International Association of Educators   |  ISSN: 1949-4270   |  e-ISSN: 1949-4289

Original article | Educational Policy Analysis and Strategic Research 2022, Vol. 17(3) 238-262

An Action Research to Eliminate Mistakes in Multiplication and Division Operations through Realistic Mathematics Education

Alper Yorulmaz & M. Cihangir Doğan

pp. 238 - 262   |  DOI: https://doi.org/10.29329/epasr.2022.461.12   |  Manu. Number: MANU-2207-04-0002.R1

Published online: September 02, 2022  |   Number of Views: 184  |  Number of Download: 340


Abstract

In the current study, it is aimed to determine the activities that need to be done to eliminate the mistakes made by primary school fourth grade students in multiplication and division operations and to present solution suggestions for eliminating these mistakes. The study employed action research, one of the qualitative research methods. The study group was constructed by the criterion sampling method, one of the purposive sampling methods. The study group is comprised of 10 fourth graders attending a primary school in the spring term of the 2016-2017 school year in the city of İstanbul and making similar mistakes. A student information form, clinical interview form and student worksheets were used as data collection tools in the study. Activities prepared in line with the principles of Realistic Mathematics Education (RME) were applied in order to eliminate the mistakes made by the students in the multiplication and division operations. When the mistakes made by the students in the multiplication and division operations were examined, it was revealed that the source of the mistakes was the operational, conceptual and problem situations. During the implementation of RME activities, it was determined that the mistakes of the students started to be eliminated. After the implementation, it was found that the mistakes of the students committed in the multiplication and division operations decreased. Thus, it can be said that RME is an effective application in reducing the mistakes in multiplication and division operations made by students in primary school.

Keywords: Multiplication operation, division operation, realistic mathematics education, mistake, primary school


How to Cite this Article?

APA 6th edition
Yorulmaz, A. & Dogan, M.C. (2022). An Action Research to Eliminate Mistakes in Multiplication and Division Operations through Realistic Mathematics Education . Educational Policy Analysis and Strategic Research, 17(3), 238-262. doi: 10.29329/epasr.2022.461.12

Harvard
Yorulmaz, A. and Dogan, M. (2022). An Action Research to Eliminate Mistakes in Multiplication and Division Operations through Realistic Mathematics Education . Educational Policy Analysis and Strategic Research, 17(3), pp. 238-262.

Chicago 16th edition
Yorulmaz, Alper and M. Cihangir Dogan (2022). "An Action Research to Eliminate Mistakes in Multiplication and Division Operations through Realistic Mathematics Education ". Educational Policy Analysis and Strategic Research 17 (3):238-262. doi:10.29329/epasr.2022.461.12.

References
  1. Altun, M. (2006). Matematik öğretiminde gelişmeler. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 19(2), 223-238. [Google Scholar]
  2. Altun, M. (2012). Eğitim fakülteleri ve sınıf öğretmenleri için matematik öğretimi. Alfa İstanbul: Aktüel Yayınları. [Google Scholar]
  3. Anghileri, J. (1989). An investigation of young children’s understanding of multiplication. Educational Studies in Mathematics, 20(4), 367–385. [Google Scholar]
  4. Arsoetar, N., & Sugiman, S. (2019). Development of student worksheets based on Realistic Mathematics Education (RME) oriented to mathematical reasoning. In Journal of Physics: Conference Series-The 6th International Conference on Research, Implementation, and Education of Mathematics and Science, Yogyakarta, Indonesia, 1397(1), p. 012091,  IOP Publishing. [Google Scholar]
  5. Ashlock, R. B. (2002). Error patterns in computation: Using error patterns to improve instruction. Upper Saddle River, NJ: Prentice Hall. [Google Scholar]
  6. Aytekin Uskun, K. (2020). İlkokul dördüncü sınıf öğrencilerinin dört işlem problemlerinde gerçekçi matematik eğitimi yaklaşımının problem çözme ve problem kurma başarılarına etkisinin araştırılması. (Yayınlanmamış yüksek lisans tezi), Kırşehir Ahi Evran Üniversitesi Sosyal Bilimler Enstitüsü, Kırşehir.  [Google Scholar]
  7. Ayvaz, A. (2010). 4. sınıf matematik dersi bölme işlemi alt öğrenme alanının edebi ürünlerle işlenmesinin öğrenci başarısı ve tutumuna etkisi. (Yayınlanmamış yüksek lisans tezi), Sakarya Üniversitesi Sosyal Bilimler Enstitüsü, Sakarya. [Google Scholar]
  8. Bakker, A. (2004). Design research ın statistics education on symbolizing and computer tools. Dissertation Utrecht University, Utrecht: Freudenthal Institute. [Google Scholar]
  9. Bamberger, H.J., Oberdorf, C., & Schultz-Ferrell, K. (2010). Math misconceptions: Pre K-Grade 5: From misunderstanding to deep understanding. Portsmouth, NH: Heinemann.  [Google Scholar]
  10. Barmby, P., Bilsborough, L., Harries, T., & Higgins, S. (2009). Primary mathematics teaching for understanding. McGraw-Hill: London. [Google Scholar]
  11. Barnes, H. (2004). Realistic mathematics education: Eliciting alternative mathematical conceptions of learnes. African Journal of Research in SMT Education, 8(1), 53-64. https://doi.org/10.1080/10288457.2004.10740560 [Google Scholar] [Crossref] 
  12. Barnes, H. (2005). The theory of realistic mathematics education as a theoretical framework for teaching low attainers in mathematics. Pythagoras, 61, 42-57. [Google Scholar]
  13. Baroody, A. J. (1999). Children’s relational knowledge of addition and subtraction. Cognition and Instruction, 17, 137–175. [Google Scholar]
  14. Baykul, Y. (1992). Matematikte başarının izlenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 8(8), 87-95. [Google Scholar]
  15. 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. [Google Scholar]
  16. Brown, J. S., & Burton, R. R. (1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2,155-192. [Google Scholar]
  17. Burns, M. (2007). About teaching mathematics: A K-8 resource (3 ed.). Sausalito, CA: Math Solution Publications. [Google Scholar]
  18. Canobi, K. H. (2005). Children’s profiles of addition and subtraction understanding. Journal of Experimental Child Psychology, 92, 220–246. https://doi.org/10.1016/j.jecp.2005.06.001 [Google Scholar] [Crossref] 
  19. Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999). Children’s mathematics: Cognitively guided instruction. Porstmouth: Heinemann. [Google Scholar]
  20. Chick, H. L., & Baker, M. K. (2005). Investigating teacher’s responses to student misconceotions. In Chick, H. L. & Vincent, J. L. (Eds.). Proceedings of the 29 th Conference of the International Group fort he Psychology of Mathematics Education (Vol.2, pp. 249-256). Melbourne: PME. [Google Scholar]
  21. Cockburn, A.D., & Littler, G. (2008). Mathematical minconceptions: A guide for primary teachers. London: Sage Publications. [Google Scholar]
  22. Cotton, T. (2016). Understanding and teaching primary mathematics. (3. Edition), Routledge: England. [Google Scholar]
  23. Çilingir, E., & Dinç Artut, P. (2016). Gerçekçi matematik eğitimi yaklaşımının ilkokul öğrencilerinin başarılarına, görsel matematik okuryazarlığı özyeterlik algılarına ve problem çözme tutumlarına etkisi. Turkish Journal of Computer and Mathematics Education, 7(3), 578-600.  [Google Scholar]
  24. Çilingir, E., & Dinç Artut, P. (2016). İlkokulda gerçekçi matematik eğitimi ile gerçekleştirilen öğretimin öğrencilerin başarısına, görsel matematik okuryazarlığıne ve problem çözme tutumlarına etkisi. Marmara Üniversitesi Atatürk Eğitim Fakültesi Dergisi, 46, 1-19. https://doi.org/10.15285/maruaebd.279963 [Google Scholar] [Crossref] 
  25. Eade, F., & Dickinson, P. (2006). Exploring realistic mathematics education in English Schools. Proceedings of The 30th Conference of The International Group for The Psychology of Mathematics Education (PME), 3, 1–8. [Google Scholar]
  26. Engelhardt, J. M. (1977). Analysis of children's computational errors: A qualitative approach. British Journal of Educational Psychology, 47(2), 149-154. https://doi.org/10.1111/j.2044-8279.1977.tb02340.x [Google Scholar] [Crossref] 
  27. Eryılmaz, A., & Sürmeli, E. (2002). Üç aşamalı sorularla öğrencilerin ısı ve sıcaklık konularındaki kavram yanılgılarının ölçülmesi, V. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, (16-18 Eylül), ODTÜ, Ankara. [Google Scholar]
  28. Fauzan, A., Slettenhaar, D., & Plomp, T. (2002). Traditional mathematics education realistic mathematics education: Hoping for changes. The Third International Conference on Mathematics Education and Society. Kopenhag. [Google Scholar]
  29. Flowers, C., Green, M., & Piel, J.A. (2008). Reversing education majors’ arithmetic misconceptions with short-term ınstruction using manipulatives. The Journal Of Educational Research. 101(4), 234-242. https://doi.org/10.3200/JOER.101.4.234-242 [Google Scholar] [Crossref] 
  30. Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Norwell: Kluwer Academic. [Google Scholar]
  31. Gravemeijer, K., & Doorman, L.M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39, 111-129. https://doi.org/10.1023/A:1003749919816 [Google Scholar] [Crossref] 
  32. Gravemeijer, K. (1994). Developing realistic mathematics education, Utrecht, Freudenthal Institute. [Google Scholar]
  33. Gravemeijer, K. P. E., Cobb, P., Bowers, J., & Whitenack, J. (2000). Symbolizing, modeling, and instructional design. In P. Cobb, E. Yackel & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design, Mahwah, NJ: Lawrence Erlbaum Associates [Google Scholar]
  34. Gür, H., Hangül, T., & Kara, A. (2014). Ortaokul ve lise öğrencilerinin “matematik kavramına ilişkin sahip oldukları metaforların karşılaştırılması. The Journal of Academic Social Science Studies, 25(1), 427- 444. [Google Scholar]
  35. Hansa, S. (2017). Exploring multiplicative reasoning with grade four learners through structured problem solving. (Unpublished MA thesis), University of the Witwatersrand, Johannesburg. [Google Scholar]
  36. Harris, A. (2001). Multiplication and division. St Martın’s College. [Google Scholar]
  37. Johnson, A. P. (2015). Eylem araştırması el kitabı. (Çev. Ed. M. Ö. Anay ve Y. Uzuner). Ankara: Anı Yayıncılık. [Google Scholar]
  38. Kalaw, M. T. B. (2012). Realistic mathematics approach, mathematical communication and problem- solving skills of high- functioning autistic children: A case study. International Peer Reviewed Journal, 2, 51- 67. [Google Scholar]
  39. Keçeli, V. (2007). Karmaşık sayılarda kavram yanılgısı ve hata ile tutum arasındaki ilişki. (Yayımlanmamış yüksek lisan tezi), Hacettepe Üniversitesi Fen Bilimleri Enstitüsü, Ankara. [Google Scholar]
  40. Makonye, J. P. (2014). Teaching functions using a realistic mathematics education approach: A theoretical perspective. International Journal of Educational Sciences, 7(3), 653-662. https://doi.org/10.1080/09751122.2014.11890228 [Google Scholar] [Crossref] 
  41. Marija, K., Lidija, M., & Simona, T. (2000). Development of ıntervention program ın mathematics ın regular classes for children with low early mathematical competence. International Special Education Congress 2000. University of Manchester, England. [Google Scholar]
  42. Marsigit, A., Dhoruri, S., & Mahmudi, A. (2007). Lesson study: Promoting student thinking on the concept of Leat Common Multiple (LCM) through realistic approach ın the 4th grade o primary mathematics teaching. The State University Of Yogyakarta, Indoesia. [Google Scholar]
  43. National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics, Reston, VA. [Google Scholar]
  44. National Joint Committee on Learning Disabilities (NJCLD). (2001). Learning disabilities: Issues on definition. In National Joint Committee on Learning Disabilities (Ed.), Collective perspectives on issues affecting learning disabilities: Position papers, statements, and reports (2nd ed., pp. 27-32). Austin, TX: Pro-Ed. [Google Scholar]
  45. Nesher, P. (1987). Towards an instructional theory: The role of learners' misconception for the learning of mathematics. For the Learning of Mathematics, 7(3), 33-39. [Google Scholar]
  46. Nures, T., & Bryant, P. E. (2008), Çocuklar ve matematik: Matematik öğretiminde yeni adımlar. (Çev.: Selma Koçak), İstanbul: Doruk Yayınları. [Google Scholar]
  47. O’Brien, R. (2001). An overview of methodological approach of action research, Roberto Richardson (Ed.), Theory and practice of action research, Brazil: Joao Pesso. [Google Scholar]
  48. Ojose, B. (2015). Students’ misconceptions in mathematics: Analysis of remedies and what research says. Ohio Journal of School Mathematics, 72, 30-34. [Google Scholar]
  49. Oliver, A. (1989). Handling pupil‟s misconceptions. Thirteen National Convention on Mathematics, Physical Science and Biology Education, (3-7 July), Pretoria. [Google Scholar]
  50. Önal, H., & Aydın, O. (2022). İlkokul öğrencilerinin dört işlem işlemsel hatalarının belirlenmesi ve çözüm önerileri. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 23, 177-210. [Google Scholar]
  51. Papadakis, S., Kalogiannakis, M., & Zaranis, N. (2017). Improving mathematics teaching in kindergarten with realistic mathematical education. Early Childhood Education Journal, 45(3), 369-378. https://doi.org/10.1007/s10643-015-0768-4 [Google Scholar] [Crossref] 
  52. 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. https://doi.org/10.1023/A:1023970123406 [Google Scholar] [Crossref] 
  53. Peters, B. (2016). Realistic Mathematics education and professional development: A case study of the experiences of primary school Mathematics teachers in Namibia.  (Unpublished doctoral dissertation), University of Stellenbosch, Stellenbosch. [Google Scholar]
  54. Radatz, H. (1980). Student’errors in the mathematical learning process: A survey. For the Learning of Mathematics, 1(1), 16-20.  [Google Scholar]
  55. Rasmussen, C., Ho, E., & Bisanz, J. (2003). Use of the mathematical principle of inversion in young children. Journal of Experimental Child Psychology, 85, 89–102. https://doi.org/10.1016/s0022-0965(03)00031-6 [Google Scholar] [Crossref] 
  56. Robinson, K. M., Ninowski, J. E., & Gray, M. L. (2006). Children’s understanding of the arithmetic concepts of inversion andassociativity. Journal of Experimental Child Psychology, 94, 349–362. https://doi.org/10.1016/j.jecp.2006.03.004 [Google Scholar] [Crossref] 
  57. Sadi, A. (2007). Misconceptions in numbers. UGRU Journal, 5, 1-7. [Google Scholar]
  58. Simon, M. A. (1993). Prospective elementary teachers' knowledge of division. Journal for Research in Mathematics Education, 24(3), 233-254. https://doi.org/10.2307/749346 [Google Scholar] [Crossref] 
  59. Tanujaya, B., Prahmana, R. C. I., & Mumu, J. (2017). Mathematics instruction, problems, challenges and opportunities: A case study in Manokwari Regency. World Transactions on Engineering and Technology Education, 15(3), 287-291. [Google Scholar]
  60. Theodora, F.R.N., & Hidayat, D. (2018). The use of realistic mathematics education in teaching the concept of equality. Journal of Holistic Mathematics Education, 1(2), 104-113. http://doi.org/10.19166/johme.v1i2.913 [Google Scholar]
  61. 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, Newcastle upon Tyne: University of Newcastle upon Tyne. [Google Scholar]
  62. Topçu, H. (2021). Gerçekçi matematik eğitimi yaklaşımının 9. Sınıf öğrencilerinin akademik başarıları, kalıcılık ve tutumlarına etkisi. (Yayınlanmamış doktora tezi), Atatürk Üniversitesi Eğitim Bilimleri Enstitüsü, Erzurum. [Google Scholar]
  63. Treffers, A. (1978). Wiskobas doelgericht. Netherlands: Utrecht. [Google Scholar]
  64. Treffers, A. (1987). Three dimensions: A model of goal and theory description in mathematics: The wiskobas project. The Netherlands: Reidel. [Google Scholar]
  65. Treffers, A. (1991). Didactical background of a mathematics program for primary education. In L. Streefland (Ed.), Realistic mathe- matics education in primary school, Utrecht: Freudenthal Institute. [Google Scholar]
  66. Uça, S., & Saracaloğlu, A. S. (2017). The use of realistic mathematics education in students’ making sense of decimals: A design research. Elementary Education Online, 16(2), 469-496. https://doi.org/10.17051/ilkonline.2017.304712 [Google Scholar] [Crossref] 
  67. Unlu, M., & Ertekin, E. (2012). Why do pre-service teachers pose multiplication problems instead of division problems in fractions?. Procedia-Social and Behavioral Sciences, 46, 490-494. https://doi.org/10.1016/j.sbspro.2012.05.148 [Google Scholar] [Crossref] 
  68. Ünal, Z.A., & İpek, A.S. (2009). Gerçekçi matematik eğitiminin ilköğretim 7. sınıf öğrencilerinin tam sayılarla çarpma konusundaki başarılarına etkisi. Eğitim ve Bilim, 34(152), 60-70. [Google Scholar]
  69. 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. [Google Scholar]
  70. Van den Heuvel-Panhuizen, M., & Wijers, M. (2005). Mathematics standarts and curricula ın the Netherlands, ZDM, 37(4), 287-307. https://doi.org/10.1007/BF02655816 [Google Scholar] [Crossref] 
  71. Van den Heuvel-Panhuizen, M. (2000). Mathematics education in the netherlands: A guided tour. Freudenthal Institute, Utrecht University, The Netherlands. [Google Scholar]
  72. Webb, D. C., Van Der Kooji, H., & Geist, M. R. (2011). Design research in the Netherlands: Introducing logarithms using realistic mathematics education. Journal of Mathematics Education at Teachers College, 2(1), 47–52. https://doi.org/10.7916/jmetc.v2i1.708 [Google Scholar] [Crossref] 
  73. Wubbels, T. H., Korthagen, F. H. J., & Broekman, H. G. B. (1997). Preparing teachers for realistic mathematics education. Educational Studies in Mathematics, 32, 1-28. [Google Scholar]
  74. Yenilmez, K., & Yaşa, E. (2008). İlköğretim öğrencilerinin geometrideki kavram yanılgıları. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 21(2), 461-483. [Google Scholar]
  75. Yılmaz, S. (2011). 7. sınıf öğrencilerinin doğrular ve açılar konusundaki hata ve kavram yanılgılarının Van Hiele geometri anlama düzeyleri açısından analizi. (Yayımlanmamış yüksek lisans tezi), Kastamonu Üniversitesi Fen Bilimleri Enstitüsü, Kastamonu. [Google Scholar]
  76. Yorulmaz, A. (2018). Gerçekçi matematik eğitiminin ilkokul dördüncü sınıf öğrencilerinin dört işlem becerilerindeki hatalarının giderilmesine etkisi. (Yayımlanmamış doktora tezi), Marmara Üniversitesi Eğitim Bilimleri Enstitüsü, İstanbul. [Google Scholar]
  77. Yorulmaz, A., Uysal, H. & Sidekli, S. (2021). The use of mind maps related to the four operations in primary school fourth-grade students as an evaluation tool. Journal of Education and Learning, 15(2), 257-266. https://doi.org/ 10.11591/edulearn.v15i2.19894 [Google Scholar] [Crossref] 
  78. Zaranis, N. (2016). The use of ICT in kindergarten for teaching addition based on realistic mathematics education. Education and Information Technologies, 21, 1-18. https://doi.org/10.1007/s10639-014-9342-8 [Google Scholar] [Crossref] 
  79. Zembat, İ. Ö. (2008), Kavram yanılgısı nedir?, M. F. Özmantar, E. Bingölbali ve H. Akkoç (Ed.), Matematiksel kavram yanılgıları ve çözüm önerileri, Ankara: Pegem Akademi. [Google Scholar]
  80. Zulkardi, Z. (2000). How to design lessons based on the realistic approach?. Literature study. University of Twente. [Online]. Available at: http://www.geocities.com/ratuilma/ rme.html [Google Scholar]