International Electronic Journal of Mathematics Education

International Electronic Journal of Mathematics Education Indexed in ESCI
Investigating a Hierarchy of Students’ Interpretations of Graphs
APA
In-text citation: (Aoyama, 2007)
Reference: Aoyama, K. (2007). Investigating a Hierarchy of Students’ Interpretations of Graphs. International Electronic Journal of Mathematics Education, 2(3), 298-318. https://doi.org/10.29333/iejme/214
AMA
In-text citation: (1), (2), (3), etc.
Reference: Aoyama K. Investigating a Hierarchy of Students’ Interpretations of Graphs. INT ELECT J MATH ED. 2007;2(3), 298-318. https://doi.org/10.29333/iejme/214
Chicago
In-text citation: (Aoyama, 2007)
Reference: Aoyama, Kazuhiro. "Investigating a Hierarchy of Students’ Interpretations of Graphs". International Electronic Journal of Mathematics Education 2007 2 no. 3 (2007): 298-318. https://doi.org/10.29333/iejme/214
Harvard
In-text citation: (Aoyama, 2007)
Reference: Aoyama, K. (2007). Investigating a Hierarchy of Students’ Interpretations of Graphs. International Electronic Journal of Mathematics Education, 2(3), pp. 298-318. https://doi.org/10.29333/iejme/214
MLA
In-text citation: (Aoyama, 2007)
Reference: Aoyama, Kazuhiro "Investigating a Hierarchy of Students’ Interpretations of Graphs". International Electronic Journal of Mathematics Education, vol. 2, no. 3, 2007, pp. 298-318. https://doi.org/10.29333/iejme/214
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Aoyama K. Investigating a Hierarchy of Students’ Interpretations of Graphs. INT ELECT J MATH ED. 2007;2(3):298-318. https://doi.org/10.29333/iejme/214

Abstract

The ability to analyse qualitative information from quantitative information, and/or to create new information from qualitative and quantitative information is the key task of statistical literacy in the 21st century. Although several studies have focussed on critical evaluation of statistical information, this aspect of research has not been clearly conceptualised as yet. This paper presents a hierarchy of the graphical interpretation component of statistical literacy. 175 participants from different educational levels (junior high school to graduate students) responded to a questionnaire and some of them were also interviewed. The SOLO Taxonomy was used for coding the students’ responses and the Rasch model was used to clarify the construction of the hierarchy. Five different levels of interpretations of graphs were identified: Idiosyncratic, Basic graph reading, Rational/Literal, Critical, and Hypothesising and Modelling. These results will provide guidelines for teaching statistical literacy.

References

  • Adams, R. J., & Khoo, S. T. (1996). Quest: Interactive item analysis system. Version 2.1 [Computer software]. Melbourne, Australia: Australian Council for Educational Research.
  • Aoyama, K.m & Stephens, M. (2003). Graph interpretation aspects of statistical literacy: A Japanese perspective, Mathematics Education Research Journal 15(3), 3-22.
  • Biggs, J., & Collis, K. (1982). Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press.
  • Biggs, J., & Collis, K. (1991). Multimodal learning and the quality of intelligent behavior. In H. Rowe (Eds.), Intelligence: Reconceptualization and Measurement (pp.57-76). Hillsdale, NJ: Erlbaum.
  • Ben-Zvi, D., & Arcavi, A. (2001). Junior high school students’ construction of global views of data and data representations. Educational Studies in Mathematics 45, 35-65.
  • Bond, T. G., & Fox, C. M. (2001). Applying the Rasch model. Fundamental measurement in the human sciences. Mahwah, NJ: Lawrence Erlbaum.
  • Curcio, F. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18 (5), 382-393.
  • Department of Education and Employment (2000). Mathematics: The national curriculum for England - Key stages 1-4. London: Bernan Associates.
  • Friel, S., Curcio, F., & Bright, G. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124-158.
  • Gal, I., & Garfield, J. (1997). Curricular goals and assessment challenges in statistics education. In I. Gal, & J. Garfield (Eds.), The assessment challenge in statistics education (pp.1-13). Amsterdam: IOS Press and The International Statistical Institute.
  • Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1) 1-24.
  • Huff, D. (1954). How to lie with statistics, New York : W. W. Norton & Company.
  • Kimura, S. (1999). Toukeizyouhoukyouikuno karikyuramuto 5-dankaino toukeitekitankyu purosesu (Curriculum of statistics education and five phases of statistical inquiry process). In Zentouken (Ed.), Toukeizyouhoukyouikuno Rironto Zyugyouzissenno Tenkai (pp. 33-46). Tsukuba: Syuppankai.
  • Kodera, T., & Shimizu, Y. (2007). Sekaiwo hiraku suugakuteki riterasi (Mathematical literacy to open the world). Akashi: Syoten.
  • Ministry of Education. (1998). Tyuugakkou gakusyusidouyouryou (The national course of study of elementary schools). Okurasyou: Insatsukyoku.
  • Monteiro, C., &Ainley, J. (2006). Student teachers interpreting media graphs. In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil: International Statistical Institute and International Association for Statistical Education. Online: http://www.stat.auckland.ac.nz/~iase.
  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston. VA: NCTM.
  • Organisation of Economic Cooperation and Development (1999). Measuring student knowledge and skills -A new framework for assessment. Paris: OECD.
  • Organisation of Economic Cooperation and Development (2004). Learning for tomorrow’s world -First results from PISA 2003. Paris: OECD.
  • Rasch, G. (1980). Probabilistic models for some intelligence and attainment tests, The University of Chicago Press.
  • Steen, L. (1990). On the shoulders of giants: New approaches to numeracy, National Academy Press.
  • Watson, J. (1997). Assessing statistical literacy using the media. In I. Gal, & J. Garfield (Eds.), The assessment challenge in statistics education (pp. 107-121). Amsterdam: IOS Press and The International Statistical Institute.
  • Watson, J., & Moritz, J. (1999). The beginning of statistical inference: Comparing two data sets. Educational Studies in Mathematics 37, 145-168.
  • Watson, J., & Callingham, R. (2003). Statistical literacy: A complex hierarchical construct, Statistics Education Research Journal, 2(2), 3-46.
  • Watson, J. M., & Moritz, J. B. (2000). Developing concepts of sampling. Journal for Research in Mathematics Education, 31 (1), 44-70.

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