Investigating the effectiveness of illustration representation-based Instruction on word problem-solving ability in mathematics

Document Type : Research Paper

Authors

1 Ph.D Candidate of Curriculum Studies, University of Isfahan, Faculty of Education and Psychology

2 Professor, Department of Education, University of Isfahan, Faculty of Education and Psychology

3 Professor, Department of Psychology, University of Isfahan, Faculty of Education and Psychology

Abstract

The aim of the present study is to investigating the effectivenessof illustration representation-based Instruction on 6th grade students' word problem-solving ability in mathematics. This research is based content analysis and semi-experimental design of the pretest-post test type, follow up with the control group. After studying and designing 40 male student of the sixth grade elementary a school in the academic year of 1396-97 in yasouj participated in this study as volunteers. They were randomly assigned to experimental and control group and the experimental group were educated for 9 sessions (one session per week) using representation-based Instruction method. Shannon entropy technique was adopted in order to analyze data in content analysis, and variance analysis test with repeated measures was used for the semi-experimental part. The results of the content analysis show that the greatest attention for the distribution and the presence of word problems is respectively directed to bare representation, essential representation, helpful representation, and finally to useless representation respectively. In addition, the results of the variance analysis with repeated measures reveals that there is a significant difference between the averages of all the components of word problem-solving ability of control group and experimental group (p < 0.05). Therefore, it can be concluded that illustration representation Instruction increases students' word problem-solving ability in mathematics. Besides, the results indicate that the effect of using illustration representation will be consistent over time. The results of pairwise comparisons of different representations also show that the effects of different representations are not the same.

Keywords


سازمان پژوهش و برنامه­ریزی آموزشی. (1396). ریاضی ششم ابتدایی. وزارت آموزش‌وپرورش.
گال، مردیت. بورگ والتر و گال، جویس. (1383). روش‌های تحقیق کمی و کیفی در علوم تربیتی و روان شناسی. ترجمه احمدرضا نصر و همکاران، ‌تهران: سمت، دانشگاه شهید بهشتی.
وزارت آموزش‌وپرورش. سند برنامه درسی ملی جمهوری اسلامی ایران. 1391.
Ainsworth, S. E., Wood, D. J., & Bibby, P. A. (1997, August). Evaluating principles for multi-representational learning environments. In 7th European Conference for Research on Learning and Instruction, Athens, Greece.
Berends, I. E., & Van Lieshout, E. C. (2009). The effect of illustrations in arithmetic problem-solving: Effects of increased cognitive load. Learning and Instruction, 19(4), 345-353.‏
Beaumont, E. S., Mudd, P., Turner, I. J., & Barnes, K. (2017). Cetacean frustration: the representation of whales and dolphins in picture books for young children. Early Childhood Education Journal, 45(4), 545-551.‏
Crisp, V., & Sweiry, E. (2006). Can a picture ruin a thousand words? The effects of visual resources in exam questions. Educational Research, 48(2), 139-154.
Carney, R. N., & Levin, J. R. (2002). Pictorial illustrations still improve students' learning from text. Educational psychology review, 14(1), 5-26.
Cai, J., & Lester, F. (2010). Why is teaching with problem solving important to student learning. National council of teachers of mathematics, 13(12), 1-6.
DeLoache, J. S. (1991). Symbolic functioning in very young children: Understanding of pictures and models. Child development, 62(4), 736-752.
DeWindt-King, A. M., & Goldin, G. A. (2003). Children’s visual imagery: Aspects of cognitive representation in solving problems with fractions. Mediterranean Journal for Research in Mathematics Education, 2(1), 1-42.
Diezmann, C. M., & English, L. D. (2001). Promoting the use of diagrams as tools for thinking. 2001 National Council of Teachers of Mathematics Yearbook: The Role of Representation in School Mathematics, 77-89.
Elia, I., Gagatsis, A., & Demetriou, A. (2007). The effects of different modes of representation on the solution of one-step additive problems. Learning and Instruction, 17(6), 658-672.
Flores, R., Koontz, E., Inan, F. A., & Alagic, M. (2015). Multiple representation instruction first versus traditional algorithmic instruction first: Impact in middle school mathematics classrooms. Educational Studies in Mathematics, 89(2), 267-281.‏
Julo, J. (2002). Des apprentissages spécifiques pour la résolution de problèmes? [Specific learning for problem solving?]. Grand N, 69, 31–52.
Hmelo-Silver, C. E., Jordan, R., Eberbach, C., & Sinha, S. (2017). Systems learning with a conceptual representation: a quasi-experimental study. Instructional Science, 45(1), 53-72.‏
Klein, D. (2003). A brief history of American K-12 mathematics education in the 20th century. Mathematical cognition, 175-259.
Lin, Y. H., Wilson, M., & Cheng, C. L. (2013). An investigation of the nature of the influences of item stem and option representation on student responses to a mathematics test. European Journal of Psychology of Education, 28(4), 1141-1161.‏
Lave, J. (1992). Word problems: A microcosm of theories of learning. Context and cognition: Ways of learning and knowing, 74-92.
Monoyiou, A., Papageorgiou, P., & Gagatsis, A. (2007). Students’ and teachers’ representations in problem solving. In Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education: Working Group (Vol. 1, pp. 141-151).
Mellone, M., Verschaffel, L., & Van Dooren, W. (2017). The effect of rewording and dyadic interaction on realistic reasoning in solving word problems. The Journal of Mathematical Behavior, 46, 1-12.‏
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics (Vol. 1). Natl Council of Teachers of Mathematics.
Parmar, R. S., & Signer, B. R. (2005). Sources of Error in Constructing and Interpreting Graphs A Study of Fourth-and Fifth-Grade Students with LD. Journal of learning disabilities, 38(3), 250-261.
Rasmussen, C., & Bisanz, J. (2005). Representation and working memory in early arithmetic. Journal of experimental child psychology, 91(2), 137-157.
Seufert, T., Jänen, I., & Brünken, R. (2007). The impact of intrinsic cognitive load on the effectiveness of graphical help for coherence formation. Computers in Human Behavior, 23(3), 1055-1071.
Schnotz, W. (2002). Commentary: Towards an integrated view of learning from text and visual displays. Educational psychology review, 14(1), 101-120.
Yu, K. C., Fan, S. C., & Lin, K. Y. (2015). ENHANCING STUDENTS’PROBLEM-SOLVING SKILLS THROUGH CONTEXT-BASED LEARNING. International Journal of Science and Mathematics Education, 13(6), 1377-1401.‏