Opportunities for learning given to prospective mathematics teachers: between ritual and explorative instruction

Adler, J., Ball, D., Krainer, K., Lin, F. L., & Novotna, J. (2005). Reflections on an emerging field: Researching mathematics teacher education. Educational Studies in Mathematics, 60(3), 359–381. doi:10.1007/s10649-005-5072-6. Ashcraft, M., Krause, J., & Hopko, D. (2007). Is math anxiety a mathematical learning disability. In Why is math so hard for some children (pp. 329–348). Baltimore: Paul H Brooks. Retrieved from http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:Is+math+anxiety+a+mathematical+learning+disability?#0 Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449. doi:10.1086/461626. Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. doi:10.1037/0033-295X.84.2.191. Beilock, S. L., Gunderson, E. A., Ramirez, G., & Levine, S. C. (2010). Female teachers’ math anxiety affects girls’ math achievement. Proceedings of the National Academy of Sciences of the United States of America, 107(5), 1860–1863. doi:10.1073/pnas.0910967107. Bill, V. L., Leer, M. N., LE Reams, & Resnick, L. B. (1992). From cupcakes to equations: The structure of discourse in a primary mathematics classroom. Verbum, 1(2), 63–85. Blackwell, L. S., Trzesniewski, K. H., & Dweck, C. S. (2007). Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. Child Development, 78(1), 246–263. doi:10.1111/j.1467-8624.2007.00995.x. Blanton, M. L. (2002). Using an undergraduate geometry course to challenge prospective teachers’ notions of discourse. Journal of Mathematics Teacher Education, 5(2), 117–152. doi:10.1023/A:1015813514009. Blömeke, S., Suhl, U., Kaiser, G., & Döhrmann, M. (2012). Family background, entry selectivity and opportunities to learn: What matters in primary teacher education? An international comparison of fifteen countries. Teaching and Teacher Education, 28(1), 44–55. doi:10.1016/j.tate.2011.08.006. Boaler, J., & Greeno, J. (2000). Identity, agency, and knowing in mathematics worlds. In J. Boaler (Ed.), Multiple perspectives on mathematics education (pp. 171–200). Westport, CT: Ablex. Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. The Teachers College Record, 110(3), 608–645. Retrieved from http://www.tcrecord.org/Content.asp?contentid=14590 Boston, M. D. (2012). Assessing instructional quality in mathematics. The Elementary School Journal, 113(1), 76–104. Boston, M. D., & Smith, M. S. (2009). Transforming secondary mathematics teaching: Increasing the cognitive demands of instructional tasks used in teachers’ classrooms. Journal for Research in Mathematics Education, 40(2), 119–156. Retrieved from http://www.jstor.org/stable/40539329 Boston, M. D., & Smith, M. S. (2011). A “task-centric approach” to professional development: Enhancing and sustaining mathematics teachers’ ability to implement cognitively challenging mathematical tasks. ZDM, 43(6–7), 965–977. doi:10.1007/s11858-011-0353-2. Brown, P., & Levinson, S. (1987). Politeness: Some universals in language. Cambridge: Cambridge University Press. Retrieved from http://scholar.google.com/scholar?q=brown+levinson+politeness&btnG=&hl=iw&as_sdt=0,5#0 Brown, T., & McNamara, O. (2011). Becoming a mathematics teacher, (2008), 31–48. doi:10.1007/978-94-007-0554-8. Brown, T., McNamara, O., Hanley, U. N. A., & Jones, L. I. Z. (1999). Primary student teachers’ understanding of mathematics and its teaching. British Educational Research Journal, 25(3), 299–322. Brownlee, J., Purdie, N., & Boulton-Lewis, G. (2001). Changing epistemological beliefs in prospective teacher education students. Teaching in Higher Education, 6(2), 247–268. Bursal, M., & Paznokas, L. (2006). Mathematics anxiety and prospective elementary teachers’ confidence to teach mathematics and science. School Science and Mathematics, 104(6), 173–180. Chapin, S. H., O’Connor, C., & Anderson, N. (2009). Classroom discussions: Using math talk to help students learn, grades K-6. 2009. Math Solutions. Retrieved from http://books.google.com/books?hl=iw&lr=&id=2NX4I6mekq8C&oi=fnd&pg=PR15&dq=sarah+michaels+catherine+o’connor+nancy&ots=4W3FYxrjB4&sig=ubfPNY0skac15MuPWyc2YwHQqkU Chazan, D., & Ball, D. (1999). Beyond being told not to tell. For the Learning of Mathematics, 19(2), 2–10. doi:10.2307/40248293. Chi, M. T. H. (1997). Quantifying qualitative analyses of verbal data: A practical guide. The Journal of the Learning Sciences, 6(3), 271–315. Retrieved from http://www.tandfonline.com/doi/abs/10.1207/s15327809jls0603_1 Clarke, S. N. (2015). The right to speak. In L. B. Resnick, C. A. Asterhan, & S. N. Clarke (Eds.), Socializing intelligence through academic talk and dialogue. Washinton, D.C.: American Educational Research Association. Cobb, P., Yackel, E., & Wood, T. (2011). Young children’s emotional acts while engaged in mathematical problem solving. In E. Yackel, K. Gravermeijer, & A. Sfard (Eds.), A journey in mathematics education research: Insights from the work of Paul Cobb (pp. 117–148). Dordrecht: Springer. Dweck, C. (2000). Self-theories: Their role in motivation, personality, and development 2000. Lillington, NC: Taylor & Francis. Eggins, S., & Slade, D. (1997). Analysing casual conversation. Cassel: London & New York. Esmonde, I., Brodie, K., Dookie, L., & Takeuchi, M. (2009). Social identities and opportunities to learn: Student perspectives on group work in an urban mathematics classroom. Journal of Urban Mathematics Education, 2(2), 18–45. Retrieved from https://tspace.library.utoronto.ca/handle/1807/32194 Even, R., & Ball, D. L. (Eds.). (2009). The Professional education and development of teachers of mathematics—The 15th ICMI study (Vol. 11). Springer. doi:10.1007/978-0-387-09601-8 Frykholm, J. A. (1996). Prospective teachers in mathematics: Struggling with the standards. Teaching and Teacher Education, 12(6), 665–681. doi:10.1016/S0742-051X(96)00010-8. Frykholm, J. A. (1999). The impact of reform: Challenges for mathematics teacher preparation. Journal of Mathematics Teacher Education, 2, 79–105. doi:10.1023/A:1009904604728. Gresalfi, M. (2009). Taking up opportunities to learn: Constructing dispositions in mathematics classrooms. The Journal of the Learning Sciences, 18(3), 327–369. Gresham, G. (2007). A study of mathematics anxiety in prospective teachers. Early Childhood Education Journal, 35(2), 181–188. doi:10.1007/s10643-007-0174-7. Hannula, M. S. (2012). Exploring new dimensions of mathematics-related affect: Embodied and social theories. Research in Mathematics Education, 14(2), 137–161. Harper, N. W., & Daane, C. J. (1998). Causes and reduction of math anxiety in prospective elementary teachers. Action in Teacher Education, 19(4), 29–38. Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21(1), 33–46. Retrieved from http://www.jstor.org/stable/10.2307/749455 Henningsen, M., & Stein, M. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549. Retrieved from http://www.jstor.org/stable/749690 Herbel-Eisenmann, B., & Cirillo, M. (Eds.). (2009). Promoting purposeful discourse: Teacher research in mathematics classrooms. Reston: NCTM. Heyd-Metzuyanim, E. (2013). The co-construction of learning difficulties in mathematics—Teacher–student interactions and their role in the development of a disabled mathematical identity. Educational Studies in Mathematics, 83(3), 341–368. Heyd-Metzuyanim, E. (2015). Vicious cycles of identifying and mathematizing—A case study of the development of mathematical failure. Journal of the Learning Sciences. doi:10.1080/10508406.2014.999270. Heyd-Metzuyanim, E., & Sfard, A. (2012). Identity struggles in the mathematics classroom: On learning mathematics as an interplay of mathematizing and identifying. International Journal of Educational Research, 51–52, 128–145. Horn, I. S. (2007). Fast kids, slow kids, lazy kids: Framing the mismatch problem in mathematics teachers’ conversations. Journal of the Learning Sciences, 16(1), 37–79. doi:10.1080/10508400709336942. Huang, Y. (2007). Pragamatics. Oxford: Oxford University Press. Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35(2), 81. doi:10.2307/30034933. Kapur, M., & Bielaczyc, K. (2012). Designing for productive failure. Journal of the Learning Sciences, 21(1), 45–83. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Book Reviews, 34, 6. Lampert, M. (1990). When the problem is no the question and the solution is not the answer: Mathematical knowing and teaching. American Eductaional Research Journal, 27, 29–63. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. New York: Cambridge University Press. Leder, G., & Forgasz, H. J. (2006). Affect and mathematics education. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 403–427). Rotterdam: Sense Publishers. Lerman, S. (2000). The social turn in mathematics education. In J. Boaler (Ed.), Multiple perspective on mathematics education (pp. 19–44). Westport, CT: Ablex. Malinsky, M., Ross, A., Pannells, T., & McJunkin, M. (2006). Math anxiety in prospective elementary school teachers. Education, 127(2), 274–279. Retrieved from http://eric.ed.gov/ERICWebPortal/recordDetail?accno=EJ765826 McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York: Macmillan Publishing Company. Meece, J. L., Wigfield, A., & Eccles, J. S. (1990). Predictors of math anxiety and its influence on young adolescents’ course enrollment intentions and performance in mathematics. Journal of Educational Psychology, 82(1), 60–70. Retrieved from http://doi.apa.org/getdoi.cfm?doi=10.1037/0022-0663.82.1.60 Nasir, N. S., & Hand, V. (2008). From the court to the classroom: Opportunities for engagement, learning, and identity in basketball and classroom mathematics. The Journal of the Learning Sciences, 17, 143–179. Nathan, M. J., Eilam, B., & Kim, S. (2007). To disagree, we must also agree: How intersubjectivity structures and perpetuates discourse in a mathematics classroom. Journal of the Learning Sciences, 16(4), 523–563. doi:10.1080/10508400701525238. Oliveira, H., & Hannula, M. S. (2008). Individual prospective mathematics teachers—Studies on their professional growth. In the international handbook of mathematics teacher education (Vol. 3, pp. 13–33). Retrieved from http://www.ie.ul.pt/pls/portal/docs/1/298339.PDF Pekrun, R., Goetz, T., Titz, W., & Perry, R. (2002). Academic emotions in students’ self-regulated learning and achievement: A program of qualitative and quantitative research. Educational Psychologist, 37(2), 91–105. doi:10.1207/S15326985EP3702. Rowland, T., Turner, F., & Thwaites, A. (2014). Research into teacher knowledge: A stimulus for development in mathematics teacher education practice. ZDM, 46(2), 317–328. doi:10.1007/s11858-013-0564-9. Sfard, A. (2008). Thinking as communicating. New York: Cambridge University Press. Sfard, A., & Lavie, I. (2005). Why cannot children see as the same what grown-ups cannot see as different?—Early numerical thinking revisited. Cognition and Instruction, 23(2), 237–309. Sfard, A., & Prusak, A. (2005). Telling identities: In search of an analytic tool for investigating learning as a culturally shaped activity. Educational Researcher, 34(4), 14–22. Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. Reston, VA: National Council of Teachers of Mathematics. 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, 313–340. Retrieved from http://www.tandfonline.com/doi/abs/10.1080/10986060802229675 Stein, M. K., Grover, B. R., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488. Retrieved from http://aer.sagepub.com/content/33/2/455.short Stein, M. K., Smith, M. S., Henningsen, M., & Silver, E. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York, NY: Teachers College Press. Retrieved from http://www.eric.ed.gov/ERICWebPortal/recordDetail?accno=ED442659 Tatto, M. T., & Senk, S. (2011). The mathematics education of future primary and secondary teachers: Methods and findings from the Teacher Education and Development Study in Mathematics. Journal of Teacher Education, 62(2), 121–137. doi:10.1177/0022487110391807. Trask, R. (1999). Key concepts in language and linguistics. London & New York: Routledge. Trujillo, K., & Hadfield, O. (1999). Tracing the roots of mathematics anxiety through in-depth interviews with prospective elementary teachers. College Student Journal, 33(2). Retrieved from http://www.freepatentsonline.com/article/College-Student-Journal/62839422.html Uusimaki, L., & Nason, R. (2004). Causes underlying prospective teachers’ negative beliefs and anxieties about mathematics. In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 369–376). Retrieved from http://www.emis.ams.org/proceedings/PME28/RR/RR141_Uusimaki.pdf Vacc, N. N., & Bright, G. W. (1999). Elementary prospective teachers’ changing beliefs and instructional use of children’s mathematical thinking. Journal for Research in Mathematics Education, 30(1), 89–110. doi:10.2307/749631. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. Wagner, D. (2007). Students’ critical awareness of voice and agency in mathematics classroom discourse. Mathematical Thinking and Learning, 9(1), 31–50. Retrieved from http://www.tandfonline.com/doi/abs/10.1080/10986060709336604 Walshaw, M. (2004). Prospective mathematics teaching in the context of schools: An exploration into the constitution of identity. Journal of Mathematics Teacher Education, 7(1), 63–86. doi:10.1023/B:JMTE.0000009972.30248.9c. Watts, R. J. (2003). Politeness. Cambridge: Cambridge University Press. Weinberger, A., & Fischer, F. (2006). A framework to analyze argumentative knowledge construction in computer-supported collaborative learning. Computers and Education, 46(1), 71–95. Retrieved from http://linkinghub.elsevier.com/retrieve/pii/S0360131505000564 Yackel, E., Cobb, P., & Wood, T. (1991). Small-group interactions as a source of learning opportunities in second-grade mathematics. Journal for Research in Mathematics Education, 22(5), 390–408. Retrieved from http://www.jstor.org/stable/749187