## Abstract

Recognizing the roles of mathematics in society is an important goal for the teaching and learning of mathematical modelling. The Likert-scales method is a simple and effective tool to assess student appreciation about the utility of mathematics; however, it does not reveal the detailed aspects of student perceptions of the roles of mathematics in society. This study aimed to answer the following research question: how can we assess the detailed aspects of student perceptions of the roles of mathematics in society? An analytical tool consisting of three viewpoints, namely, (1) personal-societal perspectives, (2) clarity of role statements, and (3) specific-general contexts, was developed. It was revealed that students’ perceptions of the roles of mathematics in society significantly changed between the phases before and after an experimental teaching program. Namely, the analytical tool developed and used in this study enabled, at least partially, the clarification of the states or changes of students’ perceptions of the roles of mathematics in society. Although further attention is required to improve the validity and reliability of the analytical tool, the present study encourages future research on this important topic.

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## References

Berry, J., & Houston, K. (1995).

*Mathematical modelling*. Oxford: Butterworth-Heinemann.Breiteig, T., Grevholm, B., & Kislenko, K. (2005). Beliefs and attitudes in mathematics teaching and learning. https://www.researchgate.net/publication/255575882_Beliefs_and_attitudes_inmathematics teaching_and_learning. Accessed 30 Oct 2017.

Brookstein, A., Hegedus, S., Dalton, S., & Tapper, J. (2011). Student attitude in mathematics classrooms. http://www.kaputcenter.umassd.edu/downloads/products/technical_reports/tr4_student_attitude.pdf. Accessed 30 Oct 2017.

Busse, A., & Kaiser, G. (2003). Context in application and modelling–An empirical approach. In Q.-X. Ye, W. Blum, S. K. Houston & Q.-Y. Jiang (Eds.),

*Mathematical modelling in education and culture*(pp. 3–15). Chichester: Horwood.Chevallard, Y. (1989). Implicit mathematics: Their impact on societal needs and demands. In J. Malone, H. Burkhardt & C. Keitel (Eds.),

*The mathematics curriculum: Towards the year 2000*(pp. 49–57). Perth: Curtin University of Technology.Chevallard, Y. (2015). Teaching mathematics in tomorrow’s society: A case for an oncoming counter paradigm. In S. J. Cho (Ed.),

*The Proceedings of the 12th International Congress on Mathematical Education*(pp. 173–187). Cham: Springer.Cochran, W. G. (1954). Some methods for strengthening the common chi-square tests.

*Biometrics, 10*(4), 417–451.Furinghetti, F., & Pehkonen, E. (2002). Rethinking characterisations of beliefs. In G. C. Leder, E. Pehkonen & G. Törner (Eds.),

*Beliefs: A hidden variable in mathematics education?*(pp. 39–57). Dordrecht: Kluwer Academic Publishers.Ikeda, T. (2013). Pedagogical reflections on the role of modelling in mathematics instruction. In G. A. Stillman, G. Kaiser, W. Blum & J. P. Brown (Eds.),

*Teaching mathematical modelling: Connecting to research and practice*(pp. 255–275). Dordrecht: Springer.Ikeda, T., & Stephens, M. (2010). Three teaching principles for fostering students’ thinking about modelling: An experimental teaching program for 9th grade students in Japan.

*Journal of Mathematical Modelling and Applications, 1*(2), 49–59.Jablonka, E. (2007). The relevance of modelling and applications: Relevant to whom and for what purpose? In W. Blum, P. L. Galbraith, H. W. Henn & M. Niss (Eds.),

*Modelling and applications in mathematics education: The 14th ICMI Study*(pp. 193–200). New York: Springer.Leder, G. C., & Forgasz, H. J. (2002). Measuring mathematical beliefs and their impact on the learning of mathematics. In G. C. Leder, E. Pehkonen & G. Törner (Eds.),

*Beliefs: A hidden variable in mathematics education?*(pp. 95–114). Dordrecht: Kluwer Academic Publishers.Maaß, K. (2010). Modelling in class and the development of belief about the usefulness of mathematics. In R. Lesh, P. L. Galbraith, C. R. Haines & A. Hurford (Eds.),

*Modeling students’ mathematical competencies*(pp. 409–420). Dordrecht: Springer.Marton, F. (2007). Towards a pedagogical theory of learning. In N. Entwistle, P. Tomlison & J. Dockrell (Eds.),

*Student learning and university teaching*(pp. 19–30). Leicester: The British Psychological Society.Matsumoto, S. (2000). Activities that expand the mathematical world through making mathematical models—considering the length of mirrors that can reflect the whole body.

*Journal of Japan Society of Mathematical Education, 82*(1), 10–17. (Japanese).Meyer, W. J. (1984). Descriptive and prescriptive models–Inventory policy. In W. J. Meyer (Ed.),

*Concepts of mathematical modeling*(pp. 60–68). New York: McGraw-Hill.Niss, M. (1989). Aims and scope of applications and modelling in mathematics curricula. In W. Blum, J. S., Berry, & Biehler, R. (Eds.), Applications and modelling in learning and teaching mathematics (pp. 22–31). Chichester: Ellis Horwood

Niss, M. (2008). Perspectives on the balance between applications & modelling and ‘pure’ mathematics in the teaching and learning of mathematics. In M. Menghini, F. Furinghetti, L. Giacardi & F. Arzarello (Eds.),

*The first century of the International Commission on Mathematical Instruction*(pp. 69–84). Rome: Accademia Nazionale dei Lincei.Niss, M. (2015). Prescriptive modelling–challenges and opportunities. In G. A. Stillman, W. Blum & M. S. Biembengut (Eds.),

*Mathematical modelling in education research and practice: Cultural, societal, and cognitive influences*(pp. 67–79). Cham: Springer.Pinker, A. (1981). The concept ‘model’ and its potential role in mathematics education.

*International Journal of Mathematical Education in Science and Technology, 12*(6), 693–707.Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.),

*Handbook of research on mathematics teaching and learning*(pp. 334–370). New York: MacMillan.Schukajlow, S., Leiss, D., Pekrun, R., Blum, W., Müller, M., & Messner, R. (2012). Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations.

*Educational Studies in Mathematics, 79*(2), 215–237.Shimada, S. (1990).

*Collected problems for teachers*. Tokyo: Kyoritsu Publisher**(Japanese)**.Stacey, K., & Turner, R. (2015). The evolution and key concepts of the PISA mathematics frameworks. In K. Stacey & R. Turner (Eds.),

*Assessing mathematical literacy: The PISA experience*. Cham: Springer.Treilibs, V., Burkhardt, H., & Low, B. (1980).

*Formulation processes in mathematical modelling*. Nottingham: Shell Centre for Mathematical Education.Usiskin, Z. (1989). The sequencing of applications and modelling in the University of Chicago School Mathematics Project 7–12 curriculum. In W. Blum, J. S. Berry & R. Biehler (Eds.),

*Applications and modelling in learning and teaching mathematics*(pp. 176–181). Chichester: Horwood.Yanagimoto, A. (2003). Environmental problems and mathematical modelling. In S. J. Lamon, W. A. Parker & S. K. Houston (Eds.),

*Mathematical modelling: A way of life*(pp. 53–60). Chichester: Horwood.Yanagimoto, A., & Yoshimura, N. (2013). Mathematical modelling of a real-world problem: The decreasing number of Bluefin tuna. In G. A. Stillman, G. Kaiser, W. Blum & J. P. Brown (Eds.),

*Teaching mathematical modelling: Connecting to research and practice*(pp. 229–239). Dordrecht: Springer.Yoshimura, N. (2015). Mathematical modelling of a societal problem in Japan: The income and expenditure of an electric power company. In G. A. Stillman, W. Blum & M. S. Biembengut (Eds.),

*Mathematical modelling in educational research and practice: Cultural, societal and cognitive influences*(pp. 251–261). Cham: Springer.Yoshimura, N., & Yanagimoto, A. (2013). Mathematical modelling of a societal problem: Pension tax issues. In G. A. Stillman, G. Kaiser, W. Blum & J. P. Brown (Eds.),

*Teaching mathematical modelling: Connecting to research and practice*(pp. 241–251). Dordrecht: Springer.

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## Appendix

### Appendix

The results of coding in the first year.

Name code | Pre-question | Post-question | ||||
---|---|---|---|---|---|---|

Category | Utility | Purpose | Category | Utility | Purpose | |

1 | C1 | C4 | P1 | |||

2 | C1 | C4 | P1 | |||

3 | C1 | C1 | ||||

4 | C1 | C4 | P1, P2 | |||

5 | C1 | C4 | P1 | |||

6 | C1 | C2 | ||||

7 | C1 | C2 | ○ | |||

8 | C1 | C2 | ○ | |||

9 | C2 | ○ | C2 | |||

10 | C2 | C3 | ○ | |||

11 | C2 | C4 | P1 | |||

12 | C1 | C3 | ||||

12 | C1 | C2 | ||||

13 | C1 | C4 | P1, P3 | |||

14 | C1 | C3 | ||||

15 | C2 | ○ | C3 | |||

16 | C2 | ○ | C4 | P2, P3 | ||

17 | C1 | C4 | P1 | |||

18 | C1 | C2 | ||||

19 | C1 | C2 | ||||

20 | C1 | C4 | P2 | |||

21 | C2 | ○ | C2 | |||

22 | C1 | C1 | ||||

23 | C1 | C1 | ||||

24 | C1 | C2 | ||||

25 | C2 | ○ | C2 | |||

26 | C1 | C4 | P3 | |||

27 | C3 | C4 | P3 | |||

28 | C1 | C3 | ○ | |||

29 | C1 | C4 | P3 | |||

30 | C2 | ○ | C2 | |||

Total number of students | 6 | 0 | 4 | 12 |

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Ikeda, T. Evaluating student perceptions of the roles of mathematics in society following an experimental teaching program.
*ZDM Mathematics Education* **50**, 259–271 (2018). https://doi.org/10.1007/s11858-018-0927-3

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DOI: https://doi.org/10.1007/s11858-018-0927-3