Research Article
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Determination of Four Operational Errors of Primary School Students and Solution Suggestions

Year 2022, Volume: 23 Issue: Özel Sayı, 177 - 210, 26.03.2022

Abstract

The aim of this study; is to determine the operational errors of primary school first and second grade students in four operations. The model of the research is a case study, one of the qualitative research methods. Working group; A total of 162 students, 83 girls and 79 boys, studying at the primary school in Istanbul in the 2015-2016 academic year, who were selected through criterion sampling, one of the purposeful sampling methods, and 84 girls and 81 boys studying at the 2nd grade level, a total of 165 students. Mathematics textbooks of primary school 1st and 2nd grade students were used as data collection tool. Content analysis method was used in the analysis of the data. As a result of the research; This error type, which is included in the category of operational errors, was made by 1st grade students with the highest rate of counting errors; It was concluded that the error types of finding the missing added and not given decreasing were followed by the error types of finding the missing number, while this error type was followed by the error types of counting errors and finding the non-given multiplier, in which the code for subtracting the small number from the large number was made at the highest rate by the 2nd grade students.

References

  • Ashlock, R. B. (2002). Error patterns in computation: Using error patterns to improve instruction. Upper Saddle River, NJ: Prentice Hall.
  • Askew, M. & William, D. (1995). Recent reserach in mathematics education. London: HMSO.
  • Baki, A. (2014). Matematik tarihi ve felsefesi. Ankara: Pegem Akademi.
  • Bamberger, H. J., Oberdorf, C. & Schultz-Ferrell, K. (2010). Math misconceptions: From misunderstanding to deep understanding. Portsmouth, NH: Heinemann.
  • Ben-Hur, M. (2006). Concept-rich mathematics instruction: building a strong foundation for reasoning and problem solving. Alexandra, VA, USA: Association for Supervision & Curriculum Development.
  • Berman, W. (2006). When will they ever learn? Learning and teaching from mistakes in the clinical context. Clinical Law Review, 13, 115-141.
  • Brown, J. S. & Burton, R. R. (1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2,155-192.
  • Burns, M. (2007). About teaching mathematics: A K-8 resource (3 ed.). Sausalito, CA: Math Solution Publications.
  • Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö.E., Karadeniz, Ş., & Demirel, F., (2012). Bilimsel Araştırma Yöntemleri. Ankara: Pegem Akademi Yayınevi.
  • Carpenter, T. P. & Moser J.M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15, 179-202.
  • Carruthers, E. & Worthington, M. (2006). Children's Mathematics, Making Marks, Making Meaning. (2nd Ed.) London: Sage Publications.
  • Chick, H. L. & Baker, M. K. (2005). Investigating Teachers Responses to Student Misconceptions. Proceedings of the 29 th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 249-256. Melbourne: PME.
  • Cockburn, A. D. (2005). Teaching Mathematics with Insight. London: Falmer Press.
  • Cockburn, A. D. & Littler, G. (2008). Mathematical misconceptions: A guide for primary teachers. London: Sage Publications.
  • Cooke, H. (2007). Mathematics for primary and early years. London: Open University.
  • Cotton, T. (2010). Understanding and teaching primary mathematics. London: Routledge.
  • Creswell, J. W. (2016). Nitel araştırma yöntemleri: Beş yaklaşıma göre nitel araştırma ve araştırma deseni (3. Baskıdan Çeviri). (Çeviri Editörleri: M. Bütün & S.B.Demir). Ankara: Siyasal Yayın Dağıtım.
  • Davis, R. B. (1984). Learning mathematics: The cognitive science approach to mathematics education. London: Croom Helm Publisher.
  • Engelhardt, J. M. (1977). Analysis of children's computational errors: A qualitative approach. British Journal of Educational Psychology, 47,149-154.
  • Fuson, K. C. (1986). Roles of representation and verbalization in the teaching of multi-digit addition and subtraction. European Journal of Psychology of Education, 1 (2), pp.3556.
  • Fox, S. & Surtees, L. (2010). Mathematics across the curriculum. London: Continuum International Pub. Group.
  • Gibbs, G. (2007). Analysing Qualitative Data. New York: SAGE Publications.
  • Glesne, C. (2012). Nitel araştırmaya giriş (Çeviri Editörleri: Ali Ersoy & Pelin Yalçınoğlu). Ankara: Anı Yayıncılık.
  • Hansen, A. (2014). Children’s errors in mathematics. Los Angeles: Learning Matters.
  • Harris, A. (2000). Addition & Subtraction. St Martın’s College.
  • Haylock, D. & Cockburn, A. (2014). Küçük çocuklar için matematiği anlama. (Çeviri Editörü: Zuhal Yılmaz). Ankara: Nobel Yayıncılık.
  • Hopkins, C., Pope, S. & Pepperell, S. (2004). Understanding Primary Mathematics. London: David Fulton.
  • Koshy, V. (2000). Children’s mistakes and misconceptions. In V. Koshy (Ed.), Mathematics for primary teachers. London: Routledge.
  • Kubanç, Y. (2012). İlköğretim 1., 2. ve 3. sınıf öğrencilerinin matematikte dört işlem konusunda yaşadığı zorluklar ve çözüm önerileri. Yayımlanmamış yüksek lisans tezi, Fırat Üniversitesi Eğitim Bilimleri Enstitüsü, Elazığ.
  • McMillan, J. H. (2000). Educational research: Fundamentals for the consumer (4th ed.). White Plains, NY: Addison Wesley Longman, Inc.
  • Merriam, S. B. (2013). Nitel araştırma: Desen ve uygulama için bir rehber (3. Baskıdan Çeviri, Çeviri Editörü: S. Turan). Ankara: Nobel Yayın Dağıtım.
  • Mooney, C., Briggs, M., Fletcher, M., Hansen, A. & McCulloch, J. (2009). Primary mathematics: Teaching theory and practice (4th ed.). Exeter, UK: Learning Matters Ltd.
  • Miles, M. B. & Huberman, A. M. (1994). Qualitative data analysis: an expanded sourcebook. Calif: SAGE Publication.
  • NCTM, (2000). Principles and standarts for school mathematics. Reston, Va. NCTM.
  • Ojose, B. (2015). Students‟ Misconceptions in Mathematics: Analysis of Remedies and What Research Says. Ohio Journal of School Mathematics, Fall 2015, Vol. 72.
  • Olkun, S. & Toluk Uçar, Z. (2012). İlköğretimde etkinlik temelli matematik öğretimi. Ankara: Maya Akademi.
  • Pearson, M. & Somekh, B. (2003). Concept mapping as a research tool a study for primary children’s representations of information and communication Technologies (ICT). Education and Information Technologies, 8 (1): 5 -22.
  • Ryan, J. & Williams, J. (2007). Children’s mathematics 4–15: learning from errors and misconceptions. Maidenhead: Open University Press. Sadi, A. (2007). Minconceptions in numbers. UGRU Journal, 5, pp.1-7.
  • Spooner, M. (2002). Errors and misconceptions in maths at key stage 2: working towards success in sats. London: David Fulton.
  • Thompson, I. (2008). From counting to deriving number facts, in I. Thompson (ed.) Teaching and Learning Early Number. Maidenhead:Open University Press.
  • Thompson, I. & Bramald, R. (2002). An investigation of the relationship between young children's understanding of the concept of place value and their competence at mental addition (Report for the Nuffield Foundation). Newcastle upon Tyne: University of Newcastle upon Tyne.
  • Van De Walle, J. A., Karp, K. S. & Bay-Williams, J. M. (2014). İlkokul ve ortaokul matematiği gelişimsel yaklaşımla öğretim. (Çeviri Editörü: Soner Durmuş). Ankara: Nobel Yayıncılık.
  • Vosniadou, S. & Verschaffel, L. (2004). Extending the conceptual change approach to mathematics learning and teaching. Special Issue of Learning and Instruction, 14(5), 445–451.
  • Yorulmaz, A. & Önal, H. (2017). Examination of the views of class teachers regarding the errors primary school students make in four operations. Universal Journal of Educational Research 5(11): 1885-1895, 2017.

İlkokul Öğrencilerinin Dört İşlem İşlemsel Hatalarının Belirlenmesi ve Çözüm Önerileri

Year 2022, Volume: 23 Issue: Özel Sayı, 177 - 210, 26.03.2022

Abstract

Bu çalışmanın amacı; ilkokul birinci ve ikinci sınıf öğrencilerinin dört işlemde yaptıkları işlemsel hatalarının belirlenmesidir. Araştırmanın modelini, nitel araştırma yöntemlerinden durum çalışması oluşturmaktadır. Çalışma grubunu; amaçlı örnekleme yöntemlerinden ölçüt örnekleme yoluyla seçilen 2015-2016 eğitim öğretim yılında İstanbul ilindeki ilkokul 1. sınıf düzeyinde öğrenim gören 83 kız ve 79 erkek toplam 162 öğrenci, 2. sınıf düzeyinde ise öğrenim gören 84 kız ve 81 erkek toplam 165 öğrenci oluşturmaktadır. Veri toplama aracı olarak ilkokul 1. sınıf ve 2. sınıf öğrencilerinin matematik ders defterleri kullanılmıştır. İçerik analizi yöntemi verilerin analizinde kullanılmıştır. Araştırma sonuçlarına bakıldığında; işlemsel hatalar kategorisi içerisinde yer alan, sayma hataları kodunun 1. sınıf öğrencileri tarafından en yüksek oran da yapıldığı, bu hata türünü; verilmeyen toplananı bulma ve verilmeyen eksileni bulma hata türlerinin izlediği, 2. sınıf öğrencileri tarafından ise büyük sayıdan küçük sayıyı çıkarma kodunun en yüksek oranda yapıldığı bu hata türünü ise sayma hataları ve verilmeyen çarpanı bulma hata türlerinin izlediği sonucuna ulaşılmıştır.

References

  • Ashlock, R. B. (2002). Error patterns in computation: Using error patterns to improve instruction. Upper Saddle River, NJ: Prentice Hall.
  • Askew, M. & William, D. (1995). Recent reserach in mathematics education. London: HMSO.
  • Baki, A. (2014). Matematik tarihi ve felsefesi. Ankara: Pegem Akademi.
  • Bamberger, H. J., Oberdorf, C. & Schultz-Ferrell, K. (2010). Math misconceptions: From misunderstanding to deep understanding. Portsmouth, NH: Heinemann.
  • Ben-Hur, M. (2006). Concept-rich mathematics instruction: building a strong foundation for reasoning and problem solving. Alexandra, VA, USA: Association for Supervision & Curriculum Development.
  • Berman, W. (2006). When will they ever learn? Learning and teaching from mistakes in the clinical context. Clinical Law Review, 13, 115-141.
  • Brown, J. S. & Burton, R. R. (1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2,155-192.
  • Burns, M. (2007). About teaching mathematics: A K-8 resource (3 ed.). Sausalito, CA: Math Solution Publications.
  • Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö.E., Karadeniz, Ş., & Demirel, F., (2012). Bilimsel Araştırma Yöntemleri. Ankara: Pegem Akademi Yayınevi.
  • Carpenter, T. P. & Moser J.M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15, 179-202.
  • Carruthers, E. & Worthington, M. (2006). Children's Mathematics, Making Marks, Making Meaning. (2nd Ed.) London: Sage Publications.
  • Chick, H. L. & Baker, M. K. (2005). Investigating Teachers Responses to Student Misconceptions. Proceedings of the 29 th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 249-256. Melbourne: PME.
  • Cockburn, A. D. (2005). Teaching Mathematics with Insight. London: Falmer Press.
  • Cockburn, A. D. & Littler, G. (2008). Mathematical misconceptions: A guide for primary teachers. London: Sage Publications.
  • Cooke, H. (2007). Mathematics for primary and early years. London: Open University.
  • Cotton, T. (2010). Understanding and teaching primary mathematics. London: Routledge.
  • Creswell, J. W. (2016). Nitel araştırma yöntemleri: Beş yaklaşıma göre nitel araştırma ve araştırma deseni (3. Baskıdan Çeviri). (Çeviri Editörleri: M. Bütün & S.B.Demir). Ankara: Siyasal Yayın Dağıtım.
  • Davis, R. B. (1984). Learning mathematics: The cognitive science approach to mathematics education. London: Croom Helm Publisher.
  • Engelhardt, J. M. (1977). Analysis of children's computational errors: A qualitative approach. British Journal of Educational Psychology, 47,149-154.
  • Fuson, K. C. (1986). Roles of representation and verbalization in the teaching of multi-digit addition and subtraction. European Journal of Psychology of Education, 1 (2), pp.3556.
  • Fox, S. & Surtees, L. (2010). Mathematics across the curriculum. London: Continuum International Pub. Group.
  • Gibbs, G. (2007). Analysing Qualitative Data. New York: SAGE Publications.
  • Glesne, C. (2012). Nitel araştırmaya giriş (Çeviri Editörleri: Ali Ersoy & Pelin Yalçınoğlu). Ankara: Anı Yayıncılık.
  • Hansen, A. (2014). Children’s errors in mathematics. Los Angeles: Learning Matters.
  • Harris, A. (2000). Addition & Subtraction. St Martın’s College.
  • Haylock, D. & Cockburn, A. (2014). Küçük çocuklar için matematiği anlama. (Çeviri Editörü: Zuhal Yılmaz). Ankara: Nobel Yayıncılık.
  • Hopkins, C., Pope, S. & Pepperell, S. (2004). Understanding Primary Mathematics. London: David Fulton.
  • Koshy, V. (2000). Children’s mistakes and misconceptions. In V. Koshy (Ed.), Mathematics for primary teachers. London: Routledge.
  • Kubanç, Y. (2012). İlköğretim 1., 2. ve 3. sınıf öğrencilerinin matematikte dört işlem konusunda yaşadığı zorluklar ve çözüm önerileri. Yayımlanmamış yüksek lisans tezi, Fırat Üniversitesi Eğitim Bilimleri Enstitüsü, Elazığ.
  • McMillan, J. H. (2000). Educational research: Fundamentals for the consumer (4th ed.). White Plains, NY: Addison Wesley Longman, Inc.
  • Merriam, S. B. (2013). Nitel araştırma: Desen ve uygulama için bir rehber (3. Baskıdan Çeviri, Çeviri Editörü: S. Turan). Ankara: Nobel Yayın Dağıtım.
  • Mooney, C., Briggs, M., Fletcher, M., Hansen, A. & McCulloch, J. (2009). Primary mathematics: Teaching theory and practice (4th ed.). Exeter, UK: Learning Matters Ltd.
  • Miles, M. B. & Huberman, A. M. (1994). Qualitative data analysis: an expanded sourcebook. Calif: SAGE Publication.
  • NCTM, (2000). Principles and standarts for school mathematics. Reston, Va. NCTM.
  • Ojose, B. (2015). Students‟ Misconceptions in Mathematics: Analysis of Remedies and What Research Says. Ohio Journal of School Mathematics, Fall 2015, Vol. 72.
  • Olkun, S. & Toluk Uçar, Z. (2012). İlköğretimde etkinlik temelli matematik öğretimi. Ankara: Maya Akademi.
  • Pearson, M. & Somekh, B. (2003). Concept mapping as a research tool a study for primary children’s representations of information and communication Technologies (ICT). Education and Information Technologies, 8 (1): 5 -22.
  • Ryan, J. & Williams, J. (2007). Children’s mathematics 4–15: learning from errors and misconceptions. Maidenhead: Open University Press. Sadi, A. (2007). Minconceptions in numbers. UGRU Journal, 5, pp.1-7.
  • Spooner, M. (2002). Errors and misconceptions in maths at key stage 2: working towards success in sats. London: David Fulton.
  • Thompson, I. (2008). From counting to deriving number facts, in I. Thompson (ed.) Teaching and Learning Early Number. Maidenhead:Open University Press.
  • Thompson, I. & Bramald, R. (2002). An investigation of the relationship between young children's understanding of the concept of place value and their competence at mental addition (Report for the Nuffield Foundation). Newcastle upon Tyne: University of Newcastle upon Tyne.
  • Van De Walle, J. A., Karp, K. S. & Bay-Williams, J. M. (2014). İlkokul ve ortaokul matematiği gelişimsel yaklaşımla öğretim. (Çeviri Editörü: Soner Durmuş). Ankara: Nobel Yayıncılık.
  • Vosniadou, S. & Verschaffel, L. (2004). Extending the conceptual change approach to mathematics learning and teaching. Special Issue of Learning and Instruction, 14(5), 445–451.
  • Yorulmaz, A. & Önal, H. (2017). Examination of the views of class teachers regarding the errors primary school students make in four operations. Universal Journal of Educational Research 5(11): 1885-1895, 2017.
There are 44 citations in total.

Details

Primary Language Turkish
Subjects Other Fields of Education
Journal Section Research Articles
Authors

Halil Önal 0000-0001-6983-3842

Oktay Aydın 0000-0003-4927-7708

Publication Date March 26, 2022
Published in Issue Year 2022 Volume: 23 Issue: Özel Sayı

Cite

APA Önal, H., & Aydın, O. (2022). İlkokul Öğrencilerinin Dört İşlem İşlemsel Hatalarının Belirlenmesi ve Çözüm Önerileri. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 23(Özel Sayı), 177-210. https://doi.org/10.29299/kefad.995959

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