International Association of Educators   |  ISSN: 1554-5210

Original article | International Journal of Progressive Education 2021, Vol. 17(5) 119-133

Predictive Power of 8th Grade Students’ Translating Among Multiple Representations Skills on their Algebraic Reasoning

Hatice Çetin, Sevcan Mercan Erdogan & Nurullah Yazici

pp. 119 - 133   |  DOI: https://doi.org/10.29329/ijpe.2021.375.9   |  Manu. Number: MANU-2103-18-0003

Published online: September 30, 2021  |   Number of Views: 10  |  Number of Download: 37


Abstract

The purpose of the present research is defining the direction and level of the relationship between 8th grade students’ translating among multiple representations skills and their algebraic reasoning and revealing the predictive power on algebraic reasoning. The research was conducted in accordance with relational survey model, which is a quantitative research method, and the study group consists of the total of 188 students, who studied at 8th grade in state schools.The data of the research were collected with the Translating Among Multiple Representations Test (TAMRT) and Algebraic Reasoning Evaluation Tool (ARET). Data were analysed using Pearson correlation and multiple linear regression analysis. Findings revealed that there is a significant relationship between students’ translating among multiple representations skills and their algebraic reasoning (r=.59; p<.01). Predictive power of students’ translating among multiple representations skill on their algebraic reasoning was found as 40%. According to the analysis on the each translating skill’s prediction of the subscales of the algebraic reasoning, only translating to graph and table representation skills predict subscales of algebraic reasoning.

Keywords: Multiple Representations, Algebraic Reasoning, 8th Grade Students


How to Cite this Article?

APA 6th edition
Cetin, H., Erdogan, S.M. & Yazici, N. (2021). Predictive Power of 8th Grade Students’ Translating Among Multiple Representations Skills on their Algebraic Reasoning . International Journal of Progressive Education, 17(5), 119-133. doi: 10.29329/ijpe.2021.375.9

Harvard
Cetin, H., Erdogan, S. and Yazici, N. (2021). Predictive Power of 8th Grade Students’ Translating Among Multiple Representations Skills on their Algebraic Reasoning . International Journal of Progressive Education, 17(5), pp. 119-133.

Chicago 16th edition
Cetin, Hatice, Sevcan Mercan Erdogan and Nurullah Yazici (2021). "Predictive Power of 8th Grade Students’ Translating Among Multiple Representations Skills on their Algebraic Reasoning ". International Journal of Progressive Education 17 (5):119-133. doi:10.29329/ijpe.2021.375.9.

References
  1. Abdullah, N., Zakaria, E., & Halim, L. (2012). The effect of a thinking strategy approach through visual representation on achievement and conceptual understanding in solving mathematical word problems. Asian Social Science, 8(16), 30-37. http://dx.doi.org/10.5539/ass.v8n16p30 [Google Scholar]
  2. Adu-Gyamfi, K. (2003). External multiple representations in mathematics teaching [Unpublished master’s tesis]. Raleigh: North Carolina State University. [Google Scholar]
  3. Adu-Gyamfi, K. (2007). Connections among representations: The nature of students’ coordinations on a linear function task [Unpublished doctoral dissertation]. North Carolina State University.  [Google Scholar]
  4. Ahmad, A., Tarmizi, R. A., & Nawawi, M. (2010). Visual representations in mathematical word problem solving among form four students in Malacca. Procedia - Social and Behavioral Sciences, 8, 356-361. https://doi.org/10.1016/j.sbspro.2010.12.050 [Google Scholar] [Crossref] 
  5. Ainstworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 183-198. https://doi.org/10.1016/j.learninstruc.2006.03.001 [Google Scholar] [Crossref] 
  6. Ainsworth, S. E., Bibby, P. A., & Wood, D. J. (1997). Information technology and multiple representations: new opportunities–new problems. Journal of Information Technology for Teacher Education, 6(1), 93-105. https://doi.org/10.1080/14759399700200006 [Google Scholar] [Crossref] 
  7. Akkan, Y. (2009). İlköğretim öğrencilerinin aritmetikten cebire geçiş süreçlerinin incelenmesi [Unpublished doctoral dissertation]. Karadeniz Technical University, Trabzon, Turkey. [Google Scholar]
  8. Akkuş Çıkla, O. (2004). The effects of multiple representations-based instruction on seventh grade students’ algebra performance, attitude toward mathematics, and representatıon preference [Unpublished doctoral dissertation]. Middle East Technical University, Ankara, Turkey.  [Google Scholar]
  9. Akkuş Çıkla, O., & Çakıroğlu, E. (2006). Seventh grade students' use of multiple representations in pattern related algebra tasks. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 31(31), 13-24. Retrieved from https://dergipark.org.tr/en/pub/hunefd/issue/7807/102391 [Google Scholar]
  10. Altun, M. (2011). Eğitim fakülteleri ve lise matematik öğretmenleri için liselerde matematik öğretimi. Bursa: Aktüel Alfa Akademi  [Google Scholar]
  11. Bal, A. P. (2014). The examination of representations used by classroom teacher candidates in solving mathematical problems. Educational Sciences: Theory & Practice, 14(6). 2349-2365. https://doi.org/10.12738/estp.2014.6.2189 [Google Scholar] [Crossref] 
  12. Carraher, D. W., Martinez, M. V., & Schliemann, A. D. (2008). Early algebra and mathematical generalization. ZDM, Mathematics Education, 40(1), 3-22. [Google Scholar]
  13. Cetin, H., & Ertekin, E. (2011). The Relationship between Eighth Grade Primary School Students' Proportional Reasoning Skills and Success in Solving Equations. International Journal of Instruction, 4(1), 47-62.  [Google Scholar]
  14. Çetin, H., & Aydın, S. (2019). The Effect of Multiple Representation Based Instruction on Mathematical Achievement: A Meta-Analysis. International Journal of Educational Research Review, 5(1), 26-36.  [Google Scholar]
  15. Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications. [Google Scholar]
  16. Çağdaşer, B. T. (2008). Cebir öğrenme alanının yapılandırmacı yaklaşımla öğretiminin 6. sınıf öğrencilerinin cebirsel düşünme düzeyleri üzerindeki etkisi [Unpublished master’s thesis]. Uludag University, Bursa, Turkey. [Google Scholar]
  17. Dede, Y. & Argün, Z. (2003). Cebir, öğrencilere niçin zor gelmektedir?.Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 180-185. [Google Scholar]
  18. Dibbs, R. A., Hott, B. L., Martin, A., Raymond, L., & Kline, T. (2020). Combining like terms: A qualitative meta-synthesis of Algebra I interventions in mathematics and special education. International Journal of Education in Mathematics, Science and Technology (IJEMST), 8(3), 219-232. [Google Scholar]
  19. Dreher, A., & Kuntze, S. (2015). Teachers facing the dilemma of multiple representations being aid and obstacle for learning: evaluations of tasks and theme-specific. Journal für Mathematik-Didaktik, 36(1), 23-44. https://doi.org/10.1007/s13138-014-0068-3 [Google Scholar] [Crossref] 
  20. Duncan, A. G. (2010). Teachers’ views on dynamically linked multiple representations, pedagogical practices and students’ understanding of mathematics using TI-N spire in Scottish secondary schools. ZDM Mathematics Education, 42, 763-774. doi:10.1007/s11858-010-0273-6. https://doi.org/10.1007/s11414-013-9386-3 [Google Scholar] [Crossref] 
  21. Dündar, S. (2015). Mathematics teacher-candidates’ performance in solving problems with different representation styles: the trigonometry example. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1379-1397. https://doi.org/10.12973/eurasia.2015.1396a [Google Scholar] [Crossref] 
  22. Durmuş, S., & Yaman, H. (2002). Mevcut teknolojilerin sunduğu çoklu temsil olanaklarının oluşturmacı yaklaşıma getireceği yenilikler: 5. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, Orta Doğu Teknik Üniversitesi: Ankara. [Google Scholar]
  23. Duval, R. (1999). Representation, vision and visualization: Cognitive functions in mathematical thinking. Basic issues for learning. In F. Hitt & M. Santos (Eds.), Proceedings of the 21st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. I, pp. 3–26). Cuernavaca: Mexico.  [Google Scholar]
  24. Erbaş, A. K. (2005). Çoklu gösterimlerle problem çözme ve teknolojinin rolü. TOJET: The Turkish Online Journal of Educational Technology, 4(4), 88-92. [Google Scholar]
  25. Ersoy, Y. & Erbaş, K. (2005). Kassel projesi cebir testinde bir grup Türk öğrencinin genel başarısı ve öğrenme güçlükleri. İlköğretim Online, 4(1),18-39.  [Google Scholar]
  26. Gagatsis, A., & Elia, I. (2004). The effects of different modes of representation on mathematical problem solving. International Group for the Psychology of Mathematics Education. Retrieved from https://files.eric.ed.gov/fulltext/ED489751.pdf [Google Scholar]
  27. Gilbert J. K. (2010).  The role of visual representations in the learning and teaching of science: An introduction. Asia-Pacific Forum on Science Learning and Teaching, 11(1), 1-19.  [Google Scholar]
  28. Goldin, G. A. (1998). Representations, learning and problem solving in mathematics. Journal of Mathematical Behavior, 17(2), 137-165. https://doi.org/10.1016/S0364-0213(99)80056-1 [Google Scholar] [Crossref] 
  29. Goldin, G. A. (2004). Representations in school mathematics: a unifying research perspectives. In J. Kilpatrick, W. G. Martin ve D. Schifter (Ed.), A Research Companion to Principles and Standards for School Mathematics (pp. 275-285). Reston, VA: NCTM. [Google Scholar]
  30. Greenes, C. E., & Findell, C. R. (1998). Groundworks: Algebra Puzzles & Problems. Creative Publications. [Google Scholar]
  31. Gürbüz, R., & Şahin, S. (2015). 8. Sınıf öğrencilerinin çoklu temsiller arasındaki geçiş becerileri. Kastamonu Eğitim Dergisi, 23(4), 1869-1888. Retrieved from https://dergipark.org.tr/en/pub/kefdergi/issue/22597/241376 [Google Scholar]
  32. Herbert, K. & Brown, R. (1997). Patterns as tools for algebraic reasoning. Teachinkilpatrig Children Mathematics, 3, 340-345. https://doi.org/10.5951/TCM.3.6.0340 [Google Scholar] [Crossref] 
  33. Herman, M. (2007). What students choose to do and have to say about use of multiple representations in college algebra. Journal of Computers in Mathematics and Science Teaching, 26(1), 27-54. Retrieved from https://www.learntechlib.org/primary/p/21086/. [Google Scholar]
  34. Hoyles, C., Noss, R., & Kaput, J. (2002). Developing new notations for a learnable mathematics in the computation alera. In Handbook of international research in mathematics education (pp. 63-88). Routledge. [Google Scholar]
  35. İpek, A. S., & Okumuş, S. (2012). İlköğretim matematik öğretmen adaylarının matematiksel problem çözmede kullandıkları temsiller. Gaziantep University Journal of Social Sciences, 11(3), 681-700. Retrieved from https://dergipark.org.tr/en/pub/jss/issue/24238/256948 [Google Scholar]
  36. İzgiol, D. (2014). Teknoloji destekli çoklu temsil temelli öğretimin öğrencilerin lineer cebir öğrenimine ve matematiğe yönelik tutumlarına etkisi [Unpublished master’s thesis]. Dokuz Eylul University, İzmir, Turkey. [Google Scholar]
  37. Kabael, U. T. & Tanışlı, D. (2010). Cebirsel düşünme sürecinde örüntüden fonksiyona öğretim. İlköğretim Online Dergisi, 9(1), 213-228. [Google Scholar]
  38. Kaf, Y. (2007). Matematikte model kullanımının 6. sınıf öğrencilerinin cebir erişilerine etkisi [Unpublished master’s thesis].  Hacettepe University, Ankara, Turkey. [Google Scholar]
  39. Kaput, J. J. (1998). Representations, inscripions, descriptions and learning: a kaleidoscope of windows. Journal of Mathematical Behavior,17(2), 265-281. [Google Scholar]
  40. Kaya, D. (2015). Çoklu temsil temelli öğretimin öğrencilerin cebirsel muhakeme becerilerine, cebirsel düşünme düzeylerine ve matematiğe yönelik tutumlarına etkisi üzerine bir inceleme [Unpublished doctoral dissertation]. Dokuz Eylul University, İzmir, Turkey. [Google Scholar]
  41. Kaya, D., Keşan, C., İzgiol, D., & Erkuş, Y. (2016). Yedinci sınıf öğrencilerinin cebirsel muhakeme becerilerine yönelik başarı düzeyi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 7(1), 142-163. [Google Scholar]
  42. Kendal, M. (2002). Teaching and learning introductory differential calculus [Unpublished doctoral dissertation]. The University of Melbourne, Australia.  [Google Scholar]
  43. Kılıç, Ç., & Özdaş, A. (2010). İlköğretim 5. sınıf öğrencilerinin kesirlerde karşılaştırma ve sıralama yapmayı gerektiren problemlerin çözümlerinde kullandıkları temsiller. Kastamonu Eğitim Dergisi, 18(2), 513-530. [Google Scholar]
  44. Kilpatrick, J., J. Swafford, J. & B. Findell. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. [Google Scholar]
  45. Kriegler, S. (2004). Just What is Algebraic Thinking?.http://www.match.ucla.edu/-kriegler/pub/algebrat.htlm, Erişim Tarihi: 07.03.2014.  [Google Scholar]
  46. López-Ibáñez, M., Prasad, T. D., & Paechter, B. (2005). Optimal pump scheduling: Representation and multiple objectives. In Proceedings of the eighth International Conference on Computing and Control for the Water Industry, 1, 117-122. [Google Scholar]
  47. Mallet, D. G. (2007). Multiple representations for systems of linear equations via computer algebra system maple. International Electronic Journal of Mathematics Education. 2(1). 16-31.  [Google Scholar]
  48. Mills, G. E., & Gay, L. R. (2016) Education research: Competencies for analysis and applications. London, England: Pearson Education. [Google Scholar]
  49. MoNE. (2009). İlköğretim matematik dersi 6-8. sınıflar öğretim programı ve kılavuzu. Ankara: MoNE. [Google Scholar]
  50. MoNE. (2017). İlköğretim matematik dersi 5-8. sınıflar öğretim programı ve kılavuzu. Ankara: MoNE. [Google Scholar]
  51. Nathan, J. M., & Koellner, K. (2007). A Framework for understanding and cultivating the transition from arithmetic to algebraic reasoning. Mathematical Thinking and Learning, 9(3), 179-192. [Google Scholar]
  52. National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: NCTM. [Google Scholar]
  53. National Council of Teachers of Mathematics [NCTM]. (2008). The role of technology in the teaching and learning of mathematics. Reston, VA: National Council of Teacher of Mathematics. [Google Scholar]
  54. Özgün Koca, S.A. (2004). The effects of multiple linked representations on students’ learning of linear relationships. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 26, 82-90. [Google Scholar]
  55. Pallant, J. (2001). SPSS Survival Manual: A Step by Step Guide to Data Analysis Using SPSS for Windows (Versions 10 and 11): SPSS Student Version 11.0 for Windows. Open University Press. [Google Scholar]
  56. Parkinson, A., & Redmond, J. A. (2002). Do cognitive styles affect learning performance in different computer media?. ACM SIGCSE Bulletin, 34(3), 39-43. [Google Scholar]
  57. Plano Clark, V. L., & Creswell, J. W. (2011). Designing and conducting mixed methods research. Sage Publications. [Google Scholar]
  58. Roschelle, J. M., Pea, R. D., Hoadley, C. M., Gordin, D. N., & Means, B. M. (2000). Changing how and what children learn in school with computer-based technologies. The future of children, 76-101. [Google Scholar]
  59. Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, meta-cognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning. New York: MacMillan. [Google Scholar]
  60. Seçer, İ. (2015). SPSS ve LISREL ile pratik veri analizi: Analiz ve raporlaştırma. Ankara: Anı Yayıncılık. [Google Scholar]
  61. Selling, S. K. (2016). Learning to represent, representing to learn. The Journal of Mathematical Behavior, 41, 191-209. [Google Scholar]
  62. Sevimli, E. (2009). Matematik öğretmen adaylarının belirli integral konusundaki temsil tercihlerinin uzamsal yetenek ve akademik başarı bağlamında incelenmesi (Unpublished master’s thesis). Marmara University, İstanbul, Turkey. [Google Scholar]
  63. Stylianou, D. A. (2002). On the interaction of visualization and analysis: the negotiation of a visual representation in expert problem solving. The Journal of Mathematical Behavior, 21(3), 303-317. [Google Scholar]
  64. TIMSS (2003). IEA’s TIMSS 2003 international report on achievement in the mathematics cognitive domains: Findings from a developmental project international association for the evaluation of educational achievement. TIMSS & PIRLS International Study Lynch School of Education, Boston College. [Google Scholar]
  65. Warren, E., & Cooper, T. J. (2009). Developing mathematics understanding and abstraction: The case of equivalence in the elementary years. Mathematics Education Research Journal, 21(2), 76-95. [Google Scholar]
  66. Yenilmez, K. & Avcu, T. (2009). Altıncı sınıf öğrencilerinin cebir öğrenme alanındaki başarı düzeyleri. Ahi Evran Üniversitesi Eğitim Fakültesi Dergisi, 10(2), 37-45.  [Google Scholar]
  67. Yenilmez, K. & Teke, M. (2008). Yenilenen matematik programının öğrencilerin cebirsel düşünme düzeylerine etkisi. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 9(15), 229-246. [Google Scholar]