References
- Crouch R, Haines C. Mathematical modelling: transitions between the real world and the mathematical world. Int J Math Educ Sci Technol. 2004;35(2):146–178.
- Stillman GA, Blum W, Biembengut MS. Mathematical modelling in educational research and practice: cultural, social and cognitive influences. Cham: Springer; 2015.
- Houston K. Teaching modelling as a way of life. Quaest Math – J S Afr Math Soc. 2001;(1):105–113.
- Li T. Mathematical education is the most important interface between mathematics and industry. In: Damlamian A, Rodrigues JF, Sträßer R, editors. Educational interfaces between mathematics and industry. Cham: Springer International; 2013. p. 51–58.
- Pais A. Portrait of an influence. In: AlrØ H, Ravn O, Valero P, editors. Critical mathematics education: past, present and future. Rotterdam: Sense; 2010. p. 133–144.
- Common Core State Standards Initiative (CCSSI). Common core state standards for mathematics. Washington (DC): National Governors Association Center for Best Practices and the Council of Chief State School Officers; 2010. Available from: http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
- Bracke M, Geiger A. Real-world modelling in regular lessons. In: Kaiser G, Blum W, Borromeo Ferri R, Stillman G, editors. Trends in teaching and learning of mathematical modelling. New York (NY): Springer; 2011. p. 529–549.
- Houston K, Maher G, Wood L, et al. Is there Life after modelling? Student conceptions of mathematics. Math Educ Res J. 2010;22(2):69–80.
- Martin F. Phenomenography: exploring different conceptions of reality. New York (NY): Praeger; 1988.
- English L. Mathematical modelling with young learners. In: Lamon SJ, Parker WA, Houston SK, editors. Mathematical modelling: a way of life. Chichester: Horwood; 2003. p. 4–14.
- Stillman G, Brown J. Evidence of implemented anticipation in mathematizing by beginning modellers. Math Educ Res J. 2014;26(4):763–789.
- Daher W. Discursive positionings and emotions in modelling activities. Int J Math Educ Sci Technol. 2015;46(8):1149–1164.
- Magiera MT, Zawojewski JS. Characterizations of social-based and self-based contexts associated with students’ awareness, evaluation, and regulation of their thinking during small-group mathematical modelling. J Res Math Educ. 2011;42(5):486–520.
- Mercer N. Words & minds. London: Routledge; 2000.
- Hunter R. Coming to “know’ mathematics through being scaffolded to ‘talk and do’ mathematics. Int J Math Teach Learn [Internet]. 2012;14(Dec):12 [ cited 2016 Feb 28]. Available from: http://www.cimt.plymouth.ac.uk/journal/hunter2.pdf
- Kaiser G, van der Kooj H, Wake G. Educational interfaces between mathematics and industry at school level. In: Damlamian A, Rodrigues JF, Sträßer R, editors. Educational interfaces between mathematics and industry. Cham: Springer International; 2013. p. 263–270.
- Stillman G, Brown J, Geiger V. Facilitating mathematisation in modelling by beginning modellers in secondary school. In: Stillman GA, Blum W, Biembengut MS, editors. Mathematical modelling in educational research and practice: cultural, social and cognitive influences. Cham: Springer; 2015. p. 93–114.
- Mason J. Modelling modelling: where is the centre of gravity of-for-when teaching modelling? In: Matos JF, Blum W, Houston SK, Carreira S, editors. Modelling and mathematics education. Chichester: Horwood; 2001. p. 39–61.
- Lesh R, English L, Sevis S, et al. Modeling as a means for making powerful ideas accessible to children at an early age. In: Hegedus S, Roschelle J, editors. The SimCalc vision and contributions: democratizing access to important mathematics. Dordrecht: Springer; 2013. p. 419–436.
- Borromeo Ferri R. Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt Didaktik Math. 2006;38(2):87–95.
- Haines C, Crouch R. Remarks on a modelling cycle and interpreting behaviours. In: Lesh R, Galbraith PL, Haines CR, Hurford A, editors. Modeling students’ mathematical modelling competencies. New York (NY): Springer; 2010. p. 145–154.
- Mason J. Modelling: what do we really want students to learn? In: Berry JS, Burghes DN, Huntley ID, James DJD, Moscardini AO, editors. Teaching and applying mathematical modelling. Chichester: Ellis Horwood; 1984. p. 215–234.
- Halmos PR. Naïve set theory. Princeton (NJ): Van Nostrand; 1960.
- Galbraith P, Stillman G, Brown J, et al. A framework for success in implementing mathematical modelling in the secondary classroom. In: Watson J, Beswick K, editors. Mathematics: essential research, essential practice. Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, Hobart. Adelaide: MERGA; 2007.
- Galbraith P, Stillman G, Brown J. Identifying key transition activities for enhanced engagement in mathematical modelling. In: Grootenboer P, Zevenbergen R, Chinnappan M, editors. Identities, cultures and learning spaces. Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, Canberra. Adelaide: MERGA; 2006.
- Lehrer R, Schauble L. What kind of explanation is a model? In: Stein MK, Kucan L, editors. Instructional explanations in the disciplines. New York (NY): Springer; 2010. p. 9–22.
- Niss M. Models and modelling in mathematics education. EMS Newslett. 2012(Dec):49–52.
- Lesh R, Caylor B. Introduction to the special issue: modeling as application versus modeling as a way to create mathematics. Int J Comput Math Learn. 2007;12(3):173–194.
- Niss M. Modeling a crucial aspect of students’ mathematical modelling. In: Lesh R, Galbraith PL, Haines CR, Hurford A, editors. Modeling students’ mathematical modelling competencies. New York (NY): Springer; 2010. p. 43–60.
- Brown JP. Inducting year 6 students into “a culture of mathematizing as a practice”. In: Stillman GA, Kaiser G, Blum W, Brown JP, editors. Teaching mathematical modeling: connecting to research and practice. Dordrecht: Springer; 2013. p. 295–305.
- Kuntze S. In-service and prospective teachers’ views about modeling tasks in the mathematics classroom—results of a qualitative empirical study. In: Kaiser G, Blum W, Borromeo Ferri R, Stillman GA, editors. Trends in the teaching and learning of mathematical modeling. Dordrecht: Springer; 2011. p. 279–288.
- Pellegrino JW, Hilton ML, editors. Education for life and work: developing transferable knowledge and skills in the 21st century. Washington (DC): National Academies Press; 2012.
- Shimizu Y, Williams G. Studying learners in intercultural contexts. In: Clements K, Bishop AJ, Kilpatrick J, et al., editors. Third international handbook in mathematics education. New York (NY): Springer; 2013. p. 145–168.
- Clarke D, Roche A, Wilkie K, et al. Demonstration lessons in mathematics education: teachers’ observation foci and intended changes in practice. Math Educ Res J. 2013;25(2):207–230.
- Stake R. Qualitative case studies. In: Denzin N, Lincoln, Y, editors. The Sage handbook of qualitative research. 2nd ed. Thousand Oaks (CA): Sage; 2005. p. 443–466.
- Corbin J, Strauss A. Basics of qualitative research. 3rd ed. Thousand Oaks (CA): Sage; 2008.
- Witzel A, Reiter H. The problem-centered interview. London: Sage; 2012.
- Stillman G. Impact of prior knowledge of task context on approaches to applications tasks. J Math Behav. 2000;19(3):333–361.
- Bauersfeld H. Classroom cultures from a social constructivist's perspective. Educ Stud Math. 1992;23:467–481.
- Imm K, Larber M. The footprint problem: a pathway to modeling. Math Teach Middle School. 2013;19(1):46–54.