First-Year Students’ Beliefs about Context Problems in Mathematics in University Science Programmes

  • Andreja Drobnic VidicEmail author


Mathematics-related beliefs play an important role in the willingness to engage in academic activities in mathematics education. Such beliefs might not be consistent with the beliefs students hold about context problems that require sufficient mathematical knowledge and the application of such knowledge to various real-life situations. This study was designed to examine the differences between students’ mathematics-related beliefs and beliefs about context problems. The variations in these beliefs could explain the different amounts of effort students put into solving context problems on one hand and in solving typical mathematical tasks on the other. The study included 261 first-year students: students in one group were enrolled in academically more demanding study programmes (n = 162), while students in the other group (n = 99) were enrolled in less demanding study programmes. The results revealed significant differences in beliefs between the two groups. A detailed analysis indicates the factors which need to be emphasised when designing problem-based mathematics education to promote the successful problem solving of context problems.

Key words

Beliefs Context problem Problem-solving difficulty Science study programmes Undergraduate mathematics education 


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  1. Beswick, K. (2011). Putting context in context: an examination of the evidence for the benefits of ‘contextualised’ tasks. International Journal of Science and Mathematics Education, 9(2), 367–390.CrossRefGoogle Scholar
  2. Boaler, J. (1993). Encouraging the transfer of ‘school’ mathematics to the ‘real world’ through the integration of process and content, context and culture. Educational Studies in Mathematics, 25(4), 341–373.CrossRefGoogle Scholar
  3. Brown, S. I. (2001). Reconstructing school mathematics: Problems with problems and the real world (p. 271). New York: Peter Lang Publishing.Google Scholar
  4. Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62, 211–230. doi: 10.1007/s10649-006-7834-1.CrossRefGoogle Scholar
  5. Chen, L., Van Dooren, W., Chen, Q. & Verschaffel, L. (2010). An investigation on Chinese teachers’ realistic problem posing and problem solving ability and beliefs. International Journal of Science and Mathematics Education, 9(4), 919–948. doi: 10.1007/s10763-010-9259-7.CrossRefGoogle Scholar
  6. Diego-Mantecón, J., Andrews, P. & Op’t Eynde, P. (2007). Refining the mathematics-related beliefs questionnaire (MRBQ), pp. 229–238. In: Proceeding of the 5th Congress of the European Society for Research in Mathematics Education, CERME5, Larnaka, Cyprus, 22–26 February 2007.Google Scholar
  7. Doerr, H. M. & English, L. D. (2006). Middle grade teachers’ learning through students’ engagement with modeling tasks. Journal of Mathematics Teacher Education, 9(1), 5–32.CrossRefGoogle Scholar
  8. Ding, L. (2014). Long live traditional textbook problems!?—constraints on faculty use of research-based problems in introductory courses. Journal of Science and Mathematics Education, 12(1), 123–144.Google Scholar
  9. Drobnič Vidic, A. (2010). The impact of problem-based learning on statistical thinking of engineering and technical high school students [the best refereed paper by an early career author]. In C. Reading (Ed.), Data and context in statistics education: towards an evidence-based society: Proceedings of the 8th International Conference on Teaching Statistics (ICOTS8), Ljubljana, Slovenia.
  10. Drobnic Vidic, A. (2011). Impact of problem-based statistics course in engineering on students’ problem solving skills. International journal of engineering education, 27(4), 885–896.Google Scholar
  11. Freudental (1968). Why to teach mathematics so as to be useful? Educational Studies of Mathematics, 1, 3–8.CrossRefGoogle Scholar
  12. Frlec, S. & Vidmar, G. (2001). Metric characteristics of the self-efficacy scale: a preliminary study. Horizons of Psychology, 10(1), 9–25.Google Scholar
  13. Gazit, A. & Patkin, D. (2012). The way adults with orientation to mathematics teaching cope with the solution of everyday real-world problems. International Journal of Mathematical Education in Science and Technology, 43(2), 167–176.CrossRefGoogle Scholar
  14. Gómez-Chacón, I., García Madruga, J., Rodríguez, R., Oscar Vila, J. & Elosúa, M. R. (2011). Mathematical beliefs and cognitive reflection: Do they predict academic achievement? In B. Roesken & M. Casper (Eds.), Current state of research on mathematical beliefs XVII, Proceedings of the MAVI-17 Conference, September 17–20, 2011. Germany: Ruhr-Universität Bochum.Google Scholar
  15. Kaldo, I. (2011). Estonian science and non-science students’ beliefs towards mathematics at university level. In B. Roesken & M. Casper (Eds.), Current state of research on mathematical beliefs XVII, Proceedings of the MAVI-17 Conference, September 17–20, 2011. Germany: Ruhr-Universität Bochum.Google Scholar
  16. Lavy, I. & Shriki, A. (2008). Investigating changes in prospective teachers’ views of a ‘Good Teacher’ while engaging in computerized project-based learning. Journal of Mathematics Teacher Education, 11(4), 259–284.CrossRefGoogle Scholar
  17. Lee, J. (2012). Prospective elementary teachers’ perceptions of real-life connections reflected in posing and evaluating story problems. Journal of Mathematics Teacher Education, 8, 223–254.CrossRefGoogle Scholar
  18. Llinares, S. & Roig, A. I. (2008). Secondary school students’ construction and use of mathematical models in solving word problems. International Journal of Science and Mathematics Education, 6(3), 505–532.CrossRefGoogle Scholar
  19. Lorenzo, M. (2005). The development, implementation, and evaluation of a problem solving heuristic. International Journal of Science and Mathematics Education, 3, 33–58.CrossRefGoogle Scholar
  20. Lubienski, S. T. (2000). Solving as a means toward mathematics for all: an exploratory look through a class lens. Journal for Research in Mathematics Education, 31(4), 454–482.CrossRefGoogle Scholar
  21. Mayer, R. E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science, 26, 49–63.CrossRefGoogle Scholar
  22. OECD. (2006). Assessing scientific, reading and mathematical literacy: a framework for PISA 2006. Paris: OECD. cop. 2006.CrossRefGoogle Scholar
  23. Op’t Eynde, P. & Hannula, M. S. (2006). The case study of Frank. Educational Studies in Mathematics, 63, 123–129.CrossRefGoogle Scholar
  24. Op’t Eynde, P. & De Corte, E. (2003). When girls value mathematics as highly as boys: an analysis of junior high students’ mathematics-related beliefs. Paper presented to the symposium, the relationship between students’ epistemological beliefs, cognition and learning, at the annual meeting of the American Educational Research Association, April 21–25, Chicago.Google Scholar
  25. Op’t Eynde, P., De Corte, E. & Verschaffel, L. (2006a). Epistemic dimensions of students’ mathematics-related belief systems. International Journal of Educational Research, 45, 57–70.CrossRefGoogle Scholar
  26. Op’t Eynde, P., De Corte, E. & Verschaffel, L. (2006b). Accepting emotional complexity”: a socio-constructivist perspective on the role of emotions in the mathematics classroom. Educational Studies in Mathematics, 63, 193–207.CrossRefGoogle Scholar
  27. Pape, S. & Wang, C. (2003). Middle school children’s strategic behaviour: Classification and relation to academic achievement and mathematical problem solving. Instructional Science, 31, 419–449.CrossRefGoogle Scholar
  28. Perrenet, J. C., Bouhuijs, P. A. J. & Smits, J. G. M. M. (2000). The suitability of problem-based learning for engineering education: Theory and practice. Teaching in Higher Education, 5(3), 345–358.CrossRefGoogle Scholar
  29. Perrenet, J. & Taconis, R. (2009). Mathematical enculturation from the students’ perspective: Shifts in problem-solving beliefs and behaviour during the bachelor programme. Educational Studies in Mathematics, 71(2), 181–198.CrossRefGoogle Scholar
  30. Physick, M. D. (2010). Exploring mathematics-related belief systems. (Education) Thesis (M.Sc.): Faculty of Education, Simon Fraser University.Google Scholar
  31. Pratt, D., Ainley, J., Kent, P., Levinson, R., Yogui, C. & Kapadi, R. (2011). Role of context in risk-based reasoning. Mathematical Thinking and Learning, 13, 322–345.CrossRefGoogle Scholar
  32. Puklek Lipušček, M., Valenčič Zuljan, M., Kalin, J., Pečjak, S. & Peklaj, C. (2010). Primary and secondary school students’ motivation and achievement in math. Didactica Slovenica, 25(2), 97–115.Google Scholar
  33. Roesken, B., Hannula, M. S. & Pehkonen, E. (2011). Dimensions of students’ views of themselves as learners of mathematics. ZDM – The International Journal in Mathematics Education, 43(4), 497–506.CrossRefGoogle Scholar
  34. Schoenfeld, A. H. (1989). Explorations of students’ mathematical beliefs and behavior. Journal for Research in Mathematics Education, 20(4), 338–355.CrossRefGoogle Scholar
  35. Song, H. & Grabowski, B. L. (2006). Stimulating intrinsic motivation for problem solving using goal-oriented contexts and peer group composition. Educational Technology Research and Development, 54(5), 445–466.CrossRefGoogle Scholar
  36. Sumpter, L. (2013). Themes and interplay of beliefs in mathematical reasoning. Journal of Science and Mathematics Education, 11(5), 1115–1135.Google Scholar
  37. Verschaffel, L. & De Corte, E. (1997). Teaching realistic mathematical modeling in the elementary school: a teaching experiment with fifth graders. Journal for Research in Mathematics Education, 28(5), 577–601.CrossRefGoogle Scholar
  38. Yan, Z. & Lianghuo, F. (2006). Focus on the representation of problem types in intended curriculum: a comparison of selected mathematics textbooks from mainland China and the United States. International Journal of Science and Mathematics Education, 4(4), 609–626.CrossRefGoogle Scholar
  39. Zimmerman, B. & Martinez-Pons, M. (1990). Student differences in self-regulated learning: Relating grade, sex, and giftedness to self-efficacy and strategy use. Journal of Educational Psychology, 82(1), 51–55.CrossRefGoogle Scholar

Copyright information

© National Science Council, Taiwan 2014

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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