLERİNDE FORMAL ARİTMETİK VE GÖRSELLEŞTİRME ARASINDAKİ BİLİŞSEL BOŞLUK. INUJFE. 2007; 8(13): 99-111.
Vancouver Orhun N. KESİR İŞLEMLERİNDE FORMAL ARİTMETİK VE GÖRSELLEŞTİRME ARASINDAKİ BİLİŞSEL BOŞLUK. İnönü Üniversitesi Eğitim Fakültesi Dergisi. 2007; 8(13): 99-111.
IEEE N. Orhun , "KESİR İŞLEMLERİNDE FORMAL ARİTMETİK VE GÖRSELLEŞTİRME ARASINDAKİ BİLİŞSEL BOŞLUK", İnönü Üniversitesi Eğitim Fakültesi Dergisi, vol. 8, no. 13, pp. 99-111, Feb. 2007

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