436
Views
3
CrossRef citations to date
0
Altmetric
Articles

Pre-service secondary mathematics teachers’ anticipation and identification of students’ thinking in the context of modelling problems

ORCID Icon & ORCID Icon
Pages 208-236 | Received 06 Jan 2019, Published online: 27 Sep 2019

References

  • Antonius, S., Haines, C., Jensen, T. H., Niss, M., & Burkhardt, H. (2007). Classroom activities and the teacher. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss, (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 295–308). New York, NY: Springer.
  • Asquith, P., Stephens, A. C., Knuth, E. J., & Alibali, M. W. (2007). Middle school mathematics teachers’ knowledge of students’ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249–272. doi: 10.1080/10986060701360910
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. doi: 10.1177/0022487108324554
  • Bartell, T. G., Webel, C., Bowen, B., & Dyson, N. (2013). Prospective teacher learning: Recognizing evidence of conceptual understanding. Journal of Mathematics Teacher Education, 16(1), 57–79. doi: 10.1007/s10857-012-9205-4
  • Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In: S. J. Cho (Ed.), The proceedings of the 12th international congress on mathematical education, 2012 July 8–15; Seoul, Korea (pp.73–96). New York, NY: Springer.
  • Blum, W., & Borromeo-Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45–58.
  • Borromeo-Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(3), 86–95. doi: 10.1007/BF02655883
  • Borromeo-Ferri, R. (2007). Teachers' ways of handling modelling problems in the classroom – what we can learn from a cognitive-psychological point of view. In: C. Bergsten, & B. Grevholm (Eds.), Developing and researching quality in mathematics teaching and learning. Proceedings of MADIF5, the 5th Swedish mathematics education research seminar, 2006 January 24–25; Malmö, Sweeden (pp. 45–54). Linköping: SMDF.
  • Borromeo-Ferri, R. (2014). Mathematical modeling–The teachers' responsibility. In B. Dickman, & A. Sanfratello (Eds.), Proceedings of conference on mathematical modeling, 2013 October 14; (pp. 26–31). New York, NY: Teachers College Columbia University.
  • Borromeo-Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. New York, NY: Springer.
  • Borromeo-Ferri, R., & Blum, W. (2010). Mathematical modelling in teacher education experiences from a modeling seminar. In: V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the sixth congress of the European society for research in mathematics education, 2009 January 28–February 1 (pp. 2046–2055). Lyon, France: INRP.
  • Borromeo-Ferri, R., & Blum, W. (2013). Barriers and motivations of primary teachers implementing modelling in mathematical lessons. In B. Ubuz, Ç. Haser, & M. A. Mariotti (Eds.), Proceedings of the eighth congress of the European society for research in mathematics education, 2013 February 6–10 (pp. 1000–1010). Ankara, Turkey: Middle East Technical University.
  • Cabana, C., Cooper, J., Dietiker, L., Douglas, L., Gulick, D., Simon, S., & Thomas, E. (2000). College preparatory mathematics 5: Calculus. Sacramento, CA: CPM Educational Program.
  • Carlson, M., Larsen, S., & Lesh, R. (2003). Integrating models and modeling perspective with existing research and practice. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning, and teaching (pp. 465–478). Mahwah, NJ: Lawrence Erlbaum.
  • Doerr, H. M. (2006). Teachers’ ways of listening and responding to students’ emerging mathematical models. ZDM, 38(3), 255–268. doi: 10.1007/BF02652809
  • Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum, P. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 69–78). New York, NY: Springer.
  • Doerr, H. M., & Lesh, R. (2003). A modeling perspective on teacher development. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: A models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 125–139). Mahwah, NJ: Lawrence Erlbaum.
  • Doerr, H. M., & Lesh, R. (2011). Models and modelling perspectives on teaching and learning mathematics in the twenty-first century. In G. Kaiser, W. Blum, R. Borromeo-Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: ICTMA 14 (pp. 247–268). New York, NY: Springer.
  • English, L. D. (2003). Reconciling theory, research, and practice: A models and modelling perspective. Educational Studies in Mathematics, 54(2&3), 225–248. doi: 10.1023/B:EDUC.0000006167.14146.7b
  • English, L. D., & Doerr, H. M. (2004). Listening and responding to students' ways of thinking. In: I. Putt, R. Faragher, & M. McLean (Eds.), Mathematics education for the third millennium: Towards 2010. Proceedings of the 27th annual conference of the mathematics education research rroup of Australia, 2004 June 27–30 Townsville, Australia (pp. 215–222). Adelaide, Australia: MERGA.
  • Galbraith, P., Stillman, G., & Brown, J. (2006). Identifying key transition activities for enhanced engagement in mathematical modeling. In: P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities, cultures and learning spaces. Proceedings of the 29th annual conference of the mathematics education research group of Australasia, Canberra, ACT Australia; 2006 July 1–5 (pp. 237–245). Adelaide, Australia: MERGA.
  • Haines, C., & Crouch, R. (2007). Mathematical modelling and applications: Ability and competence frameworks. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 417–424). New York, NY: Springer.
  • Intermath. Bouncing Ball [Internet]. Available from http://intermath.org/bouncing-ball/.
  • Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202.
  • Jung, H., & Newton, J. A. (2018). Preservice mathematics teachers’ conceptions and enactments of modeling standards. School Science and Mathematics, 118(5), 169–178. doi: 10.1111/ssm.12275
  • Kaiser, G., Blum, W., Borromeo-Ferri, R., & Stillman, G. (2011). Trends in teaching and learning of mathematical modelling–preface. In G. Kaiser, W. Blum, R. Borromeo-Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 1–5). Dordrecht, The Netherlands: Springer.
  • Kaiser, G., Schwarz, B., & Tiedemann, S. (2010). Future teachers’ professional knowledge on modelling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 433–444). New York, NY: Springer.
  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302–310. doi: 10.1007/BF02652813
  • Koellner-Clark, K., & Lesh, R. (2003). A modeling approach to describe teacher knowledge. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning, and teaching (pp. 159–173). Mahwah, NJ: Lawrence Erlbaum.
  • Lesh, R., Cramer, K., Doerr, H. M., Post, T., & Zawojewski, J. S. (2003). Model development sequences. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning, and teaching (pp. 35–58). Mahwah, NJ: Lawrence Erlbaum.
  • Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: A models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3–33). Mahwah, NJ: Lawrence Erlbaum.
  • Lesh, R., & Kelly, A. (2000). Multitiered teaching experiments. In A. Kelly, & R. Lesh (Eds.), Research design in mathematics and science education (pp. 197–230). Mahwah, NJ: Lawrence Erlbaum.
  • Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2–3), 109–129. doi: 10.1080/10986065.2003.9679996
  • Lewis, C., Perry, R., & Hurd, J. (2004). A deeper look at lesson study. Educational Leadership, 61(5), 6–11.
  • Llinares, S., Fernández, C., & Sánchez-Matamoros, G. (2016). Changes in how prospective teachers anticipate secondary students’ answers. EURASIA Journal of Mathematics, Science and Technology Education, 12(8), 2155–2170.
  • Norton, A., McCloskey, A., & Hudson, R. A. (2011). Prediction assessments: Using video-based predictions to assess prospective teachers’ knowledge of students’ mathematical thinking. Journal of Mathematics Teacher Education, 14(4), 305–325. doi: 10.1007/s10857-011-9181-0
  • Schorr, R., & Lesh, R. (2003). A modelling approach for providing teacher development. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning, and teaching (pp. 141–158). Mahwah, NJ: Lawrence Erlbaum.
  • Şen-Zeytun, A., Çetinkaya, B., & Erbaş, A. K.. (2010). Mathematics teachers' covariational reasoning levels and predictions about students' covariational reasoning abilities. Educational Sciences: Theory and Practice, 10(3), 1601–1612.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. doi: 10.3102/0013189X015002004
  • Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340. doi: 10.1080/10986060802229675
  • Stillman, G., & Brown, J. P. (2011). Pre-service secondary mathematics teachers’ affinity with using modelling tasks in teaching years 8–10. In G. Kaiser, W. Blum, R. Borromeo-Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: ICTMA14 (pp. 289–298). New York, NY: Springer.
  • Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A framework for success in implementing mathematical modelling in the secondary classroom in mathematics. In: J. Watson, & K. Beswick (Eds.), Mathematics: Essential research, essential practice. Proceedings of the 30th annual conference of the mathematics education research group of Australia, 2007 July 2–6; Hobart, Tasmania (pp. 688–707) Adelaide, Australia: MERGA.
  • Stockero, S. L., Rupnow, R. L., & Pascoe, A. E. (2017). Learning to notice important student mathematical thinking in complex classroom interactions. Teaching and Teacher Education, 63, 384–395. doi: 10.1016/j.tate.2017.01.006
  • Swetz, F., & Hartzer, J. S. (1991). Mathematical modeling in the secondary school curriculum: A resource guide of classroom exercises. Reston: NCTM.
  • van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education, 24(2), 244–276. doi: 10.1016/j.tate.2006.11.005

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.