Research Article

Argumentation in mathematics and science university textbooks: Similarities and differences in linguistic structures

Jenny M. Hellgren 1 2 3 * , Ewa Bergqvist 1 2 , Magnus Österholm 1 2
More Detail
1 Department of Science and Mathematics Education, Umeå University, Umeå, SWEDEN2 Umeå Mathematics Education Research Centre (UMERC), Umeå, SWEDEN3 Umeå Science Education Research (UmSER), Umeå, SWEDEN* Corresponding Author
European Journal of Science and Mathematics Education, 13(1), January 2025, 1-15, https://doi.org/10.30935/scimath/15746
Published Online: 23 December 2024, Published: 01 January 2025
OPEN ACCESS   245 Views   133 Downloads
Download Full Text (PDF)

ABSTRACT

Argumentation is a key skill in most school subjects and academic disciplines, including mathematics and science. It is possible that similarities and differences between how argumentation is expressed in different subjects can contribute to, or disrupt, students’ transferrable argumentation skills. The purpose of this study is therefore to increase the understanding of such similarities and differences concerning the use of argumentation in mathematics and science texts. To reach this goal, the study compares argumentation with a focus on argumentation markers and argumentative structures in first-semester university textbooks in mathematics, chemistry, and biology. Results show that common linguistic argumentation markers in mathematics and science textbooks include for example because, if, thus, so, and therefore and that there is significantly more argumentation in the mathematics textbook compared to the science textbooks. Further, the results indicate differences in patterns of how argumentation is used, including for example that the mathematics textbook contains more complex argumentation compared with the chemistry textbook. Thereby, the subject-specific languages in the disciplines have the potential to offer students different examples of argumentation.

CITATION (APA)

Hellgren, J. M., Bergqvist, E., & Österholm, M. (2025). Argumentation in mathematics and science university textbooks: Similarities and differences in linguistic structures. European Journal of Science and Mathematics Education, 13(1), 1-15. https://doi.org/10.30935/scimath/15746

REFERENCES

  1. Aberdein, A., & Dove, I. J. (Eds.). (2013). The argument of mathematics. Springer. https://doi.org/10.1007/978-94-007-6534-4
  2. Adams, R. A., & Essex, C. (2013). Calculus: A Complete Course (8th ed.). Pearson.
  3. Burton, L., & Morgan, C. (2000). Mathematicians writing. Journal for Research in Mathematics Education JRME, 31(4), 429–453. https://doi.org/10.2307/749652
  4. Butler, F. A., Bailey, A. L., Stevens, R., Huang, B., & Lord, C. (2004). Academic English in fifth-grade mathematics, science, and social studies textbooks. Center for Research on Evaluation Standards and Student Testing CRESST. https://cresst.org/publications/cresst-publication-3013/
  5. Chang, R. (2010). Chemistry (10th ed.). McGraw-Hill.
  6. Clark, D. B., Sampson, V., Weinberger, A., & Erkens, G. (2007). Analytic frameworks for assessing dialogic argumentation in online learning environments. Educational Psychology Review, 19(3), 343–374. https://doi.org/10.1007/s10648-007-9050-7
  7. Conner, A., & Kittleson, J. M. (2009). Epistemic understandings in mathematics and science: Implications for learning. In Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education (vol. 1, pp. 106–111).
  8. Cowen, C. C. (1991). Teaching and testing mathematics reading. The American Mathematical Monthly, 98(1), 50–53. https://doi.org/10.1080/00029890.1991.11995704
  9. Davis, J. D. (2012). An examination of reasoning and proof opportunities in three differently organized secondary mathematics textbook units. Mathematics Education Research Journal, 24(4), 467–491. https://doi.org/10.1007/s13394-012-0047-2
  10. Develaki, M. (2020). Comparing crosscutting practices in STEM disciplines. Science & Education, 29(4), 949–979. https://doi.org/10.1007/s11191-020-00147-1
  11. Dove, I. J. (2009). Towards a theory of mathematical argument. Foundations of Science, 14(1–2), 137–152. https://doi.org/10.1007/s10699-008-9156-5
  12. Driver, R., Newton, P., & Osborne, J. (2000). Establishing the norms of scientific argumentation in classrooms. Science Education, 84(3), 287–312. https://doi.org/10.1002/(SICI)1098-237X(200005)84:3<287::AID-SCE1>3.0.CO;2-A
  13. Dunbar, K. (2001). Scientific reasoning and discovery, cognitive psychology of. In N. J. Smelser, & P. B. Baltes (Eds.), International encyclopedia of the social & behavioral sciences (pp. 13746–13749). Pergamon. https://doi.org/10.1016/B0-08-043076-7/01602-8
  14. Erduran, S., Simon, S., & Osborne, J. (2004). TAPping into argumentation: Developments in the application of Toulmin’s Argument Pattern for studying science discourse. Science Education, 88(6), 915–933. https://doi.org/10.1002/sce.20012
  15. Faize, F. A., Husain, W., & Nisar, F. (2017). A critical review of scientific argumentation in science education. Eurasia Journal of Mathematics, Science and Technology Education, 14(1), 475–483. https://doi.org/10.12973/ejmste/80353
  16. Fischer, F., Kollar, I., Ufer, S., Sodian, B., Hussmann, H., Pekrun, R., Neuhaus, B., Dorner, B., Pankofer, S., & Fischer, M. (2014). Scientific reasoning and argumentation: Advancing an interdisciplinary research agenda in education. Frontline Learning Research, 2(3), 28–45. http://journals.sfu.ca/flr/index.php/journal/article/view/96
  17. Freeman, J. B. (1991). Dialectics and the macrostructure of arguments: A theory of argument structure. Walter de Gruyter & Co. https://doi.org/10.1515/9783110875843
  18. Fuentes, P. (1998). Reading comprehension in mathematics. The Clearing House, 72(2), 81–88. https://doi.org/10.1080/00098659809599602
  19. Herrenkohl, L. R., & Cornelius, L. (2013). Investigating elementary students’ scientific and historical argumentation. Journal of the Learning Sciences, 22(3), 413–461. https://doi.org/10.1080/10508406.2013.799475
  20. Inglis, M., & Alcock, L. (2012). Expert and novice approaches to reading mathematical proofs. Journal for Research in Mathematics Education, 43(4), 358–390. https://doi.org/10.5951/jresematheduc.43.4.0358
  21. Kartika, H., Budiarto, M. T., & Fuad, Y. (2021). Argumentation in K-12 mathematics and science education: A content analysis of articles. International Journal of Research in Education and Science, 7(1), 51–64. https://doi.org/10.46328/ijres.1389
  22. Kartika, H., Budiarto, M. T., Fuad, Y., & Bonyah, E. (2023). Bibliometrics analysis of research on argumentation in mathematics education. International Journal of Education in Mathematics, Science and Technology, 11(5), 1346–1365. https://doi.org/10.46328/ijemst.2904
  23. Konior, J. (1993). Research into the construction of mathematical texts. Educational Studies in Mathematics, 24(3), 251–256. https://doi.org/10.1007/BF01275425
  24. Konstantinidou, A., & Macagno, F. (2013). Understanding students’ reasoning: Argumentation schemes as an interpretation method in science education. Science and Education, 22, 1069–1087. https://doi.org/10.1007/s11191-012-9564-3
  25. McKenna, M. C., & Robinson, R. D. (1990). Content literacy: A definition and implications. Journal of Reading, 34(3), 184–186.
  26. NCTM. (2000). Principles and standards for school mathematics (vol. 1). National Council of Teachers of Mathematics.
  27. Neugebauer, S. R., & Gilmour, A. F. (2020). The ups and downs of reading across content areas: The association between instruction and fluctuations in reading motivation. Journal of Educational Psychology, 112(2), 344–363. https://doi.org/10.1037/edu0000373
  28. Newton, D. P., & Newton, L. D. (2006a). Could elementary mathematics textbooks help give attention to reasons in the classroom? Educational Studies in Mathematics, 64(1), 69–84. https://doi.org/10.1007/s10649-005-9015-z
  29. Newton, D. P., & Newton, L. D. (2006b). Could elementary textbooks serve as models of practice to help new teachers and non-specialists attend to reasoning in music? Music Education Research, 8(1), 3–16. https://doi.org/10.1080/14613800600570660
  30. Newton, L. D., & Newton, D. P. (2006c). Can explanations in children’s books help teachers foster reason-based understandings in religious education in primary schools? British Journal of Religious Education, 28(3), 225–234. https://doi.org/10.1080/01416200600811311
  31. Newton, L. D., Newton, D. P., Blake, A., & Brown, K. (2002). Do primary school science books for children show a concern for explanatory understanding? Research in Science & Technological Education, 20(2), 227–240. https://doi.org/10.1080/0263514022000030471
  32. Niss, M. A., & Højgaard, T. (Eds.) (2011). Competencies and mathematical learning: Ideas and inspiration for the development of mathematics teaching and learning in Denmark. Roskilde Universitet.
  33. Nussbaum, E. M. (2011). Argumentation, dialogue theory, and probability modeling: Alternative frameworks for argumentation research in education. Educational Psychologist, 46(2), 84–106. https://doi.org/10.1080/00461520.2011.558816
  34. Osborne, J., Erduran, S., & Simon, S. (2004). Enhancing the quality of argumentation in school science. Journal of Research in Science Teaching, 41(10), 994–1020. https://doi.org/10.1002/tea.20035
  35. Österholm, M., & Bergqvist, E. (2013). What is so special about mathematical texts? Analyses of common claims in research literature and of properties of textbooks. ZDM - the International Journal on Mathematics Education, 45(5), 751–763. https://doi.org/10.1007/s11858-013-0522-6
  36. Pera, M. (1994). The discourses of science. University of Chicago Press.
  37. Rasmussen, C., Wawro, M., & Zandieh, M. (2015). Examining individual and collective level mathematical progress. Educational Studies in Mathematics, 88(2), 259–281. https://doi.org/10.1007/s10649-014-9583-x
  38. Reece, J. B., Urry, L. A., Cain, M. L., Minorsky, P. V., & Jackson, R. B. (2013). Campbell Biology. Benjamin Cummings.
  39. Remmers, H. H., & Grant, A. (1928). The vocabulary load of certain secondary school mathematics textbooks. The Journal of Educational Research, 18(3), 203–210. https://doi.org/10.1080/00220671.1928.10879878
  40. Ribeck, J. (2015). Steg för steg. Naturvetenskapligt ämnesspråk som räknas [Step by step. A computational analysis of Swedish textbook language] [Doctoral dissertation, University of Gothenburg].
  41. Shanahan, C., Shanahan, T., & Misischia, C. (2011). Analysis of expert readers in three disciplines: History, mathematics, and chemistry. Journal of Literacy Research, 43(4), 393–429. https://doi.org/10.1177/1086296X11424071
  42. Shanahan, T., & Shanahan, C. (2008). Teaching disciplinary literacy to adolescents: Rethinking content-area literacy. Harvard Educational Review, 78(1), 40–59. https://doi.org/10.17763/haer.78.1.v62444321p602101
  43. Shanahan, T., & Shanahan, C. (2012). What is disciplinary literacy and why does it matter? Topics in Language Disorders, 32(1), 7–18. https://doi.org/10.1097/TLD.0b013e318244557a
  44. Stacey, K., & Vincent, J. (2009). Modes of reasoning in explanations in Australian eighth-grade mathematics textbooks. Educational Studies in Mathematics, 72(3), 271–288. https://doi.org/10.1007/s10649-009-9193-1
  45. Swedish National Agency for Education. (2018). Curriculum for the compulsory school, preschool class and school-age educare (revised 2018). Skolverket. https://www.skolverket.se/publikationer?id=3984
  46. Thompson, D. R., Sharon, L. S., & Johnson, G. J. (2012). Opportunities to learn reasoning and proof in high school mathematics textbooks. Journal for Research in Mathematics Education, 43(3), 253–295. https://doi.org/10.5951/jresematheduc.43.3.0253
  47. Toulmin, S. E. (1958). The uses of argument. Cambridge University Press.
  48. Triantafillou, C., Spiliotopoulou, V., & Potari, D. (2016). The nature of argumentation in school mathematics and physics texts: The case of periodicity. International Journal of Science and Mathematics Education, 14(4), 681–699. https://doi.org/10.1007/s10763-014-9609-y