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  • Open Access

Exploring student estimates of astronomical scales: Impact of question formulation and visualization

Willem Keppens*, Mieke De Cock, and Hans Van Winckel

Wim Van Dooren

Jan Sermeus

  • Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200C, 3001 Leuven, Belgium

  • Faculty of Psychology and Educational Sciences, KU Leuven, Dekenstraat 2, 3000 Leuven, Belgium

  • Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200C, 3001 Leuven, Belgium; Faculty of Psychology and Educational Sciences, KU Leuven, Dekenstraat 2, 3000 Leuven, Belgium; and Royal Observatory of Belgium, Planetarium, Bouchoutlaan 10, 1020 Brussels, Belgium

  • *Contact author: willem.keppens@kuleuven.be
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Phys. Rev. Phys. Educ. Res. 21, 010159 – Published 11 June, 2025

DOI: https://doi.org/10.1103/cv8n-mshc

Abstract

Estimating astronomical scales requires multiple complex mental processes, such as spatial thinking and interpreting large numbers. As such, it is a nontrivial question how these estimates can be most efficiently assessed. There is reason to believe that results from previous studies probing astronomical scale estimates are possibly susceptible to effects inherent in the questioning methods used. In this study, an interactive online survey was constructed and administered to 201 students in their last year of high school. To probe their estimates of spatial scales in the Solar neighborhood, we formulated five questions, two of those probing estimates on the relative sizes of astronomical bodies and three on the relative distances between those bodies. These questions were formulated in two different ways, and the effect of these formulations was studied. In one formulation, students were asked to numerically compare the magnitude of two sizes or distances, while in the other, these estimates were made in terms of the travel time of an imaginary spacecraft. After every answer, students were confronted with a customized visualization, which they could either agree with and move on to the next question or disagree and reconsider their previous answer until they agreed. Studying the effect of these visualizations on the students’ answers was another objective of this work. Most students had difficulties estimating both the relative sizes of the considered celestial bodies and the distances between them. The range of estimates covered many orders of magnitude for all questions, and for the distance-related questions, there was a clear trend of underestimation. We found a significant impact of question formulation on the magnitudes of student estimates. However, we found no indication that one question formulation led to more reliable results than the other. The effect of the visualizations was smaller than anticipated but noticeably larger for the size-related questions than for the distance-related questions. Self-assessments of certainty were made by the students after every answer, and those were found not to correlate with the accuracy of the answers. The implications of these findings are discussed.

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References (78)

  1. M. Schneps, J. Ruel, G. Sonnert, M. Dussault, M. Griffin, and P. Sadler, Conceptualizing astronomical scale: Virtual simulations on handheld tablet computers reverse misconceptions, Comput. Educ. 70, 269 (2014).
  2. D. Landy, N. Silbert, and A. Goldin, Getting off at the end of the line: The estimation of large numbers, in Proceedings of the Annual Meeting of the Cognitive Science Society (Cognitive Science Society, Austin, TX, 2012), Vol. 34.
  3. D. Landy, A. Charlesworth, and E. Ottmar, Categories of large numbers in line estimation, Cogn. Sci. 41, 326 (2017).
  4. A. Brass and S. Harkness, Pre-service teachers’ conceptions of the magnitude of large numbers, Invest. Math. Learn. 9, 53 (2017).
  5. S. Kastberg and V. Walker, Insights into our understandings of large numbers, Teach. Child. Math. 14, 530 (2008).
  6. J. M. Bailey, K. Coble, G. Cochran, D. Larrieu, R. Sanchez, and L. R. Cominsky, A multi-institutional investigation of students’ preinstructional ideas about cosmology, Astron. Educ. Rev. 11, 46 (2012).
  7. F. Korur, Exploring seventh-grade students’ and pre-service science teachers’ misconceptions in astronomical concepts, Eurasia J. Math. Sci. Technol. Educ. 11, 1041 (2015).
  8. A. Lelliott and M. Rollnick, Big ideas: A review of astronomy education research 1974-2008, Int. J. Sci. Educ. 32, 1771 (2010).
  9. P. A’Hearn. Student understanding of scale and structure in astronomy: What classroom strategies are effective?, Master’s thesis, California State University, San Bernardino, 2010, theses Digitization Project, 3863.
  10. M. Cole, C. Cohen, J. Wilhelm, and R. Lindell, Spatial thinking in astronomy education research, Phys. Rev. Phys. Educ. Res. 14, 010139 (2018).
  11. M. Jones, G. Gardner, A. Taylor, E. Wiebe, and J. Forrester, Conceptualizing magnification and scale: The roles of spatial visualization and logical thinking, Res. Sci. Educ. 41, 357 (2011).
  12. P. Sadler. The initial knowledge state of high school astronomy students, Ph.D. thesis, Harvard University, Cambridge, MA, 1992.
  13. R. Trumper, A cross-college age study of science and nonscience students’ conceptions of basic astronomy concepts in preservice training for high-school teachers, J. Sci. Educ. Technol. 10, 189 (2001).
  14. L. Shore and R. Kilburn, The effect of astronomy teaching experience on the astronomy interest and conceptions of elementary school teachers, in Proceedings of the 3rd international seminar on Misconceptions and Educational Strategies in Science and Mathematics (Misconceptions Trust, Ithaca, NY, 1993), Vol. 1.
  15. J. Mant and M. Summers, A survey of british primary school teachers’™ understanding of the earth’s place in the universe, Educ. Res. 37, 3 (1995).
  16. C. Bakas and T. Mikropoulos, Design of virtual environments for the comprehension of planetary phenomena based on students’ ideas, Int. J. Sci. Educ. 25, 949 (2003).
  17. W. Miller and F. Brewer, Misconceptions of astronomical distances, Int. J. Sci. Educ. 32, 1549 (2010).
  18. V. Rajpaul, C. Lindstrøm, M. Engel, M. Brendehaug, and S. Allie, Phys. Rev. Phys. Educ. Res. 14, 020108 (2018).
  19. J. Piaget, The Child’s Conception of the World (Routledge & Kegan Paul, New York, 1929).
  20. U. Kanli, Using a two-tier test to analyse students’ and teachers’ alternative concepts in astronomy, Sci. Educ. Int. 26, 148 (2015).
  21. P. Hewson and M. Hewson, Effect of instruction using students’ prior knowledge and conceptual change strategies on science learning, J. Res. Sci. Teach. 20, 731 (1983).
  22. R. Driver and J. Easley, Pupils and paradigms: A review of literature related to concept development in adolescent science students, Stud. Sci. Educ. 5, 61 (1978).
  23. M. McCloskey, Naive theories of motion, in Mental Models, edited by D. Gentner and A. Stevens (Psychology Press, Hove, East Sussex, 1983), pp. 299–324.
  24. Proceedings of the Second International Seminar: Misconceptions and Educational Strategies in Science and Mathematics, edited by J. Novak (Cornell University, Department of Education, Ithaca, NY, 1987).
  25. N. F. Comins, Heavenly Errors: Misconceptions about the Real Nature of the Universe (Columbia University Press, New York, NY, 2001).
  26. S. Vosniadou and W. Brewer, Mental models of the earth: A study of conceptual change in childhood, Cogn. Psychol. 24, 535 (1992).
  27. U. Kanli, A study on identifying the misconceptions of pre-service and in-service teachers about basic astronomy concepts, Eurasia J. Math. Sci. Technol. Educ. 10, 471 (2014).
  28. P. M. Sadler, in Proceedings of the Second International Seminar: Misconceptions and Educational Strategies in Science and Mathematics (Cornell University, Ithaca, NY, 1987), Vol. 3, pp. 422–425.
  29. W. Bisard, R. Aron, M. Francek, and B. Nelson, Assessing selected physical science and earth science misconceptions of middle school through university preservice teachers, J. Coll. Sci. Teach. 24, 38 (1994).
  30. M. LoPresto and S. Murrell, An astronomical misconceptions survey, J. Coll. Sci. Teach. 40, 14 (2011).
  31. M. Zeilik and V. Morris, An examination of misconceptions in an astronomy course for science, mathematics, and engineering majors, Astron. Educ. Rev. 2, 101 (2003).
  32. H. Bekaert, H. Van Winckel, W. Van Dooren, A. Steegen, and M. De Cock, Identifying students’ mental models of the apparent motion of the sun and stars, Phys. Rev. Phys. Educ. Res. 18, 010130 (2022).
  33. J. Plummer, A cross-age study of children’s knowledge of apparent celestial motion, Int. J. Sci. Educ. 31, 1571 (2009).
  34. S. Slater, S. Price Schleigh, and D. Stork, Analysis of individual test of astronomy standards (toast) item responses, J. Astron. Earth Sci. Educ. 2, 89 (2015).
  35. H. Kalkan and K. Kiroglu, Science and nonscience students’ ideas about basic astronomy concepts in preservice training for elemantary school teachers, Astron. Educ. Rev. 6, 15 (2007).
  36. S. Serttaş and A. Türkoğlu, Diagnosing students’ misconceptions of astronomy through concept cartoons, Particip. Educ. Res. 7, 164 (2020).
  37. R. Trumper, University students’ conceptions of basic astronomy concepts, Phys. Educ. 35, 9 (2000).
  38. A. Lightman and P. Sadler, Teacher predictions versus actual student gains, Phys. Teach. 31, 162 (1993).
  39. P. Bitzenbauer, S. Navarrete, F. Hennig, M. Ubben, and J. Veith, Cross-age study on secondary school students’™ views of stars, Phys. Rev. Phys. Educ. Res. 19, 020165 (2023).
  40. I. Testa, S. Leccia, and E. Puddu, Astronomy textbook images: Do they really help students?, Phys. Educ. 49, 332 (2014).
  41. C. Chen, M.Schneps, and G. Sonnert, Order matters: Sequencing scale-realistic versus simplified models to improve science learning, J. Sci. Educ. Technol. 25, 806 (2016).
  42. M. Cin, Alternative views of the solar system among Turkish students, Int. Rev. Educ. 53, 39 (2007).
  43. L. Agan, Stellar ideas: Exploring students’ understanding of stars, Astron. Educ. Rev. 3, 77 (2004).
  44. E. Laski and R. Siegler, Is 27 a big number? correlational and causal connections among numerical categorization, number line estimation, and numerical magnitude comparison, Child Dev. 78, 1723 (2007).
  45. L. J. Rips, How many is a zillion? sources of number distortion, J. Exp. Psychol. 39, 1257 (2013).
  46. R. Siegler and J. Opfer, The development of numerical estimation: Evidence for multiple representations of numerical quantity, Psychol. Sci. 14, 237 (2003).
  47. M. Ebersbach, A. Frick, K. Luwel, P. Onghena, and L. Verschaffel, The relationship between the shape of the mental number line and familiarity with numbers in 5- to 9-year old children: Evidence for a segmented linear model, J. Exp. Child Psychol. 99, 1 (2008).
  48. E. Slusser, R. Santiago, and H. Barth, Developmental change in numerical estimation, J. Exp. Psychol. 142, 193 (2013).
  49. A. Favia, N. Comins, G. Thorpe, and D. Batuski, A direct examination of college student misconceptions in astronomy: A new instrument, J. Rev. Astron. Educ. Outreach 1, 21 (2014).
  50. K. Craik, The Nature of Explanation (University Press, Cambridge, United Kingdom, 1943).
  51. P. Johnson-Laird, Mental Models Towards a Cognitive Science of Language, Inference, and Consciousness, Cognitive Science Series Vol. 6 (Harvard University Press, Cambridge, MA, 1983
  52. J. K. Doyle and D. N. Ford, Mental models concepts for system dynamics research, Sys. Dyn. Rev. 14, 3 (1998).
  53. M. Ubben, J. Hartmann, and A. Pusch, Holes in the atmosphere of the universe: An empirical qualitative study on mental models of students regarding black holes, Astron. Educ. J. 2 (2022).
  54. L. van Ments and J. Treur, Mental models and their dynamics, adaptation, and control: A self-modeling network modeling approach, in Studies in Systems, Decision and Control, 1st ed. (Springer International Publishing AG, Cham, 2022), Vol. 394, pp. 3–26.
  55. E. Corpuz and N. Rebello, Investigating students’ mental models and knowledge construction of microscopic friction. i. implications for curriculum design and development, Phys. Rev. ST Phys. Educ. Res. 7, 020102 (2011).
  56. J. Gilbert and C. Boulter, International Handbook of Science Education, edited by B. Fraser and K. Tobin (Kluwer Academic Publishers, London, 1998), pp. 53–56.
  57. H. Bekaert, Studying learning opportunities in a planetarium environment, Ph.D. thesis, KU Leuven, 2024.
  58. G. Özdemir and D. Clark, An overview of conceptual change theories, Eurasia J. Math. Sci. Technol. Educ. 3, 351 (2007).
  59. D. Harlow and in Bianchini, Science Education in Theory and Practice, edited by B. Akpan and T. Kennedy, Springer Texts in Education (Springer International Publishing AG, Cham, 2020), pp. 389–401.
  60. A. diSessa, Toward an epistemology of physics, Cognit. Instr. 10, 105 (1993).
  61. S. Vosniadou, The development of students’ understanding of science, Front. Educ. 4, 1 (2019).
  62. T. Konkle and A. Oliva, Canonical visual size for real-world objects, J. Exp. Psychol. 37, 23 (2011).
  63. M. Szubielska and B. Bałaj, Mental size scaling of three-dimensional objects perceived visually or tactilely, Adv. Cognit. Psychol. 14, 139 (2018).
  64. A. Gardony, M. Eddy, T. Brunyé, and H. Taylor, Cognitive strategies in the mental rotation task revealed by EEG spectral power, Brain Cognit. 118, 1 (2017).
  65. R. Shepard and J. Metzler, Mental rotation of three-dimensional objects, Science 171, 701 (1971).
  66. S. D. Muthukumaraswamy, B. W. Johnson, and J. P. Hamm, A high density ERP comparison of mental rotation and mental size transformation, Brain Cognit. 52, 271 (2003).
  67. M. Fourtassi, G. Rode, and L. Pisella, Using eye movements to explore mental representations of space, Ann. Phys. Rehabil. Med. 60, 160 (2017).
  68. R. Johansson, J. Holsanova, and K. Holmqvist, Pictures and spoken descriptions elicit similar eye movements during mental imagery, both in light and in complete darkness, Cogn. Sci. 30, 1053 (2006).
  69. M. Fourtassi, A. Hajjioui, C. Urquizar, Y. Rossetti, G. Rode, and L. Pisella, Iterative fragmentation of cognitive maps in a visual imagery task, PLoS One 8, e68560 (2013).
  70. T. Tretter, M. Jones, T. Andre, A. Negishi, and J. Minogue, Conceptual boundaries and distances: Students’ and experts’ concepts of the scale of scientific phenomena, J. Res. Sci. Teach. 43, 282 (2006).
  71. S. Jung, S. Roesch, E. Klein, T. Dackermann, J. Heller, and K. Moeller, The strategy matters: Bounded and unbounded number line estimation in secondary school children, Cognit. Dev. 53, 100839 (2019).
  72. J. Sharp, Children’™s astronomical beliefs: A preliminary study of year 6 children in south-west England, Int. J. Sci. Educ. 18, 685 (1996).
  73. T. Makwela, Probing student engagement with size and distance in introductory astronomy, Ph.D. thesis, University of Cape Town, 2022.
  74. C. Eames, R. Eames, and K. Boeke, Powers of Ten (1978).
  75. K. Yu, K. Sahami, and J. Dove, Learning about the scale of the solar system using digital planetarium visualizations, Am. J. Phys. 85, 550 (2017).
  76. S. L. Franconeri, L. M. Padilla, P. Shah, J. M. Zacks, and J. Hullman, The science of visual data communication: What works, Psychol. Sci. Publ. Interest 22, 110 (2021).
  77. A. V. Pandey, K. Rall, M. L. Satterthwaite, O. Nov, and E. Bertini, How deceptive are deceptive visualizations?: An empirical analysis of common distortion techniques, in CHI 2015: Proceedings of the 33rd Annual CHI Conference on Human Factors in Computing Systems: Seoul, Republic of Korea (ACM, New York, NY, 2015), Vol. 2015, pp. 1469–1478.
  78. A. diSessa, Knowledge in pieces, in Constructivism in the Computer Age, edited by G. Forman and P. Pufall (Lawrence Erlbaum Associates, Hillsdale, NY, 1988), pp. 49–70.

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Phys. Rev. Phys. Educ. Res. 21, 010159– Published 11 June, 2025
  • Received 19 February 2025
  • Accepted 19 May 2025
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