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The Influence of Different Representations on Solving Concentration Problems at Elementary School

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Abstract

This study investigated the students’ learning process of the concept of concentration at the elementary school level in Taiwan. The influence of different representational types on the process of proportional reasoning was also explored. The participants included nineteen third-grade and eighteen fifth-grade students. Eye-tracking technology was used in conducting the experiment. The materials were adapted from Noelting’s (1980a) “orange juice test” experiment. All problems on concentration included three stages (the intuitive, the concrete operational, and the formal operational), and each problem was displayed in iconic and symbolic representations. The data were collected through eye-tracking technology and post-test interviews. The results showed that the representational types influenced students’ solving of concentration problems. Furthermore, the data on eye movement indicated that students used different strategies or rules to solve concentration problems at the different stages of the problems with different representational types. This study is intended to contribute to the understanding of elementary school students’ problem-solving strategies and the usability of eye-tracking technology in related studies.

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References

  • Ametller J, Pintó R (2002) Students’ reading of innovative images of energy at secondary school level. Int J Sci Educ 24(3):285–312

    Article  Google Scholar 

  • Anderson JR, Bothell D, Douglass S (2004) Eye movements do not reflect retrieval processes: limits of the eye-mind hypothesis. Psychol Sci 15(4):225–231

    Article  Google Scholar 

  • Chang KT, Antes J, Lenzen T (1985) The effect of experience on reading topographic relief information: analyses of performance and eye movements. Cartogr J 22:88–94

    Article  Google Scholar 

  • Duchowski AT (2003) Eye tracking methodology: theory and practice, 1st edn. Springer, London

    Google Scholar 

  • Goldberg JH, Kotval XP (1999) Computer interface evaluation using eye movements: methods and constructs. Int J Ind Ergon 24:631–645

    Article  Google Scholar 

  • Hegarty M, Carpenter PA, Just MA (1991) Diagrams in the comprehension of scientific text. In: Barr R, Kamil ML, Mosenthal P, Pearson PD (eds) Handbook of reading research, vol 2. Longman, New York, pp 641–668

    Google Scholar 

  • Henderson JM, Hollingsworth A (1998) Eye movements during scene viewing: an overview. In: Underwood G (ed) Eye guidance in reading and scene perception. Elsevier, Oxford, pp 269–294

    Chapter  Google Scholar 

  • Inhelder B, Piaget J (1958) The growth of logical thinking: from childhood to adolescence. Basic, New York

    Book  Google Scholar 

  • Just MA, Carpenter PA (1984) Using eye fixations to study reading comprehension. In: Kieras DE, Just MA (eds) New methods in reading comprehension research. Erlbaum, Hillsdale, NJ, pp 152–182

    Google Scholar 

  • Kozma R (2003) The material features of multiple representations and their cognitive and social affordances for science understanding. Learn Instr 13(2):205–226

    Article  Google Scholar 

  • Kozma R, Russell J (1997) Multimedia and understanding: expert and novice responses to different representation of chemical phenomena. J Res Sci Teach 34(9):949–968

    Article  Google Scholar 

  • Linn M (2003) Technology and science education: starting points, research programs, and trends. Int J Sci Educ 25(6):727–758

    Article  Google Scholar 

  • Mackworth NH, Morandi AJ (1967) The gaze selects informative details with pictures. Percept Psychophys 7:173–178

    Article  Google Scholar 

  • Mathewson JH (1999) Visual-spatial thinking: an aspect of science overlooked by educators. Sci Educ 83(1):33–54

    Article  Google Scholar 

  • Noelting G (1980a) The development of proportion reasoning and the ratio concept: part i—differentiation of stages. Educ Stud Math 11:217–253

    Article  Google Scholar 

  • Noelting G (1980b) The development of proportion reasoning and the ratio concept: part ii—problem structure at successive stages; problem solving strategies and the mechanism of adaptive restructuring. Educ Stud Math 11:331–363

    Article  Google Scholar 

  • Patrick MD, Carter G, Wiebe EN (2005) Visual representations of DNA replication: middle grades students’ perceptions and interpretations. J Sci Educ Technol 14(3):353–365

    Article  Google Scholar 

  • Piaget J (1952) The child’s conception of number. Routledge & Kegan Paul, London

    Google Scholar 

  • Piaget J (1974) The child’s conception of quantities (A. J. Pomerans, Trans.). Routledge & Kegan Paul, London

  • Rayner K, Rotello CM, Stewart AJ, Keir J, Duffy SA (2001) Integrating text and pictorial information: eye movements when looking at print advertisements. J Exp Psychol 7:219–226

    Google Scholar 

  • Schnotz W, Kulhavy RW (eds) (1994) Comprehension of graphics. Elsevier, Amsterdam

    Google Scholar 

  • Schnotz W, Bannert W, Seufert T (2002) Towards a integrative view of text and picture comprehension: visualization effects on the construction of mental models. In: Graessser A, Otero J, Leon JA (eds) The psychology of science text comprehension. Erlbaum, Hillsdale, NJ, pp 385–416

    Google Scholar 

  • Seufert T (2003) Supporting coherence formation in learning from multiple representations. Learn Instr 13(2):227–237

    Article  Google Scholar 

  • Slykhuis DA, Wiebe EN, Annetta LA (2005) Eye-tracking students’ attention to PowerPoint photographs in a science education setting. J Sci Educ Technol 14(5–6):509–520

    Article  Google Scholar 

  • Stavy R, Tirosh D (2000) How students (Mis-)understand science and mathematics: intuitive rules. Teachers College, New York

    Google Scholar 

  • Stavy R, Strauss S, Orpaz N, Carmi G (1982) U-shaped behavioral growth in ration comparisons, or that’s funny I would not have thought you were U-ish. In: Strauss S, Stavy R (eds) U-shaped behavioral growth. Academic, New York, pp 11–36

    Google Scholar 

  • Steffe LP, Parr RB (1968) The development of the concepts of ratio and fraction in the fourth, fifth and sixth year of elementary school. Department of Health, Education and Welfare, Washington D. C.

    Google Scholar 

  • Tai RH, Loeher JF, Brigham FJ (2004) Introduction to the use of eye-gaze tracking to study participant behavior during problem-solving. In NARST (ed) Annual meeting of the national association for research in science teaching, Vancouver, 2004. NARST

  • van Sommeren M, Reimann P, Boshuizen H, de Jong TD (eds) (1998) Learning with multiple representations. Permagon, Amsterdam

    Google Scholar 

  • Von Keitz B (1988) Eye-movement research: do consumers use the information they are offered? Market Res Today 16:217–224

    Google Scholar 

Download references

Acknowledgments

The authors would like to thank the National Science Council of Taiwan for financially supporting this research under Contract No. NSC 99-2511-S-017-004-MY3 and NSC 99-2511-S-017-005-MY3.

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Correspondence to Chia-Ju Liu.

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Liu, CJ., Shen, MH. The Influence of Different Representations on Solving Concentration Problems at Elementary School. J Sci Educ Technol 20, 621–629 (2011). https://doi.org/10.1007/s10956-011-9293-4

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