Research in Science Education

, Volume 45, Issue 6, pp 807–840 | Cite as

Uncovering Implicit Assumptions: a Large-Scale Study on Students’ Mental Models of Diffusion

  • Marilyne Stains
  • Hannah SevianEmail author


Students’ mental models of diffusion in a gas phase solution were studied through the use of the Structure and Motion of Matter (SAMM) survey. This survey permits identification of categories of ways students think about the structure of the gaseous solute and solvent, the origin of motion of gas particles, and trajectories of solute particles in the gaseous medium. A large sample of data (N = 423) from students across grade 8 (age 13) through upper-level undergraduate was subjected to a cluster analysis to determine the main mental models present. The cluster analysis resulted in a reduced data set (N = 308), and then, mental models were ascertained from robust clusters. The mental models that emerged from analysis were triangulated through interview data and characterised according to underlying implicit assumptions that guide and constrain thinking about diffusion of a solute in a gaseous medium. Impacts of students’ level of preparation in science and relationships of mental models to science disciplines studied by students were examined. Implications are discussed for the value of this approach to identify typical mental models and the sets of implicit assumptions that constrain them.


Mental models Diffusion Cognitive constraints Cluster analysis Chemistry education 



The authors are grateful to the many students who participated in this study, and their teachers who helped to facilitate its possibility. The authors wish to thank Vicente Talanquer for insightful discussions that enhanced this research. This study was supported, in part, by the US National Science Foundation (NSF) award EHR-0412390.

Conflict of Interest

Part of this work was conducted while one of the authors (HS) was under employment of the NSF, with support through an Independent Research and Development Plan. The findings and opinions expressed are solely those of the authors, and do not necessarily reflect the opinions, positions, or conclusions of the NSF.


  1. Andersson, B. (1986). The Experiential Gestalt of Causation - a Common Core to Pupils Preconceptions in Science. European Journal of Science Education, 8(2), 155–171.CrossRefGoogle Scholar
  2. Baker, S.E. & Edwards, R. (2012). How many qualitative interviews is enough? National Center for Research Methods Review Paper, Swindon, UK: Economic Research Council. Accessed 5 May 2014.
  3. Ben-Zvi, R., Eylon, B. S., & Silberstein, J. (1986). Is an atom of copper malleable? Journal of Chemical Education, 63, 64–66.CrossRefGoogle Scholar
  4. Borges, A. T., & Gilbert, J. K. (1998). Models of magnetism. International Journal of Science Education, 20(3), 361–378.CrossRefGoogle Scholar
  5. Borges, A. T., & Gilbert, J. K. (1999). Mental models of electricity. International Journal of Science Education, 21(1), 95–117.CrossRefGoogle Scholar
  6. Boz, Y. (2006). Turkish pupils’ conceptions of the particulate nature of matter. Journal of Science Education and Technology, 15(2), 203–213.CrossRefGoogle Scholar
  7. Brown, D. E., & Hammer, D. (2008). Conceptual change in Physics. In S. Vosniadou (Ed.), The international handbook of research on conceptual change (pp. 127–154). New York, NY: Routledge.Google Scholar
  8. Chi, M. T. H. (2005). Commonsense conceptions of emergent processes: why some misconceptions are robust. Journal of the Learning Sciences, 14(2), 161–199.CrossRefGoogle Scholar
  9. Chi, M. T. H., & Roscoe, R. D. (2002). The process and challenges of conceptual change. In M. Limón & L. Mason (Eds.), Reconsidering conceptual change: issues in theory and practice. Dordrecht London: Kluwer Academic.Google Scholar
  10. Chiou, G. L., & Anderson, O. R. (2010). A study of undergraduate Physics students’ understanding of heat conduction based on mental model theory and an ontology-process analysis. Science Education, 94(5), 825–854.CrossRefGoogle Scholar
  11. Chiu, M. H., Chou, C.-C., & Liu, C.-J. (2002). Dynamic processes of conceptual change: analysis of constructing mental models of chemical equilibrium. Journal of Research in Science Teaching, 39(8), 688–712.CrossRefGoogle Scholar
  12. Chiu, M. H., & Lin, J. W. (2007). Exploring the characteristics and diverse sources of students’ mental models of acids and bases. International Journal of Science Education, 29(6), 771–803.CrossRefGoogle Scholar
  13. Clement, J. J., & Steinberg, M. S. (2002). Step-wise evolution of mental models of electric circuits: a “learning-aloud” case study. Journal of the Learning Sciences, 11(4), 389–452.CrossRefGoogle Scholar
  14. Coll, R. K., & Treagust, D. F. (2003a). Investigation of secondary school, undergraduate, and graduate learners’ mental models of ionic bonding. Journal of Research in Science Teaching, 40(5), 464–486.CrossRefGoogle Scholar
  15. Coll, R. K., & Treagust, D. F. (2003b). Learners’ mental models of metallic bonding: a cross-age study. Science Education, 87(5), 685–707.CrossRefGoogle Scholar
  16. diSessa, A. (1993). Toward an epistemology of physics. Cognition and Instruction, 10(2–3), 105–225.CrossRefGoogle Scholar
  17. diSessa, A. (2002). Why ‘conceptual change’ is a good idea. In M. Limón & L. Mason (Eds.), Reconsidering conceptual change: issues in theory and practice. Dordrecht London: Kluwer Academic.Google Scholar
  18. Driver, R., Squires, A., Rushword, P., & Wood-Robinson, V. (1994). Making sense of secondary science: research into children’s ideas. London: Routledge.Google Scholar
  19. Duit, R. (1991). On the role of analogies and metaphors in learning science. Science Education, 75(6), 649–672.CrossRefGoogle Scholar
  20. Duncan, R. G., & Rivet, A. E. (2013). Science learning progressions. Science, 339(6118), 396–397.CrossRefGoogle Scholar
  21. Evans, E. M., Rosengren, K. S., Lane, J. D., & Price, K. L. S. (2012). Encountering counterintuitive ideas: constructing a developmental learning progression for evolution understanding. In K. S. Rosengren, S. K. Brem, E. M. Evans, & G. M. Sinatra (Eds.), Evolution challenges: integrating research and practice in teaching and learning about evolution (pp. 174–196). Cambridge: Oxford University Press.CrossRefGoogle Scholar
  22. Gilbert, J. K., Boulter, C., & Rutherford, M. (1998a). Models in explanations, part 1: horses for courses? International Journal of Science Education, 20(1), 83–97.CrossRefGoogle Scholar
  23. Gilbert, J. K., Boulter, C., & Rutherford, M. (1998b). Models in explanations, Part 2: whose voice? Whose ears? International Journal of Science Education, 20(2), 187–203.CrossRefGoogle Scholar
  24. Gleick, J. (1992). Genius: the life and science of Richard Feynman (1st ed.). New York: Pantheon Books.Google Scholar
  25. Greca, I. M., & Moreira, M. A. (2000). Mental models, conceptual models, and modelling. International Journal of Science Education, 22(1), 1–11.CrossRefGoogle Scholar
  26. Gupta, A., Hammer, D., & Redish, E. F. (2010). The case for dynamic models of learners’ ontologies in physics. Journal of the Learning Sciences, 19, 285–321.CrossRefGoogle Scholar
  27. Harrison, A. G., & Treagust, D. F. (1996). Secondary students’ mental models of atoms and molecules: implications for teaching chemistry. Science Education, 80(5), 509–534.CrossRefGoogle Scholar
  28. Hubber, P. (2006). Year 12 students’ mental models of the nature of light. Research in Science Education, 36(4), 419–439.CrossRefGoogle Scholar
  29. Jansoon, N., Coll, R. K., & Somsook, E. (2009). Understanding mental models of dilution in Thai students. International Journal of Environmental & Science Education, 4(2), 147–168.Google Scholar
  30. Kaufman, D. R., Vosniadou, S., diSessa, A., & Thagard, P. (2000). Scientific explanation, systematicity, and conceptual change. Paper presented at the Twenty-First Annual Meeting of the Cognitive Science Society.Google Scholar
  31. Lawrence Hall of Science (Producer). (2006, 02/19/2010). Chemical interactions. Full option science system for middle school. Accessed 9 Dec 2013
  32. Meijer, M. R., Bulte, A. M. W., & Pilot, A. (2013). Macro–micro thinking with structure–property relations: integrating ‘meso-levels’ in secondary education. In G. Tsaparlis & H. Sevian (Eds.), Concepts of matter in science education (pp. 417–435). Dordrecht: Springer.Google Scholar
  33. Meir, E., Perry, J., Stal, D., Maruca, S., & Klopfer, E. (2005). How effective are simulated molecular-level experiments for teaching diffusion and osmosis? Cell Biology Education, 4(3), 235–248.CrossRefGoogle Scholar
  34. Merritt, J., & Krajcik, J. (2013). Learning progression developed to support students in building a particle model of matter. In G. Tsaparlis & H. Sevian (Eds.), Concepts of matter in science education (pp. 11–44). Dordrecht: Springer.CrossRefGoogle Scholar
  35. Odom, A. L. (1995). Secondary and college biology students misconceptions about diffusion and osmosis. American Biology Teacher, 57(7), 409–415.CrossRefGoogle Scholar
  36. Özdemir, G., & Clark, D. B. (2007). An overview of conceptual change. Eurasia Journal of Mathematics, Science & Technology Education, 3(4), 351–361.Google Scholar
  37. Panizzon, D. (2003). Using a cognitive structural model to provide new insights into students’ understandings of diffusion. International Journal of Science Education, 25(12), 1427–1450.CrossRefGoogle Scholar
  38. Pittman, K. M. (1999). Student-generated analogies: another way of knowing? Journal of Research in Science Teaching, 36(1), 1–22.CrossRefGoogle Scholar
  39. Pozo, J. I., & Gomez Crespo, M. A. (2005). The embodied nature of implicit theories: the consistency of ideas about the nature of matter. Cognition and Instruction, 23(3), 351–387.CrossRefGoogle Scholar
  40. Sevian, H., & Stains, M. (2013). Implicit assumptions and progress variables in a learning progression about structure and motion of matter. In G. Tsaparlis & H. Sevian (Eds.), Concepts of matter in science education (pp. 67–92). Dordrecht: Springer.Google Scholar
  41. Sevian, H., & Talanquer, V. (2014). Rethinking chemistry: A learning progression on chemical thinking. Chemistry Education Research and Practice, 15(1), 10–23.Google Scholar
  42. Shepardson, D. P., Wee, B., Priddy, M., & Harbor, J. (2007). Students’ mental models of the environment. Journal of Research in Science Teaching, 44(2), 327–348.CrossRefGoogle Scholar
  43. Stains, M.N., Escriu-Suñé, M., Molina, M., & Sevian, H. (2011). Assessing secondary and college students’ understanding of the particulate nature of matter: Development and validation of the Structure And Motion of Matter (SAMM) survey. Journal of Chemical Education, 88(10), 1359–1365.Google Scholar
  44. Stains, M., & Sevian, H. (2010). The Structure and Mation of Matter Survey (SAMM) Accessed 9 December 2013
  45. Taber, K., & Garcia-Franco, A. (2010). Learning processes in chemistry: drawing upon cognitive resources to learn about the particulate nature of matter. Journal of the Learning Sciences, 19, 99–142.CrossRefGoogle Scholar
  46. Talanquer, V. (2006). Commonsense chemistry: a model for understanding students’ alternative conceptions. Journal of Chemical Education, 83(5), 811–816.CrossRefGoogle Scholar
  47. Talanquer, V. (2009). On cognitive constraints and learning progressions: the case of structure of matter. International Journal of Science Education, 31(15), 2123–2136.CrossRefGoogle Scholar
  48. Talanquer, V. (2010). Exploring dominant types of explanations built by general chemistry students. International Journal of Science Education, 32(18), 2393–2412. doi: 10.1080/09500690903369662.CrossRefGoogle Scholar
  49. Tuminaro, J., & Redish, E. F. (2007). Elements of a cognitive model of physics problem solving: epistemic games. Physical Review Special Topics-Physics Education Research, 3(2), 020101.CrossRefGoogle Scholar
  50. Valanides, N. (2000). Primary student teachers’ understanding of the particulate nature of matter and its transformations during dissolving. Chemistry Education: Research and Practice in Europe, 1, 249–262.Google Scholar
  51. Venville, G., Bryer, L., & Treagust, D. F. (1994). Training students in the use of analogies to enhance understanding in science. Australian Science Teachers Journal, 40, 60–68.Google Scholar
  52. Viennot, L. (2001). Reasoning in physics: the part of common sense. Dordrecht, The Netherlands: Kluwer Academic.Google Scholar
  53. Vogel, S. (1994). Dealing honestly with diffusion. The American Biology Teacher, 56(7), 405–407.CrossRefGoogle Scholar
  54. Vosniadou, S. (1994). Capturing and modeling the process of conceptual change. Learning and Instruction, 4(1), 45–69.CrossRefGoogle Scholar
  55. Vosniadou, S. (2002). Mental models in conceptual development. In L. Magnani & N. J. Nersessian (Eds.), Model-based reasoning : science, technology, values (p. xiii). New York: Kluwer Academic. 404 p.Google Scholar
  56. Vosniadou, S. (2012). Reframing the classical approach to conceptual change: preconceptions, misconceptions and synthetic models. Second international handbook of science education (pp. 119–130): New York: Springer.Google Scholar
  57. Vosniadou, S., & Brewer, W. F. (1992). Mental models of the Earth—a study of conceptual change in childhood. Cognitive Psychology, 24(4), 535–585.CrossRefGoogle Scholar
  58. Vosniadou, S., & Brewer, W. F. (1994). Mental models of the day-night cycle. Cognitive Science, 18(1), 123–183.CrossRefGoogle Scholar
  59. Westbrook, S. L., & Marek, E. A. (1991). A cross-age study of student understanding of the concept of diffusion. Journal of Research in Science Teaching, 28(8), 649–660.CrossRefGoogle Scholar
  60. Wiser, M., Frazier, K. E., & Fox, V. (2013). At the beginning was amount of material: a learning progression for matter for early elementary grades. In G. Tsaparlis & H. Sevian (Eds.), Concepts of matter in science education (pp. 93–120). Dordrecht: Springer.Google Scholar
  61. Wiser, M., & Smith, C. (2008). Learning and teaching about matter in grades K-8: when should the atomic-molecular theory be introduced? In S. Vosniadou (Ed.), The international handbook of research on conceptual change. New York, NY: Routledge.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of Nebraska LincolnLincolnUSA
  2. 2.Department of ChemistryUniversity of Massachusetts BostonBostonUSA

Personalised recommendations