The Effect of Multiple Representation Based Instruction on Mathematical Achievement: A Meta-Analysis

Yıl 2020, Cilt: 5 Sayı: 1, 26 - 36, 01.01.2020

Hatice Çetin , Serhat Aydın

https://doi.org/10.24331/ijere.647531

Öz

The aim of this study is to determine the overall effect of multiple representation based instruction
on mathematical achievement. Meta-analysis method was used for this aim. The sample of the study
consisted of 33 experimental studies within 10 publications which were selected according to certain
criteria. In data analysis, mean effect size of the selected studies was examined. The effect size
distribution of the selected studies demonstrated a heterogeneous structure which led to a
preference for random effects model (Q=66.320; p=.000).The data of the current study were analyzed
using Comprehensive Meta-Analysis (CMA), which is a specialized statistical software.  The result of
the Z-test revealed a statistically significant effect size (Z=7.015; p<.05). In order to find evidence for
reliability, both a graphic approach (funnel plot) and Orwin's fail-safe N method were used to assess
the potential publication bias. Findings of these tests suggested no bias in the data. As a result, the
current investigation revealed that there was an overall medium and positive relationship between
multiple representation based instruction and mathematical achievement.

Anahtar Kelimeler

Mathematical achievement, mathematics instruction, meta-analysis, multiple representation

Kaynakça

• Abdullah, N., Halim, L., & Zakaria, E. (2014). VStops: A thinking strategy and visual representation approach in mathematical word problem solving toward enhancing stem literacy. Eurasia Journal of Mathematics, Science & Technology Education, 10(3).
• Açıkel, C. (2009). Meta-analiz ve kanita dayali tip'taki yeri [Meta-analysis and in its place in evidence based medicine]. Klinik Psikofarmakoloji Bülteni, 19(2). Adiguzel, T., & Akpinar, Y. (2004). Improving school children's mathematical word problem solving skills through computer-based multiple representations. Association for Educational Communications and Technology. Adu-Gyamfi, K. (2007). Connections among representations: The nature of students’ coordinations on a linear function task. (Unpublished PhD). North Carolina State University. 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. Ainstworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 183-198. Ainsworth, S. (2008). The educational value of multiple-representations when learning complex scientific concepts. In Visualization: Theory and practice in science education (pp. 191-208). Dordrecht: Springer Akkoç, H. (2006). Fonksiyon kavramının çoklu temsillerinin çağrıştırdığı kavram görüntüleri [Concept Images Evoked by Multiple Representations of Function Concept]. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 30(30), 1-10. Akkus, O., & Cakiroglu, E. (2010). The effects of multiple representations-based instruction on seventh grade students’ algebra performance. In Proceedings of CERME 6, January 28th-February 1st 2009, Lyon France (Vol. 6, pp. 420-429). Çetin, H. (2016). Sorgulayıcı öğrenme yaklaşımıyla çoklu temsil destekli tam sayı öğretiminin 6. sınıf öğrencilerinin başarılarına, model tercihlerine ve temsiller arası geçiş becerilerine etkisi (Yayınlanmamış doktora tezi). Necmettin Erbakan University. Bakioğlu, A., & Özcan, Ş. (2016). Meta analiz [Meta-analysis]. Ankara: Nobel Akademik Yayıncılık Eğitim Danışmanlık. 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. Borenstein, M., Hedges, L. V., Higgins, J. P., & Rothstein, H. R. (2011). Introduction to meta-analysis: John Wiley & Sons. Can, C. (2014). Fonksiyonlar konusunun çoklu temsiller ile öğretiminin öğrenci başarısına etkisinin incelenmesi [Investigation of the effect on student achievement of teaching functions using multiple representations (Unpublished doctoral dissertation). (Yayınlanmamış yüksek lisans tezi). Balıkesir Üniversitesi, Fen Bilimleri Enstitüsü, Balıkesir. Dinçer, S. (2014). Eğitim bilimlerinde uygulamalı meta-analiz [Applied meta-analysis in educational sciences]. Pegem Yayıncılık, 2014(1), 1-133. 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. Duncan, A. G. (2010). Teachers’ views on dynamically linked multiple representations, pedagogical practices and students’ understanding of mathematics using TI-Nspire in Scottish secondary schools. ZDM Mathematics Education, 42, 763-774. doi:10.1007/s11858-010-0273-6 Durmuş, S., ve Yaman, H. (2002). Mevcut teknolojilerin sunduğu çoklu temsil olanaklarının oluşturmacı yaklaşıma getireceği yenilikler [The innovations brought about by multiple representation opportunities offered by existing technologies ]: 5. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, Orta Doğu Teknik Üniversitesi: Ankara. Ellis, P. D. (2010). The essential guide to effect sizes: Statistical power, meta-analysis, and the interpretation of research results: Cambridge University Press. Garay, A. (Ed.) (2001). Using multiple coordinated representations in a technology-intensive setting to teach linear functions at the college level. University Of Illnois At Urbana-Champaign (0090). 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. Goerdt, S. L. (2007). The effect of emphasizing multiple representations on calculus students' understanding of the derivative concept. University of Minnesota. 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. Gürbüz, R., & Şahin, S. (2015). 8. sınıf öğrencilerinin çoklu temsiller arasindaki geçiş becerileri [8th Graders' Skills to Shift Between Multiple Representations]. Kastamonu Eğitim Dergisi, 23(4), 1869-1888. Hwang, W. Y., Chen, N.-S., Dung, J. J., & Yang, Y. L. (2007). Multiple representation skills and creativity effects on mathematical problem solving using a multimedia whiteboard system. Journal of Educational Technology & Society, 10(2). İpek, A. S., & Baran, D. (2011). İlköğretim Matematik Öğretmen Adaylarinin Teknoloji Destekli Temsillerle İlgili Düşünceleri. In 5th International Computer & Instructional Technologies Symposium. Retrieved December (Vol. 11, p. 2011). İzgiol, D. (2014). Teknoloji destekli çoklu temsil temelli öğretimin öğrencilerin lineer cebir öğrenimine ve matematiğe yönelik tutumlarına etkisi [The effect of technology aided multiple representation based instruction on students' attitudes towards mathematics and learning linear algebra (Unpublished doctoral dissertation)]. (Yayınlanmamış Yüksek Lisans Tezi). Dokuz Eylül Üniversitesi Eğitim Bilimleri Enstitüsü, İzmir. Kaya, D. (2015). Çoklu temsil temelli öğretimin öğrencilerin cebirsel muhakeme becerilerine, cebirsel düşünme düzeylerine ve matematiğe yönelik tutumlarına etkisi üzerine bir inceleme [An investigation on the effect of multiple representation based instruction on students' algebraic reasoning skills, algebraic thinking levels and attitudes towards mathematics (Unpublished doctoral dissertation)]. (Yayınlanmamış yüksek lisans tezi). Dokuz Eylül Üniversitesi, Eğitim Bilimleri Enstitüsü, İzmir. Kendal, M. (2002). Teaching and learning introductory differential calculus. (Unpublished doctoral dissertation). The University of Melbourne, Australia. Lesh, R., Post, T. R., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In Problems of representations in the teaching and learning of mathematics: Lawrence Erlbaum. Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage Publications, Inc. 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. Miles, M. B., Huberman, A. M., & Huberman. (1994). Qualitative data analysis: An expanded sourcebook: Sage. Mulyanto, H., Gunarhadi, G., & Indriayu, M. (2018). The effect of problem based learning model on student mathematics learning outcomes viewed from critical thinking skills. International Journal of Educational Research Review, 3(2), 37-45. Nash, D. J. (2012). Pictorial representations in mathematical understanding. Caldwell College. National Council of Teachers of Mathematics [NCTM]. (2008). The role of technology in the teaching and learning of mathematics. Reston, VA: NationalCouncil of Teacher of Mathematics. Nugroho, M. A. C. A., Budiyono & Slamet, I. (2019). Experimentation of innovative learning models in terms of students multiple ıntelligences among middle school students in Demak District. International Journal of Educational Research Review, 4(2), 262-268. Ozgun-Koca, S. A. (2001). Computer-based representations in mathematics classrooms: the effects of multiple linked and semi-linked representations on students' learning of linear relationships. The Ohio State University, Rider, R. L. (2004). The effects of multi-representational methods on students' knowledge of function concepts in developmental college mathematics. (Unpublished dissertation). North Carolina State University, the Graduate Faculty, Raleigh. Schmidt, F. L., & Hunter, J. E. (2014). Methods of meta-analysis: Correcting error and bias in research findings: Sage publications. Sun, Y. (2006). The role of instructional representations on students' written representations and achievements. (Unpublished dissertation). Texas A&M University, Welkowitz, J., Cohen, B. H., & Lea, R. B. (2011). Introductory statistics for the behavioral sciences: John Wiley & Sons. Yakar, E. A., & Yilmaz, S. (2017). Mathematical language skills of 7th grade students in the process of transforming the real life situation into a mathematical expression in algebra. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 18(1) 292-310. DOI: 10.17679/inuefd.306995.