İlkokul Dördüncü Sınıf Öğrencilerinin Problem Çözme Sürecinde Oluşturduğu Görsel Temsillerin İncelenmesi

Saniye Nur Ergan; Gökhan Özsoy

doi:10.53444/deubefd.763452

İlkokul Dördüncü Sınıf Öğrencilerinin Problem Çözme Sürecinde Oluşturduğu Görsel Temsillerin İncelenmesi

Abstract

Bu araştırmanın amacı, öğrencilerin problem çözme sürecinde oluşturduğu görsel temsillerin türlerinin ve görsel temsil türlerinin problemin doğru çözülmesi temelinde nasıl bir dağılım gösterdiğinin incelenmesidir. Bu amaçla çalışma bir tarama araştırması olarak tasarlanmıştır. Araştırma verileri Ordu ilinde öğrenim görmekte olan 162 dördüncü sınıf öğrencisinden elde edilmiştir. Verilerin toplanmasında 12 matematik probleminden oluşan bir envanter kullanlmıştır. Çalışmaya katılan 162 öğrencinin cevap kâğıdından elde edilen toplam 1909 görsel temsil analiz edilmiştir. Verilerin analizinde betimsel analiz ve içerik analizi yöntemleri kullanılmıştır. Araştırma sonucunda; dördüncü sınıf öğrencilerinin problem çözme sürecince oluşturduğu üç temsil türü (şematik, resimsel ve işlemsel) tanımlanmıştır. Problem çözme sürecinde şematik temsil oluşturan öğrencilerin %87.4 oranında probleme doğru cevap verdiği görülmüştür. Resimsel temsil oluşturulan durumlarda problemin yanlış çözülme oranının %91.9 olduğu ve işlemsel temsil oluşturulan durumlarda ise %67.5 oranında probleme yanlış cevap verildiği görülmüştür.

Keywords

görsel temsiller, problem çözme, sözel problemler, ilkokul matematik öğretimi

References

Anwar, R. B., Purwanto, P., As’ari, A. R., Sisworo, S., & Rahmawati, D. (2019, February). The process of schematic representation in mathematical problem solving. In Journal of Physics: Conference Series(Vol. 1157, No. 3, p. 032075). IOP Publishing.
Blatto-Vallee, G., Kelly, R. R., Gaustad, M. G., Porter, J., & Fonzi, J. (2007). Visual–spatial representation in mathematical problem solving by deaf and hearing students. Journal of Deaf Studies and Deaf Education, 12(4), 432-448.
Boonen, A. J., van Wesel, F., Jolles, J., & van der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15-26.
Booth, R. D., & Thomas, M. O. (1999). Visualization in mathematics learning: Arithmetic problem-solving and student difficulties. The Journal of Mathematical Behavior, 18(2), 169–190.
Bozan, M., & Küçüközer, H. (2007). Elemantary school students’ errors in solving problems releated to pressure subjects. Elementary Education Online, 6(1), 24-34.
Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62(2), 211-230.
Csíkos, C., Szitányi, J., & Kelemen, R. (2012). The effects of using drawings in developing young children’s mathematical word problem solving: A design experiment with third-grade Hungarian students. Educational Studies in Mathematics, 81(1), 47-65.
De Corte, E., Verschaffel, L. ve De Win, L. (1985). Influence of rewording verbal problems on children's problem representations and solutions. Journal of Educational Psychology, 77(4), 460.
Diezmann, C. M. ve English, L. D. (2001). Promoting the use of diagrams as tools for thinking. In 2001 National Council of Teachers of Mathematics Yearbook: The Role of Representation in School Mathematics (pp. 77-89). National Council of Teachers of Mathematics.
Fuchs, L. S., Fuchs, D., Prentice, K., Burch, M., Hamlett, C. L., Owen, R., & Schroeter, K. (2003). Enhancing third-grade student'mathematical problem solving with self-regulated learning strategies. Journal of educational psychology, 95(2), 306.

Fueyo, V. ve Bushell, D. (1998). Using number line procedures and peer tutoring to improve the mathematics computation of low‐performing first graders. Journal of applied behavior analysis, 31(3), 417-430.
Goldin, G. A. (2002). Representation in mathematical learning and problem solving. In L. English (Ed.), Handbook of international research in mathematics education (pp. 197– 218). Mahwah, NJ: LEA.
Greeno, J. G. ve Hall, R. P. (1997). Practicing representation: Learning with and about representational forms. The Phi Delta Kappan, 78( 5), 361-367.
Hacıömeroğlu, G. ve Hacıömeroğlu, E. S. (2014). Turkish Adaptation of the Mathematical Processing Instrument and Pre-service Teachers’ Problem Solving Preferences. Journal of Theoretical Educational Science, 6(2).
Heffernan, N. T. ve Koedinger, K. R. (1997). The composition effect in symbolizing: The role of symbol production vs. text comprehension. In Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society (pp. 307-312).
Hegarty, M., & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of educational psychology, 91(4), 684.
Hoffman, B. (2010). “I think I can, but I'm afraid to try”: The role of self-efficacy beliefs and mathematics anxiety in mathematics problem-solving efficiency. Learning and individual differences, 20(3), 276-283.
Kaput, J. J. (1987). Representation systems and mathematics. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics, Hillsdale, NJ: Erlbaum.
Karaoğlan,D. (2009). The relationship between 6th grade students’ problem solving achievement and mathematics achievement scores after completing instructıon on problem solving. Unpublished Master’s Thesis). Middle East Technıcal Unıversity, Institute of Social Sciences, Ankara. Retrieved from http://tez2. yok. gov. tr.
Karasar, N. (2016). Bilimsel irade algı çerçevesi ile bilimsel araştırma yöntemi kavramlar ilkeler teknikler. Nobel yayıncılık
Kintsch, W. ve Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological review, 92(1), 109.
Koedinger, K. R. ve Nathan, M. J. (2004). The real story behind story problems: Effects of representations on quantitative reasoning. The journal of the learning sciences, 13(2), 129-164.
Kozhevnikov, M., Motes, M. A., & Hegarty, M. (2007). Spatial visualization in physics problem solving. Cognitive science, 31(4), 549-579.
Krawec, J. L. (2010). Problem representation and mathematical problem solving of students with varying abilities (Doctoral dissertation, Doctoral dissertation, University of Miami, Miami).
Kubanç, Y. (2012). İlköğretim 1., 2. ve 3. sınıf öğrencilerinin Matematikte Dört İşlem Konusunda Yaşadığı Zorluklar Ve Çözüm Önerileri(Yayınlanmamış Yüksek Lisans Tezi, Fırat Üniversitesi Eğitim Bilimleri Enstitüsü)
Kümbetoğlu, B. (2008). Sosyolojide ve Antropolojide Niteliksel Yöntem ve Araştırma. İstanbul: Bağlam Yayıncılık.
Larkin, J. H. ve Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive science, 11(1), 65-100.
Lazakidou, G., & Retalis, S. (2010). Using computer supported collaborative learning strategies for helping students acquire self-regulated problem-solving skills in mathematics. Computers & Education, 54(1), 3-13.
Lean, G., & Clements, M. K. (1981). Spatial ability, visual imagery, and mathematical performance. Educational Studies in Mathematics, 12(3), 267-299.
Lesh, R. (1999). The development of representational abilities in middle school mathematics. Development of mental representation: Theories and application, 323-350
Memnun, D. S., & Altun, M. (2012). Rbc+ c modeline göre doğrunun denklemi kavramının soyutlanması üzerine bir çalışma: özel bir durum çalışması. Cumhuriyet Uluslararası Eğitim Dergisi, 1(1), 17-37.
Montague, M. (1992). The effects of cognitive and metacognitive strategy instruction on the mathematical problem solving of middle school students with learning disabilities. Journal of learning disabilities, 25(4), 230-248.
Montague, M. (2007). Self-regulation and mathematics instruction. Learning Disabilities Research ve Practice, 22, 75–83.
Montague, M., & Applegate, B. (2000). Middle school students' perceptions, persistence, and performance in mathematical problem solving. Learning Disability Quarterly, 23(3), 215-227.
Montague, M., Applegate, B., & Marquard, K. (1993). Cognitive strategy instruction and mathematical problem-solving performance of students with learning disabilities. Learning Disabilities Research & Practice.
Montague, M., Warger, C., & Morgan, T. H. (2000). Solve it! Strategy instruction to improve mathematical problem solving. Learning Disabilities Research & Practice, 15(2), 110-116.
Morano, S., & Riccomini, P. J. (2019). Is a Picture Worth 1,000 Words? Investigating Fraction Magnitude Knowledge Through Analysis of Student Representations. Assessment for Effective Intervention, 1534508418820697.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.
Novick, L. R., Hurley, S. M. ve Francis, M. (1999). Evidence for abstract, schematic knowledge of three spatial diagram representations. Memory ve Cognition, 27(2), 288-308.
Özsoy, G. (2014). Problem çözme becerisi ile matematik başarısı arasındaki ilişki. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 25(3), 179-190.
Özsoy, G. (2018). Pre-service Teachers’ Use of Visual Representations. International Electronic Journal of Elementary Education, 11(1), 49-54.
Pape, S. J. ve Tchoshanov, M. A. (2001). The role of representation (s) in developing mathematical understanding. Theory into practice, 40(2), 118-127.
Passolunghi, M. C., & Mammarella, I. C. (2010). Spatial and visual working memory ability in children with difficulties in arithmetic word problem solving. European Journal of Cognitive Psychology, 22(6), 944-963
Pimm, D. (2002). Symbols and meanings in school mathematics. Routledge.
Polya, G. (2006). How to Solve It. Princeton and Oxford: Princeton University.
Rellensmann, J., Schukajlow, S., & Leopold, C. (2017). Make a drawing. Effects of strategic knowledge, drawing accuracy, and type of drawing on students’ mathematical modelling performance. Educational Studies in Mathematics, 95(1), 53-78.
Riding, R. J. ve Pearson, F. (1994). The relationship between cognitive style and intelligence. Educational Psychology, 14(4), 413-425.
Sriutai, M., Boonlue, S., Neanchaleay, J., & Murphy, E. (2018). Using Pictorial Maps to Scaffold Problem Solving in Primary-Grade Arithmetic. International Journal of Innovation in Science and Mathematics Education (formerly CAL-laborate International), 26(5).
Stylianou, D. A. (2010). Teachers’ conceptions of representation in middle school mathematics. Journal of Mathematics Teacher Education, 13(4), 325-343.
Suwarsono, S. (1982). Visual imagery in the mathematical thinking of seventh-grade students. (Unpublished doctoral dissertation). Monash University, Melbourne, Australia
Tai, W. C., & Lin, S. W. (2015). Relationship between problem-solving style and mathematical literacy. Educational Research and Reviews, 10(11), 1480-1486.
Tambychik, T., & Meerah, T. S. M. (2010). Students’ difficulties in mathematics problem-solving: What do they say?. Procedia-Social and Behavioral Sciences, 8, 142-151.
Uesaka, Y., Manalo, E. ve Ichikawa, S. I. (2007). What kinds of perceptions and daily learning behaviors promote students' use of diagrams in mathematics problem solving? Learning and Instruction, 17(3), 322-335.
Uttal, D. H., Scudder, K. V. ve DeLoache, J. S. (1997). Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics. Journal of applied developmental psychology, 18(1), 37-54.
Van de Walle,. J.,A., Karp, K. S. ve Bay-Williams, J.M. (2013). İlkokul ve Ortaokul Matematiği, Gelişimsel Yaklaşımla Öğretim. (7. Baskı, Çev. Edit. Soner Durmuş). Nobel Ankara: Akademik.
Van Garderen, D. (2006). Spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities. Journal of learning disabilities, 39(6), 496-506.
Van Garderen, D., & Montague, M. (2003). Visual‐spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18(4), 246-254
van Garderen, D., & Scheuermann, A. M. (2015). Diagramming word problems: A strategic approach for instruction. Intervention in School and Clinic, 50(5), 282-290.
Xin, Y. P., Jitendra, A. K. ve Deatline-Buchman, A. (2005). Effects of mathematical word Problem—Solving instruction on middle school students with learning problems. The Journal of Special Education, 39(3), 181-192.
Yıldırım, A. ve Şimşek, H. (2008). Sosyal Bilimlerde Nitel Araştırma Yöntemleri (7. Baskı), Ankara: Seçkin Yayınevi.
Zawojewski, J. S. ve Lesh, R. (2003). A models and modeling perspective on problem solving. In R. Lesh and H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving (pp. 317-328). Mahwah, NJ: LEA

Details

Primary Language

Turkish

Subjects

Studies on Education

Journal Section

Research Article

Authors

Saniye Nur Ergan ^*
0000-0003-4782-7710
Türkiye

Gökhan Özsoy
0000-0002-1250-624X
Türkiye

Publication Date

June 30, 2021

Submission Date

July 3, 2020

Acceptance Date

June 25, 2021

Published in Issue

Year 2021 Number: 51

DOI

https://doi.org/10.53444/deubefd.763452

IZ

https://izlik.org/JA52XE79TW

APA

Ergan, S. N., & Özsoy, G. (2021). İlkokul Dördüncü Sınıf Öğrencilerinin Problem Çözme Sürecinde Oluşturduğu Görsel Temsillerin İncelenmesi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, 51, 57-75. https://doi.org/10.53444/deubefd.763452

AMA

1.Ergan SN, Özsoy G. İlkokul Dördüncü Sınıf Öğrencilerinin Problem Çözme Sürecinde Oluşturduğu Görsel Temsillerin İncelenmesi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi. 2021;(51):57-75. doi:10.53444/deubefd.763452

Chicago

Ergan, Saniye Nur, and Gökhan Özsoy. 2021. “İlkokul Dördüncü Sınıf Öğrencilerinin Problem Çözme Sürecinde Oluşturduğu Görsel Temsillerin İncelenmesi”. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, nos. 51: 57-75. https://doi.org/10.53444/deubefd.763452.

EndNote

Ergan SN, Özsoy G (June 1, 2021) İlkokul Dördüncü Sınıf Öğrencilerinin Problem Çözme Sürecinde Oluşturduğu Görsel Temsillerin İncelenmesi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi 51 57–75.

IEEE

[1]S. N. Ergan and G. Özsoy, “İlkokul Dördüncü Sınıf Öğrencilerinin Problem Çözme Sürecinde Oluşturduğu Görsel Temsillerin İncelenmesi”, Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, no. 51, pp. 57–75, June 2021, doi: 10.53444/deubefd.763452.

ISNAD

Ergan, Saniye Nur - Özsoy, Gökhan. “İlkokul Dördüncü Sınıf Öğrencilerinin Problem Çözme Sürecinde Oluşturduğu Görsel Temsillerin İncelenmesi”. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi. 51 (June 1, 2021): 57-75. https://doi.org/10.53444/deubefd.763452.

JAMA

1.Ergan SN, Özsoy G. İlkokul Dördüncü Sınıf Öğrencilerinin Problem Çözme Sürecinde Oluşturduğu Görsel Temsillerin İncelenmesi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi. 2021;:57–75.

MLA

Ergan, Saniye Nur, and Gökhan Özsoy. “İlkokul Dördüncü Sınıf Öğrencilerinin Problem Çözme Sürecinde Oluşturduğu Görsel Temsillerin İncelenmesi”. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, no. 51, June 2021, pp. 57-75, doi:10.53444/deubefd.763452.

Vancouver

1.Saniye Nur Ergan, Gökhan Özsoy. İlkokul Dördüncü Sınıf Öğrencilerinin Problem Çözme Sürecinde Oluşturduğu Görsel Temsillerin İncelenmesi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi. 2021 Jun. 1;(51):57-75. doi:10.53444/deubefd.763452

Cited By

Visual Reasoning in Mathematics Education: A Conceptual Framework Proposal

Acta Didactica Napocensia

https://doi.org/10.24193/adn.14.1.9