The Impact of the Cognitive Conflict Approach on the Elimination of the Misconception in Square Root Numbers
top of page
Asian Institute of Research, Journal Publication, Journal Academics, Education Journal, Asian Institute
Asian Institute of Research, Journal Publication, Journal Academics, Education Journal, Asian Institute

Education Quarterly Reviews

ISSN 2621-5799

asia institute of research, journal of education, education journal, education quarterly reviews, education publication, education call for papers
asia institute of research, journal of education, education journal, education quarterly reviews, education publication, education call for papers
asia institute of research, journal of education, education journal, education quarterly reviews, education publication, education call for papers
asia institute of research, journal of education, education journal, education quarterly reviews, education publication, education call for papers
crossref
doi
open access

Published: 15 December 2022

The Impact of the Cognitive Conflict Approach on the Elimination of the Misconception in Square Root Numbers

Hasan Güveli, Adnan Baki, Ebru Güveli

Recep Tayyip Erdoğan University (Turkey), Trabzon University (Turkey)

asia institute of research, journal of education, education journal, education quarterly reviews, education publication, education call for papers
pdf download

Download Full-Text Pdf

doi

10.31014/aior.1993.05.04.604

Pages: 39-52

Keywords: Square Root Numbers, Misconceptions, Three Tiered Test, Cognitive Conflict Approach, Secondary School Mathematics

Abstract

This study aims to determine the effect of the cognitive conflict approach on the elimination of misconceptions in square root numbers. For this purpose, this study was conducted with 8th-grade students of a secondary school in a region of Turkey. A three tiered diagnostic test was used to determine the impact of the 5-step cognitive conflict approach in the study. This test was used as a pre-test before applications and the same test was used as a post-test after applications in the same class. The test results of the students were divided into 4 groups called "misconception", "lack of knowledge", "lack of confidence", "scientific knowledge", and these groups were also divided into categories (A, B, ...). 5-step cognitive conflict approach made some transformations between categories. The greatest transformation was the transformation of misconceptions into scientific knowledge. However, it was seen that some misconceptions (B category) continued after the applications. In light of these findings, it is suggested that teachers pay attention to the mathematical language and mathematical representations they use during instruction. Moreover, the topic of root numbers should definitely be explained using the Pythagorean Theorem, and the guidebooks should be revised accordingly.

References

  1. Bagni, G. (2000). "Simple" rules and general rules in some high school student's mistakes. Journal Für Mathematik Didaktik, 21(2),124–138. https://doi.org/10.1007/BF03338913

  2. Baki, A. (2014). Matematik tarihi ve felsefesi [History and Philosophy of Mathematics], 1.press, Pegem publication.

  3. Baki, A., Güveli, E & Güveli, H. (2019, 26-28 September). Detection of misconceptions in rooted numbers with a three tiered test, 4th International Turkish Computer and Mathematics Education Symposium, 1365-1377. Trabzon/Turkey.

  4. Baser, M. (2006). Fostering conceptual change by cognitive conflict based instruction on student understanding of heat and temperature concepts. Eurasia Journal of Mathematics, Science and Technology Education, 2(2). 96-114. http://www.ejmste.com/ 022006/ d6.pdf

  5. Bingölbali, E. & Özmantar, M.F. (2010). İlköğretimde karşılaşılan matematiksel zorluklar ve çözüm Önerileri [Mathematical Difficulties in Primary Education and Solution Suggestions], 2. press, Pegem publication.

  6. Bozdağ, H. C. (2017). Üç aşamalı kavramsal ölçme aracı ile öğrencilerin sindirim sistemi konusundaki kavram yanılgılarının tespiti [Determining The Misconceptions of Students on Digestive System by Using 3-Tier Conceptual Measuring Scale]. BartinUniversity Journal of Faculty of Education, 6(3), 878-901. https://doi.org/10.14686/buefad.308999

  7. Bulut-Baran, D., Güveli, E. & Güveli, H. (2021). Üslü ifadeler konusu ile ilgili üç aşamalı kavram testi geliştirme çalışması [A Study on Developing a Three-Tier Concept Test on Exponential Expressions], Cumhuriyet International Journal of Education, 10 (3), 1150-1167. DOI:10.30703/cije.819260

  8. Cangelosi, R., Madrid, S., Cooper, S., Olson, J., & Hartter, B. (2013). The negative sign and exponential expressions: Unveiling students' persistent errors and misconceptions. The Journal of Mathematical Behavior, 32(1), 69–82. http://dx.doi.org/10.1016/j.jmathb.2012.10.002.

  9. Chabay, R., & Sherwood, B. (2006). Restructuring the introductory electricity and magnetism course. American Journal of Physics, 74(4), 329–336. https://doi.org/10.1119/1.2165249

  10. Chan, C., Burtis, J., & Bereiter, C. (1997). Knowledge building as a mediator of conflict in conceptual change. Cognition and Instruction, 15(1), 1-40. https://doi.org/10.1207/s1532690xci1501_1

  11. Crison, C. (2012). What is the square root of sixteen? Is this the question? Mathematics Teaching, 230(1), 21-22. https://discovery.ucl.ac.uk/id/eprint/1477145

  12. Çiğdemoğlu, C. & Arslan, H. Ö. (2017). Atmosfer ile ilgili çevre problemleri konularında kavram yanılgılarını tespit eden üç aşamalı tanı testinin Türkçeye uyarlanması [Adaptation of a Three-Tier Diagnostic Test Identified Misconceptions on the Atmosphere Related Environmental Problems to Turkish]. Yüzüncü Yıl University Journal of Education Faculty, 14(1), 671-699. https://doi.org/10.23891/efdyyu.2017.26

  13. Dega, B.G., Kriek, J. & Mogese, T.F. (2013). Students' conceptual change in electricity and magnetism using simulations: A comparison of cognitive perturbation and cognitive conflict. Journal of Research in Scıence Teaching, 50 (6), 677–698. https://doi.org/10.1002/tea.21096

  14. Demastes, S., Settlage, J., & Good, R. (1995). Students' conceptions of natural selection and its role in evolution: Cases of replication and comparison. Journal of Research in Science Teaching, 32(5),535–550. DOI:10.1002/tea.3660320509

  15. Dreyfus, A., Jungwirth, E., & Eliovitch, R. (1990). Applying the "Cognitive Conflict" strategy for conceptual change - some implications, difficulties, and problems. Science Education, 74, 555-569. https://doi.org/10.1002/sce.3730740506

  16. Duatepe-Paksu, A. (2008). Üslü ve köklü sayılardaki öğrenme güçlükleri [Learning Difficulties with Exponents and Radicals]. In Özmantar, M. F., Bingölbali, E. & Akkoç, H. (Eds). Matematiksel kavram yanılgıları ve çözüm önerileri [Mathematical Misconceptions and Solution Suggestions]. pp:9-39. Pegem publication.

  17. Duit, R. & Treagust, D. (2003). Conceptual change: a powerful framework for improving science teaching and learning. International Journal of Science Education, 25(6), 671-688. https://doi.org/10.1080/09500690305016

  18. Dykstra, D. I., Boyle, C. F., & Monach, I. A. (1992). Studying conceptual change in learning physics. Science Education, 76(6), 615–652. https://doi.org/10.1002/sce.3730760605

  19. Gelebek, M. S. (2011). Birleştirilmiş sınıf öğretmenlerinin yapılandırmacılık temelli yeni ilköğretim programının birleştirilmiş sınıflarda uygulananmasına ilişkin görüşlerinin incelenmesi (Kilis ili örneği) [An Analysis of Multigrade Class Teachers? Opinions Related to The New Constructivism-Based Primary School Programme Applied in Multigrade Classes (A Case in Kilis Province)] [Master Thesis, Gaziantep University], YÖK Thesis Center, https://tez.yok.gov.tr/UlusalTezMerkezi/

  20. Grayson, D. J. (1994). Concept substitution: An instructional strategy for promoting conceptual change. Research in Science Education, 24, 102–111. https://doi.org/10.1007/BF02356334

  21. Hake, R. R. (1998). Interactive-engagement versus traditional methods: A six-thousand student survey of mechanics test data for introductory physics courses. American Journal of Physics, 66(1), 64–74. https://doi.org/10.1119/1.18809

  22. Hewson, P W. & Hewson, M. G. (1984). The role of conceptual conflict in conceptual change and the design of science instruction. Instructional Science, 13, 1-3. https://www.jstor.org/stable/23369069

  23. Irawati, C. M. Zubainur & Ali R. M. (2018, September). Cognitive conflict strategy to minimize students' misconception on the topic of addition of algebraic expression. The 6th South East Asia Design Research International Conference (6th SEA-DR IC). IOP Conf. Series: Journal of Physics: Conf. Series 1088. 1-6. DOI:10.1088/1742-6596/1088/1/012084

  24. İşleyen, T. & Mercan, E. (2013). Examining the difficulties experienced by 8th grade students on the subject of square root numbers. Journal of Theory and Practice in Education, 9(4), 529–543. https://dergipark.org.tr/en/pub/eku/issue/5458/73997

  25. Kılınç, S. & Torun, F. (2011). Adil dünya inancı [Blief in a Just World]. Current Approaches in Psychiatry, 3(1), 1-14. https://dergipark.org.tr/en/pub/pgy/issue/11159/133415

  26. Kırbulut, Z. D. & Geban, Ö. (2014). Using three-tier diagnostic test to assess students’misconceptions of states of matter. Eurasia Journal of Mathematics, Science and Technology Education, 10(5), 509-521. https://doi.org/10.12973/eurasia.2014.1128a

  27. Lee, G., Kwon, J., Park, S., Kim, J., Kwon, H., & Park, H. (2003). Development of instrument for measuring CC in secondary-level science classes. Journal of Research in Science Teaching, 40(6), 585-603. https://doi.org/10.1002/tea.10099

  28. Liang, S. (2016). Teaching the concept of limit by using conceptual conflict strategy and Desmos graphing calculator. International Journal of Research in Education and Science (IJRES), 2(1), 35-48. https://files.eric.ed.gov/fulltext/EJ1105103.pdf

  29. Limon, M. (2001). On the cognitive conflict as an instructional strategy for conceptual change: A critical appraisal. Learning and Instruction, 11, 357–380. https://doi.org/10.1016/S0959-4752(00)00037-2

  30. Böge, H. & Akıllı, R. (2019). Ortaokul ve İmam Hatip Ortaokulu-8 Ders Kitabı [Secondary School and Imam Hatip Secondary School-8 Textbook]. In Prof. Dr. Murat Peker (Ed). MEB publication.

  31. Mufit, F., Festiyed, F., Fauzan, A. & Lufri, L., (2018, 5-6 October). Impact of learning model based on cognitive conflict toward student's conceptual understanding. IOP Conf. Series: Materials Science and Engineering, ICOMSET, IOP Publishing, 335, 1-7. DOI 10.1088/1757-899X/335/1/012072

  32. Nussbaum, J. & Novice, S. (1982). Alternative frameworks, conceptual conflict and accommodation: Toward a principled teaching strategy. Instructional Science, 11(3), 183–200. https://www.jstor.org/stable/23368317

  33. Okumuş-Güler, M. (2022). Yüzdeler konusu ile ilgili kavram yanılgılarının bilişsel çelişki yaklaşımı ile giderilmesi [Elimination of Misconceptions About Percentages with The Cognitive Conflict Approach] [Unpublished Master Thesis]. RTE University Graduate School of Education.

  34. Özkan, E. (2011). Misconceptions in radicals in high school mathematics. Procedia – Social and Behavioral Sciences, 15(1), 120-127. https://doi.org/10.1016/j.sbspro.2011.03.060

  35. Planinic, M., Krsnik R., Pecina P., & Susac, A. (2005, 4-7 July). Overview and comparison of basic teaching techniques that promote conceptual change in students. Paper presented at the annual meeting of the 1st European Physics Education Conference. Bad Honnef, Germany.

  36. Posner, G. J., Strıke, K. A., Hewson, P. W. And Gertzog, W. A. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Science Education, 66 (2), 211-227. https://doi.org/10.1002/sce.3730660207

  37. Roach, D., Gibson, D. & Weber, K. (2004). Why is Square Root of 25 not Plus or Minus 5? Mathematics Teacher, 97 (1), 12–13. http://www.nctm.org.

  38. Sertöz, S. (2002). Matematiğin Aydınlık Dünyası [The Bright World of Mathematics]. Tübitak publication.

  39. Shahbari, J. A., & Peled, I. (2015). Resolving Cognitive Conflict in a Realistic Situation with Modeling Characteristics: Coping with a Changing Reference in Fractions. International Journal of Science and Mathematics Education, 13(4), 891–907. https://doi.org/10.1007/s10763-014-9509-1

  40. Simon, M., Tzur, R., Heinz, K., & Kinzel, M. (2004). Explicating a mechanism for conceptual learning: Elaborating the construct of reflective abstraction. Journal for Research in Mathematics Education, 35(5), 305-329. https://doi.org/10.2307/30034818

  41. Sirotic, N., & Zazkis, R. (2007). Irrational numbers on the number line-Where are they?.International Journal of Mathematics Education, Science and Technology, 38(4), 477-488. https://doi.org/10.1080/00207390601151828

  42. Swan, M. (2001). Dealing with misconceptions in mathematics. In Pater Gates (Ed). Issues in Mathematics Teaching (147-165). Routledge-Falmer.

  43. Taşlıdere E., Korur F. & Eryılmaz A. (2012, 27-30 June). Kavram yanılgılarının üç-aşamalı sorularla farklı bir şekilde değerlendirilmesi [A Different Way of Misconceptions with Three-Stage Questions Figure Evaluation], X. National Science and Mathematics Education Congress, Niğde.

  44. Yaman, İ. (2013). Effects of instructions based on cognitive bridging and cognitive conflict on 9th grade students’ understanding of force and motion, epistemological beliefs, and self-effıcacy [Unpublished Doctoral Thesis] Middle East Technical University Cyprus.

  45. Yıldırım, A. & Şimşek, H. (2000). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative Research Methods in The Social Sciences], (2. press), Seçkin publication.

  46. Zembat, İ.Ö. (2008). Kavram Yanılgısı Nedir? [What is Misconception?]. In M. F. Özmantar, E. Bingölbali and H. Akkoç (Eds.). Matematiksel Kavram Yanılgıları ve Çözüm Önerileri [Mathematical Misconceptions and  Solution Suggestions]. Pegem publication.

  47. Zohar, A. & Aharon-Kravetsky, S. (2005). Exploring the effects of cognitive conflict and direct teaching for  students of different academic levels. Journal of Research in Science Teaching, 42, 829-855. https://doi.org/10.1002/tea.20075

bottom of page