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pp. **395-419** | Article Number: **mathedu.2016.012**

Published Online: **March 02, 2016**

Article Views: **2059** | Article Download: **2988**

**Abstract**

In the article, three Danish secondary level mathematics teachers’ beliefs about the use of technological tools in the teaching of mathematics and their beliefs about mathematics as a scientific discipline are identified and classified - and the process also aspects of their beliefs about the teaching and learning of mathematics. The potential relationships between these sets of beliefs are also explored. Results show that the teachers not only manifest different beliefs about the use of technology and mathematics as a discipline, but that one set of beliefs can influence the other set of beliefs. The article concludes with a discussion of the research findings and their validity as well as their implications for both practice and research in mathematics education.

**Keywords: ** mathematics teachers’ beliefs, beliefs about mathematics as a discipline, beliefs about use of technology, lever potential, blackboxing

**References**

Artigue, M. (2002). Learning mathematics in a CAS environment: the genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. *International Journal of Computers for Mathematical Learning*, *7*(3), 245–274. doi: 10.1023/A:1022103903080

Beswick, K. (2005). The beliefs/practice connection in broadly defined contexts. *Mathematics Education Research Journal*,*17*(2), 39-68. doi: 10.1007/BF03217415

Beswick, K. (2012). Teachers' beliefs about school mathematics and mathematicians' mathematics and their relationship to practice. *Educational Studies in Mathematics*, *79*(1), 127-147. doi: 10.1007/s10649-011-9333-2

Blömeke, S. & Kaiser, G. (2015). Effects of motivation on the belief systems of future mathematics teachers from a comparative perspective. In B. Pepin & B. Roesken-Winter (Eds.),* From Beliefs to Dynamic Affect Systems in Mathematics Education. Exploring a Mosaic of Relationships and Interactions* (pp. 227-243). Switzerland: Springer. doi: 10.1007/978-3-319-06808-4_11

Buchberger, B. (2002). Computer algebra: the end of mathematics? *ACM SIGSAM Bulletin*, *36*(1), 3-9.

Carter, G. & Norwood, K.S. (1997). The relationship between teacher and student beliefs about mathematics. *School Science and Mathematics*, *97*(2), 62-67. doi: 10.1111/j.1949-8594.1997.tb17344.x

Cooney, T.J., Shealy, B.E. & Arvold, B. (1998). Conceptualizing belief structures of preservice secondary mathematics teachers. *Journal for Research in Mathematics Education*, *29*(3), 306-333.

De Guzman, M., Hodgson, B.R., Robert, A. & Villani, V. (1998). Difficulties in the passage from secondary to tertiary education. *In Proceedings of the International Congress of Mathematicians *(pp. 747-762). Berlin: Documenta mathematica.

Dogan, M. (2007). Mathematics trainee teachers’ attitudes to computers. In M. Joubert (Ed.), *Proceedings of the British Society for Research into Learning Mathematics* *28*(2), (pp. 19-24). United Kingdom: BSRLM.

Dreyfus, T. (1994) The role of cognitive tools in mathematics education. In R. Biehler, R.W. Scholz, R. Sträßer & B. Winkelmann (Eds.), *Didactics of Mathematics as a Scientific Discipline* (pp. 201–211). Dordrecht: Kluwer. doi: 10.1007/0-306-47204-X

Drijvers, P., Doorman, M., Boon, P., Reed, H. & Gravemeijer, K. (2010). The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom. *Educational Studies in Mathematics*, *75*(2), 213-234. doi: 10.1007/s10649-010-9254-5

Erens, R. & Eichler, A. (2015). The use of technology in calculus classrooms – beliefs of high school teachers. In C. Bernack-Schüler, R. Erens, T. Leuders & A. Eichler (Eds.), *Views and Beliefs in Mathematics Education. Results of the 19th MAVI Conference* (pp. 133-144). Germany: Springer. doi: 10.1007/978-3-658-09614-4_11

Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), *Mathematics Teaching: The State of the Art* (pp. 249-254). New York: Falmer.

Fleener, M.J. (1995). The relationship between experience and philosophical orientation: a comparison of preservice and practicing teachers’ beliefs about calculators. *Journal of Computers in Mathematics and Science Teaching*, *14*(3), 359-376.

Forgasz, H.J. (2002). Teachers and computers for secondary mathematics. *Education and Information Technologies*, *7*(2), 111-125. doi: 10.1023/A:1020301626170

Furinghetti, F. & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In G.C. Leder, E. Pehkonen and G. Törner (Eds.), *Beliefs: A hidden variable in mathematics education?* (pp. 39-57). Dordrecht: Kluwer. doi: 10.1007/0-306-47958-3_3

Fullan, M.G. (1991). *The New Meaning of Educational Change*. New York: Teachers College Press

Gill, M.G., Ashton, P.T. & Algina, J. (2004). Changing preservice teachers’ epistemological beliefs about teaching and learning in mathematics: An intervention study. *Contemporary Educational Psychology*, *29*(2), 164-185. doi: 10.1016/j.cedpsych.2004.01.003

Georgsen, M., Fougt, S.S., Mikkelsen, S.L.S. & Lorentzen, R.F. (2014). *Interventionsdesign i demonstrationsskoleprojektet IT-fagdidaktik og lærerkompetencer i et organisatorisk perspektiv*. Retrieved from: http://auuc.demonstrationsskoler.dk/ sites/default/ files/IT-fagdidaktik/interventionsdesign_i_demonstrationsskoleprojektet.pdf

Green, T.F. (1971). *The Activities of Teaching*. New York: McGraw-Hill.

Goos, M. (2014). Technology integration in secondary school mathematics: the development of teachers’ professional identities. In A. Clark-Wilson, O. Robutti & N. Sinclair (Eds.), *The Mathematics Teacher in the Digital Era. An International Perspective on Technology Focused Professional Development* (pp. 139-161). Dordrecht: Springer. doi: 10.1007/978-94-007-4638-1_7

Hanzsek-Brill, M.B. (1997). *The relationships among components of elementary teachers’ mathematics education knowledge and their uses of technology in the mathematics classroom*. Unpublished doctoral dissertation. Athens, Georgia: University of Georgia.

Jankvist, U.T. (2015). Changing students’ images of “mathematics as a discipline”. *The Journal of Mathematical Behavior*,*38*, 41-56. doi: 10.1016/j.jmathb.2015.02.002

Jankvist, U.T., Misfeldt, M. & Iversen, S.M. (preprint). When students are subject to various teachers’ varying policies: A bricolage framework for the case of CAS in teaching.

Kuhs, T. M., & Ball, D. L. (1986). *Approaches to teaching mathematics: mapping the domains of knowledge, skills, and disposition* (Research Memo). Lansing, MI: Michigan State University, Center on Teacher Education.

Kvale, S. (1996). *Interviews : an introduction to qualitative research interviewing*. Thousand Oaks, Calif.: Sage Publications.

Lagrange, J. (2005). Using symbolic calculators to study mathematics: the case of tasks and techniques. The case of tasks and techniques. In D. Guin, K. Ruthven & L. Trouche (Eds.), *The Didactical Challenge of Symbolic Calculators. Turning a Computational Device into a Mathematical Instrument* (pp. 113-135). New York: Springer. doi: 10.1007/0-387-23435-7_6

Lavicza, Z. (2010). Integrating technology into mathematics teaching at the university level. *ZDM*, *42*(1), 105-119. doi: 10.1007/s11858-009-0225-1

Leatham, K.R. (2006). Viewing mathematics teachers’ beliefs as sensible systems. *Journal of Mathematics Teacher Education*, *9*(1), 91-102. doi: 10.1007/s10857-006-9006-8

Leatham, K.R. (2007). Pre-service secondary mathematics teachers’ beliefs about the nature of technology in the classroom. *Canadian Journal of Science, Mathematics and Technology*, *7*(2/3), 183-207. doi: 10.1080/14926150709556726

Leder, G.C. (2015). Foreword. In B. Pepin & B. Roesken-Winter (Eds.),* From Beliefs to Dynamic Affect Systems in Mathematics Education. Exploring a Mosaic of Relationships and Interactions* (pp. v-x). Switzerland: Springer. doi: 10.1007/978-3-319-06808-4

Liljedahl, P. (2009). Teachers’ insights into the relationship between beliefs and practice. In J. Maaß & W. Schlöglmann (Eds.), *Beliefs and Attitudes in Mathematics Education. New Research Results* (pp. 33-44). Rotterdam: Sense Publishers.

McCulloch, A.W. (2011). Affect and graphing calculator use. *The Journal of Mathematical Behavior*, 30(2), 166-179. doi: 10.1016/j.jmathb.2011.02.002

Nabb, K.A. (2010). CAS as a restructuring tool in mathematics education. *Proceedings of the 22nd International Conference on Technology in Collegiate Mathematics*. Chicago, IL.

Op’t Eynde, P., de Corte, E., & Verschaffel, L. (2002). Framing students’ mathematics-related beliefs. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), *Beliefs: A hidden variable in mathematics education?* (pp. 13–37). Dordrecht: Kluwer Academic Publishers (Chapter 2).

Pajares, M.F. (1992). Teachers’ beliefs and educational research: cleaning up a messy construct. *Review of Educational Research*, *62*(3), 307-332. doi: 10.3102/00346543062003307

Partnership For 21st Century Skills (2011). *Outcomes for P21 Math Skills Map*. Washington, DC: Author. Retrieved from http://www.p21.org/storage/documents/ P21_Math_Map.pdf

Partnership For 21st Century Skills (2004). *ICT Literacy Map*. Tuczon, Az: Author. Retrieved from http://21ctlearning.pbworks.com/f/ictmap_math.pdf

Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F.K. Lester Jr. (Ed.), *Second Handbook of Research on Mathematics Teaching and Learning* (pp. 257-315). Charlotte, NC: Information Age Publishing.

Rokeach, M. (1960). *The open and closed mind*. New York: Basic Books.

Schmidt, M.E. (1999). Middle grade teachers’ beliefs about calculator use: pre-project and two years later. *Focus on Learning Problems in Mathematics*, *21*(1), 18-34.

Schoenfeld, A.H. (2007). Method. In F.K. Lester, Jr. (Ed.), *Second Handbook of Research on Mathematics Teaching and Learning* (pp. 69-107). Charlotte, NC: Information Age Publishing.

Skott, J. (2015). Towards a participatory approach to ‘beliefs’ in mathematics education. In B. Pepin & B. Roesken-Winter (Eds.),* From Beliefs to Dynamic Affect Systems in Mathematics Education. Exploring a Mosaic of Relationships and Interactions* (pp. 3-23). Switzerland: Springer. doi: 10.1007/978-3-319-06808-4_1

Swan, M. (2007). The impact of task-based professional development on teachers’ practices and beliefs: a design research study. *Journal of Mathematics Teacher Education*, *10*(4), 217-237. doi: 10.1007/s10857-007-9038-8

Tharp, M.L., Fitzsimmons, J.A. & Ayers, R.L.B. (1997). Negotiating a technological shift: teacher perception of the implementation of graphic calculators. *Journal of Computers in Mathematics and Science Teaching*, *16*(4), 551-575.

Thomas, M.O.J. & Palmer, J.M. (2014). Teaching with digital technology: obstacles and opportunities. In A. Clark-Wilson, O. Robutti & N. Sinclair (Eds.), *The Mathematics Teacher in the Digital Era. An International Perspective on Technology Focused Professional Development* (pp. 71-89). Dordrecht: Springer. doi: 10.1007/978-94-007-4638-1_4

Thompson, A.G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D.A. Grouws (Ed.), *Handbook of Research on Mathematics Teaching and Learning* (pp. 127-146). New York: Macmillan.

Van Zoest, L.R., Jones, G.A., & Thornton, C.A. (1994). Beliefs about mathematics teaching held by pre-service teachers involved in a first grade mentorship program. *Mathematics Education Research Journal*, *6*(1), 37-55. doi: 10.1007/BF03217261

Walen, S.B., Williams, S.R. & Garner, B.E. (2003). Pre-service teachers learning mathematics using calculators: a failure to connect current and future practice. *Teaching and Teacher Education*, *19*(4), 445-462. doi: 10.1016/S0742-051X(03)00028-3

Wilkins, J.L.M & Brand, B.R. (2004). Change in preservice teachers’ beliefs: an evaluation of a mathematics methods course. *School Science and Mathematics*, *104*(5), 226-232. doi: 10.1111/j.1949-8594.2004.tb18245.x

Winsløw, C. (2003). Semiotic and discursive variables in CAS-based didactical engineering. *Educational Studies in Mathematics*, *52*(3), 271-288. doi: 10.1023/A:1024201714126