Examining Teachers’ Knowledge of Line Graph Task: a Case of Travel Task

  • Sitti Maesuri Patahuddin
  • Tom Lowrie


Teachers should possess a robust knowledge of graph interpretation in a world that requires increasingly scientific citizens. This study aimed to investigate teachers’ knowledge of interpreting a context-based line graph, by understanding the types of difficulties teachers have in interpreting such graphs. The study also sought to determine whether there were gender differences in teachers’ graph interpretation skills and determine whether these interpretation skills were different among teachers with varying teaching experiences. Sixty-one teachers from ten districts in one Indonesian province participated in this study. Empirically derived items were developed to identify the teacher’s conceptual understanding of line graphs with Curcio’s (Journal for Research in Mathematics Education, 18(5), 382–393, 1987) level of interpretation applied to explain the difficulties encountered. This study revealed that most of the teachers had difficulty answering questions that required ‘reading beyond the data’. Specifically, these teachers interpreted the graph as an iconic representation of a real event rather than an abstract representation of data (i.e., speed vs. time). Performance differences in teachers’ understanding of the graph were dependent on the grade level they taught, with differences especially evident in the interpretation of moderate and difficult items. There were no differences in teachers’ understanding by gender or years of teaching experience. The results highlight the importance of focusing on teacher professional development centering on teachers’ knowledge of graph comprehension.


Context-based line graph Curcio’s level of interpretation Gradient Graph as a picture 



The authors would like to thank all participants involved in this research. We would also like to thank Muhammad Darwis and Siti Rokhmah for their assistance in the instrument development, Rika Febrilia for her assistance in data analysis, and Robyn Lowrie for proofreading. This paper makes use of data from the project ‘Promoting mathematics engagement and learning opportunities for disadvantaged communities in West Nusa Tenggara, Indonesia’.

Funding information

This research was supported in part by a grant from Australian Government Department of Foreign Affairs and Trade [grant number 70861].


  1. Adams, D. D., & Shrum, J. W. (1990). The effects of microcomputer-based laboratory exercises on the acquisition of line graph construction and interpretation skills by high school biology students. Journal of Research in Science Teaching, 27(8), 777–787.CrossRefGoogle Scholar
  2. Ainley, J. (2000). Transparency in graphs and graphing tasks: An iterative design process. The Journal of Mathematical Behavior, 19(3), 365–384.CrossRefGoogle Scholar
  3. Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183–198.CrossRefGoogle Scholar
  4. Ali, N., & Peebles, D. (2013). The effect of gestalt laws of perceptual organization on the comprehension of three-variable bar and line graphs. Human Factors, 55(1), 183–203.CrossRefGoogle Scholar
  5. Arteaga, P., Batanero, C., Contreras, J. M., & Cañadas, G. R. (2015). Statistical graphs complexity and reading levels: A study with prospective teachers. Statistique et Enseignement, 6(1), 3–23.Google Scholar
  6. Ates, S., & Stevens, J. T. (2003). Teaching line graphs to tenth grade students having different cognitive developmental levels by using two different instructional modules. Research in Science & Technological Education, 21(1), 55–66.CrossRefGoogle Scholar
  7. Bell, A., & Janvier, C. (1981). The interpretation of graphs representing situations. For the Learning of Mathematics, 2(1), 34–42.Google Scholar
  8. Berg, C., & Boote, S. (2017). Format effects of empirically derived multiple-choice versus free-response instruments when assessing graphing abilities. International Journal of Science and Mathematics Education, 15(1), 19–38.CrossRefGoogle Scholar
  9. Berg, C., & Phillips, D. G. (1994). An investigation of the relationship between logical thinking structures and the ability to construct and interpret line graphs. Journal of Research in Science Teaching, 31(4), 323–344.CrossRefGoogle Scholar
  10. Bertin, J. (1983). Semiology of graphics: Diagrams, networks, maps (WJ Berg, Trans.). Madison, WI: The University of Wisconsin Press, Ltd..Google Scholar
  11. Billings, E. M., & Klanderman, D. (2000). Graphical representations of speed: Obstacles preservice K-8 teachers experience. School Science and Mathematics, 100(8), 440–450.CrossRefGoogle Scholar
  12. Boote, S. K. (2014). Assessing and understanding line graph interpretations using a scoring rubric of organized cited factors. Journal of Science Teacher Education, 25(3), 333–354.CrossRefGoogle Scholar
  13. Boote, S. K., & Boote, D. N. (2017). Leaping from discrete to continuous independent variables: Sixth graders’ science line graph interpretations. The Elementary School Journal, 117(3), 455–484.CrossRefGoogle Scholar
  14. Brasell, H. M., & Rowe, M. B. (1993). Graphing skills among high school physics students. School Science and Mathematics, 93(2), 63–70.CrossRefGoogle Scholar
  15. Clement, J. (1985). Misconceptions in graphing. In L. Streetfland (Ed.), Proceedings of the Ninth International Conference of the International Group for the Psychology of Mathematics Education (IGPME) (Vol. 1, pp. 369–375). Utrecht, The Netherlands: IGPME.Google Scholar
  16. Curcio, F. R. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18(5), 382–393.CrossRefGoogle Scholar
  17. Elby, A. (2000). What students’ learning of representations tells us about constructivism. The Journal of Mathematical Behavior, 19(4), 481–502.CrossRefGoogle Scholar
  18. Fausset, C. B., Rogers, W. A., & Fisk, A. D. (2008). Understanding the required resources in line graph comprehension. Proceedings of the Human Factors and Ergonomics Society Annual Meeting, 52(22), 1830–1834. Scholar
  19. Fleiss, J. L., Levin, B., & Paik, M. C. (2013). Statistical methods for rates and proportions. Hoboken, NJ: Wiley.Google Scholar
  20. Freedman, E. G., & Shah, P. (2002). Toward a model of knowledge-based graph comprehension. In M. Hegarty, B. Meyer, & N. H. Narayanan (Eds.), International Conference on Theory and Application of Diagrams (pp. 18–30). Heidelberg, Germany: Springer.Google Scholar
  21. Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124–158.CrossRefGoogle Scholar
  22. Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1), 1–25.CrossRefGoogle Scholar
  23. Glazer, N. (2011). Challenges with graph interpretation: A review of the literature. Studies in Science Education, 47(2), 183–210.CrossRefGoogle Scholar
  24. Hannula, M. S. (2003). Locating fraction on a number line. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 17–24). Honolulu, HI: Psychology of Mathematics Education.Google Scholar
  25. Haslam, S. A., & McGarty, C. (2014). Research methods and statistics in psychology. Los Angeles, CA: SAGE Publication Ltd..Google Scholar
  26. Jacobbe, T., & Horton, R. M. (2010). Elementary school teachers’ comprehension of data displays. Statistics Education Research Journal, 9(1), 27–45.Google Scholar
  27. Janvier, C. (1981). Use of situations in mathematics education. Educational Studies in Mathematics, 12(1), 113–122.CrossRefGoogle Scholar
  28. Kerslake, D. (1981). Graphs. In K. M. Hart, M. Brown, D. Kuchemann, D. Kerslake, G. Ruddock, & M. McCartney (Eds.), Children’s understanding of mathematics (Vol. 11-16, pp. 120–136). London, England: John Murray.Google Scholar
  29. Kosslyn, S. M. (1985). Mental representation. Bulletin of the British Psychological Society, 38, A68–A68.Google Scholar
  30. Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60(1), 1–64.CrossRefGoogle Scholar
  31. Lowrie, T., & Diezmann, C. M. (2005). Fourth-grade students’ performance on graphical languages in mathematics. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 30th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 265–272). Melbourne, Australia: International Group for the Psychology of Mathematics Education.Google Scholar
  32. Lowrie, T., & Diezmann, C. M. (2007a). Solving graphics problems: Student performance in junior grades. The Journal of Educational Research, 100(6), 369–378.CrossRefGoogle Scholar
  33. Lowrie, T., & Diezmann, C. M. (2007b). Middle school students’ interpreting graphical tasks: Difficulties within a graphical language. In C. S. Lim, S. Fatimah, G. Munirah, S. Hajar, M. Y. Hashimah, W. L. Gan, & T. Y. Hwa (Eds.), Proceedings of the 4th East Asia Regional Conference on Mathematics Education (pp. 430–436). Penang, Malaysia: Universiti Sains Malaysia.Google Scholar
  34. Lowrie, T., & Diezmann, C. M. (2009). National numeracy tests: A graphic tells a thousand words. Australian Journal of Education, 53(2), 141–158.Google Scholar
  35. Lowrie, T., & Diezmann, C. M. (2011). Solving graphics tasks: Gender differences in middle-school students. Learning and Instruction, 21(1), 109–125.CrossRefGoogle Scholar
  36. Lowrie, T., Diezmann, C. M., & Logan, T. (2011). Understanding graphicacy: Students’ making sense of graphics in mathematics assessment tasks. International Journal for Mathematics Teaching and Learning. Retrieved from
  37. Mokros, J. R., & Tinker, R. F. (1987). The impact of microcomputer-based labs on children’s ability to interpret graphs. Journal of Research in Science Teaching, 24(4), 369–383.CrossRefGoogle Scholar
  38. Nemirovsky, R. (1996). A functional approach to algebra: Two issues that emerge. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra (pp. 295–313). Dordrecht, The Netherlands: Kluwer Academic Publishers.CrossRefGoogle Scholar
  39. 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.CrossRefGoogle Scholar
  40. Peden, B. F., & Hausmann, S. E. (2000). Data graphs in introductory and upper level psychology textbooks: A content analysis. Teaching of Psychology, 27(2), 93–97.CrossRefGoogle Scholar
  41. Peebles, D., & Ali, N. (2009). Differences in comprehensibility between three-variable bar and line graphs. In N. Taatgen, H. v. Rijn, J. Nerbonne, & L. Schoemaker (Eds.), Proceedings of the Thirty-first Annual Conference of the Cognitive Science Society (pp. 2938–2943). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  42. Peebles, D., & Ali, N. (2015). Expert interpretation of bar and line graphs: The role of graphicacy in reducing the effect of graph format. Frontiers in Psychology, 6, 1673. Scholar
  43. Roth, W.-M., & McGinn, M. K. (1997). Graphing: Cognitive ability or practice? Science Education, 81(1), 91–106.CrossRefGoogle Scholar
  44. Rowland, T., Turner, F., & Thwaites, A. (2014). Research into teacher knowledge: A stimulus for development in mathematics teacher education practice. ZDM, 46(2), 317–328.CrossRefGoogle Scholar
  45. Shah, P., & Carpenter, P. A. (1995). Conceptual limitations in comprehending line graphs. Journal of Experimental Psychology: General, 124(1), 43–61. Scholar
  46. Shah, P., & Freedman, E. G. (2011). Bar and line graph comprehension: An interaction of top-down and bottom-up processes. Topics in Cognitive Science, 3(3), 560–578.CrossRefGoogle Scholar
  47. Shah, P., & Hoeffner, J. (2002). Review of graph comprehension research: Implications for instruction. Educational Psychology Review, 14(1), 47–69.CrossRefGoogle Scholar
  48. Shah, P., Mayer, R. E., & Hegarty, M. (1999). Graphs as aids to knowledge construction: Signaling techniques for guiding the process of graph comprehension. Journal of Educational Psychology, 91(4), 690–702.CrossRefGoogle Scholar
  49. Shah, P., Freedman, E. G., & Vekiri, I. (2005). The Cambridge handbook of visuospatial thinking. In P. Shah & A. Miyake (Eds.), The comprehension of quantitative information in graphical displays (pp. 426–476). New York, NY: Cambridge University Press.Google Scholar
  50. Svec, M. T. (1995). Effect of micro-computer based laboratory on graphing interpretation skills and understanding of motion. Paper presented at the Annual Meeting of the National Association for Research in Science Teaching. Retrieved from ERIC database. (ED383551).Google Scholar
  51. Tynjälä, P. (2008). Perspectives into learning at the workplace. Educational Research Review, 3(2), 130–154.CrossRefGoogle Scholar
  52. Wainer, H. (1992). Understanding graphs and tables. Educational Researcher, 21(1), 14–23.CrossRefGoogle Scholar
  53. Zacks, J., & Tversky, B. (1999). Bars and lines: A study of graphic communication. Memory and Cognition, 27, 1073–1079.CrossRefGoogle Scholar
  54. Zacks, J., Levy, E., Tversky, B., & Schiano, D. (2002). Graphs in print. In M. Anderson, B. Meyer, & P. Olivier (Eds.), Diagrammatic representation and reasoning (pp. 187–206). London, England: Springer.CrossRefGoogle Scholar

Copyright information

© Ministry of Science and Technology, Taiwan 2018

Authors and Affiliations

  1. 1.Faculty of EducationUniversity of CanberraCanberraAustralia

Personalised recommendations