• Eun-Jung ParkEmail author
  • Kyunghee ChoiEmail author


In general, mathematical representations such as formulae, numbers, and graphs are the inseparable components in science used to better describe or explain scientific phenomena or knowledge. Regardless of their necessity and benefit, science seems to be difficult for some students, as a result of the mathematical representations and problem solving used in scientific inquiry. In this regard, several studies have attributed students’ decreasing interest in science to the presence of these mathematical representations. In order to better understand student learning difficulties caused by mathematical components, the current study investigates student understanding of a familiar science concept and its mathematical component (pH value and logarithms). Student responses to a questionnaire and a follow-up interview were examined in detail. “Measure” and “concentration” were key criteria for students’ understanding of pH values. In addition, only a few students understood logarithms on a meaningful level. According to students’ understanding of scientific phenomena and mathematical structures, five different student models and the critical features of each type were identified. Further analysis revealed the existence of three domains that characterize these five types: object, operation, and function. By suggesting the importance of understanding scientific phenomena as a “function,” the current study reveals what needs to be taught and emphasized in order to help students obtain a level of scientific meaning that is appropriate for their grade.


learning difficulty logarithms mathematical representation pH value and scale typology understanding of science concepts 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Akatugba, A. H. & Wallace, J. (2009). An integrative perspective on students' proportional reasoning in high school physics in a west african context. International journal of science education, 31(11), 1473–1493.Google Scholar
  2. Capon, N. & Kuhn, L. (1979). Logical reasoning in the supermarket: adult females’ use of a proportional strategy in an everyday context’. Developmental Psychology, 6, 544–573.Google Scholar
  3. Confrey, J. (1991). Learning to listen: a student’s understanding of powers of ten. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 111–138). Netherlands: Kluwer.Google Scholar
  4. Cros, D., Chastrette, M. & Fayol, M. (1988). Conceptions of second year university students of some fundamental notions in chemistry. European Journal of Science Education, 10(3), 331–336.CrossRefGoogle Scholar
  5. Cros, D., Maurin, M., Amouroux, R., Chastrette, M., Leber, J. & Fayol, A. (1986). Conceptions of first year university students of the constituents of matter and the notions of acids and bases. European Journal of Science Education, 8(3), 305–313.CrossRefGoogle Scholar
  6. DePierro, E., Garafalo, F. & Toomey, R. (2008). Helping students make sense of logarithms and logarithmic relationships. Journal of Chemical Education, 85(9), 1226–1228.CrossRefGoogle Scholar
  7. Dhindsa, H. S. (2002). Preservice science teachers’ conceptions of pH. Australian Journal of Education in Chemistry, 60, 19–24.Google Scholar
  8. Hilton, T. L. & Lee, V. E. (1988). Student interest and persistence in science: changes in the educational pipeline in the last decade. Journal of Higher Education, 59(5), 510–526.CrossRefGoogle Scholar
  9. Hoffer, A. (1988). Ratios and proportional thinking. In T. Post (Ed.), Teaching mathematics in grades K-8: research based methods (pp. 285–313). Boston: Allyn and Bacon.Google Scholar
  10. Jenkins, E. W. (1994). Public understanding of science and science education for action. Journal of Curriculum Studies, 26(6), 610–611.CrossRefGoogle Scholar
  11. Kjaernsli, M. & Lie, S. (2011). Students’ preference for science careers: International comparisons based on PISA 2006. International Journal of Science Education, 33(1), 121–144.CrossRefGoogle Scholar
  12. Lamon, S. J. (1994). Ratio and proportion: Cognitive foundations in unitizing and norming. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 89–121). Albany, NY: SUNY Press.Google Scholar
  13. Lawton, C. A. (1993). Contextual factors affecting errors in proportional reasoning. Journal for Research in Mathematics Education, 24, 460–466.CrossRefGoogle Scholar
  14. Leopold, D. G. & Edgar, B. (2008). Degree of mathematics fluency and success in second-semester introductory chemistry. Journal of Chemical Education, 85(5), 724–731.CrossRefGoogle Scholar
  15. Liang, C. B. & Wood, E. (2005). Working with logarithms: students’ misconceptions and errors. The Mathematics Educator, 8(2), 53–70.Google Scholar
  16. Linke, R. D. & Venz, M. I. (1979). Misconceptions in physical science among non-science background students: II. Research in Science Education, 9, 103–109.CrossRefGoogle Scholar
  17. National Science Board (1986). Crisis in undergraduate education. Science News, 129, 249.CrossRefGoogle Scholar
  18. National Science Board (2004). Science and engineering indicators 2004: Elementary and secondary education, mathematics and science coursework and student achievement.
  19. Organization for Economic Co-operation and Development (2007). PISA 2006: science competences for tomorrow’s world. Paris: OECD.Google Scholar
  20. Osborne, J. & Collins, S. (2000). Pupils’ and parents’ views of the school science curriculum. London: King’s College London.Google Scholar
  21. Osborne, J. & Collins, S. (2001). Pupils’ views of the role and value of the science curriculum: a focus-group study. International Journal of Science Education, 23(5), 441–467.CrossRefGoogle Scholar
  22. Osborne, J., Simon, S. & Collins, S. (2003). Attitudes towards science: a review of the literature and its implication. International Journal of Science Education, 25(9), 1049–1079.CrossRefGoogle Scholar
  23. Park, E. J. & Choi, K. (2010). Analysis of mathematical structure to identify students’ understanding of a scientific concept: pH value and scale. Journal of the Korean Association for Research in Science Education, 30(7), 920–932.Google Scholar
  24. Ross, B. & Munby, H. (1991). Concept mapping and misconceptions: a study of high-school students’ understandings of acids and bases. International Journal of Science Education, 13(1), 11–23.CrossRefGoogle Scholar
  25. Sfard, A. (1991). On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36.CrossRefGoogle Scholar
  26. Sheppard, K. (2006). High school students’ understanding of titrations and related acid–base phenomena. Chemistry Education Research and Practice, 7(1), 32–45.CrossRefGoogle Scholar
  27. Simpkins, S. D., Davis-Kean, P. & Eccles, J. S. (2006). Math and science motivation: a longitudinal examination of the links between choices and beliefs. Developmental Psychology, 42, 70–83.CrossRefGoogle Scholar
  28. Smith, E. & Confrey, J. (1994). Multiplicative structures and the development of logarithms: what was lost by the invention of function? In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics. Albany: State University of New York Press.Google Scholar
  29. Stokking, K. M. (2000). Predicting the choice of physics in secondary education. International Journal of Science Education, 22(12), 1261.CrossRefGoogle Scholar
  30. Swarat, S., Light, G., Park, E.-J. & Drane, D. (2011). A typology of undergraduate students’ conceptions of size and scale: identifying and characterizing conceptual variation. Journal of Research in Science Teaching, 48(5), 512–533.CrossRefGoogle Scholar
  31. Tariq, V. N. (2002). A decline in numeracy skills among bioscience undergraduates. Journal of Biological Education, 36(2), 76–83.CrossRefGoogle Scholar
  32. Tariq, V. N. (2008). Defining the problem: mathematical errors and misconceptions exhibited by first-year bioscience undergraduates. International Journal of Mathematical Education in Science and Technology, 39(7), 889–904.CrossRefGoogle Scholar
  33. Tourniaire, F. & Pulos, S. (1985). Proportional reasoning: a review of the literature. Educational studies in mathematics, 16(2), 181–204.CrossRefGoogle Scholar
  34. Turnbull, H. W. (1969). The great mathematicians. New York: New York University Press.Google Scholar
  35. Vidyapati, T. J. & Seetharamappa, J. (1995). Higher secondary school students’ concepts of acids and bases. School Science Review, 77(287), 82–84.Google Scholar
  36. Watters, D. J. & Watters, J. J. (2006). Student understanding of pH: “I don’t know what the log actually is, I only know where the button is on my calculator”. Biochemistry and Molecular Biology Education, 34(4), 278–284.CrossRefGoogle Scholar
  37. Whitfield, R. C. (1980). Educational research & science teaching. School Science Review, 60, 411–430.Google Scholar

Copyright information

© National Science Council, Taiwan 2012

Authors and Affiliations

  1. 1.Department of Science EducationEwha Womans UniversitySeoulSouth Korea
  2. 2.Department of Science EducationEwha Womans UniversitySeoulSouth Korea

Personalised recommendations