Table of Contents Author Guidelines Submit a Manuscript
Education Research International
Volume 2019, Article ID 7426959, 20 pages
https://doi.org/10.1155/2019/7426959
Research Article

Preservice Teachers’ Learning to Respond on the Basis of Children’s Mathematical Understanding

1UW-Green Bay, Green Bay, WI 54311, USA
2Iowa State University, Ames, IA 50011, USA

Correspondence should be addressed to Mary Gichobi; moc.liamg@1akojnrm

Received 8 August 2018; Revised 9 March 2019; Accepted 10 April 2019; Published 2 May 2019

Academic Editor: Yi-Shun Wang

Copyright © 2019 Mary Gichobi and Alejandro Andreotti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Allen, Eight Questions on Teacher Preparation: What Does the Research Say? Education Commission of the States, Denver, CO, USA, 2003.
  2. S. Blömeke, F.-J. Hsieh, G. Kaiser, and W. H. Schimidt, International Perspectives on Teacher Knowledge Beliefs and Opportunities TEDS-M Results, Springer, Berlin, Germany, 2014.
  3. Conference Board of Mathematical Sciences (CBMS), The Mathematics Education for Teacher II Issues in Mathematics Education, vol. 17, American Mathematical Society and Mathematical Association of America, Providence, RI, USA, 2012.
  4. Association of Mathematics Teacher Educators (AMTE), Standards for Preparing Teachers of Mathematics, 2017, http://amte.net/standards.
  5. National Council for Accreditation of Teacher Education (NCATE), Transforming teacher education through clinical experience: A national strategy to prepare effective teachers Report of the Blue-Ribbon Panel on Clinical Preparation and Partnership for Improved Student Learning, 2010, http://www.ncate.org/.
  6. M. E. Strutchens, R. Huang, L. Losano, and D. Potari, The Mathematics Education of Prospective Secondary Teachers Around the World, Springer International Publishing AG Switzerland, Cham, Switzerland, 2016.
  7. M. T. Tatto, J. Schwille, S. Senk, L. Ingvarson, R. Peck, and G. Rowley, “Teacher Education and Development Study in Mathematics (TEDS-M): policy, practice, and readiness to teach primary and secondary mathematics,” in Conceptual Framework, Teacher Education and Development International Study Center, College of Education, Michigan State University, East Lansing, MI, USA, 2008. View at Google Scholar
  8. D. Ball, L. Sleep, T. Boerst, and H. Bass, “Combining development of practice and the practice of development of teacher education,” Elementary School Journal, vol. 109, no. 5, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. M. Cochran-Smith and K. Zeichner, Studying Teacher Education: The Report of AERA Panel on Research and Teacher Education, American Educational Research Association Lawrence Erlbaum Associates, Inc., Washington, DC, USA, 2005.
  10. P. Grossman and M. McDonald, “Back to the future: directions for research in teaching and teacher education,” American Educational Research Journal, vol. 45, no. 1, pp. 184–205, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. J. Hiebert and A. K. Morris, “Building a knowledge base for teacher education: an experience in K-8 mathematics teacher preparation,” Elementary School Journal, vol. 109, no. 5, pp. 475–490, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. M. McDonald, E. Kazemi, and S. S. Kavanagh, “Core practices and pedagogies of teacher education,” Journal of Teacher Education, vol. 64, no. 5, pp. 378–386, 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. A. K. Morris, J. Hiebert, and S. Spitzer, Mathematics Knowledge for Teaching and Planning and Evaluating Instruction: What Can Pre-Service Teachers Learn? The National Council of Teachers of Mathematics, Inc., Reston, VA, USA, 2009, http://www.nctm.org.
  14. T. G. Bartell, C. Webel, B. Bowen, and N. Dyson, “Prospective teacher learning: recognizing evidence of conceptual understanding,” Journal of Mathematics Teacher Education, vol. 16, no. 1, pp. 57–79, 2013. View at Publisher · View at Google Scholar · View at Scopus
  15. A. R. McDuffie, M. Q. Foote, C. Bolson et al., “Using video analysis to support prospective K-8 teachers’ noticing of students’ multiple mathematical knowledge bases,” Journal of Mathematics Teacher Education, vol. 17, pp. 245–270, 2013. View at Publisher · View at Google Scholar · View at Scopus
  16. J. R. Star and S. K. Strickland, “Learning to observe: using video to improve preservice mathematics teachers’ ability to notice,” Journal of Mathematics Teacher Education, vol. 11, no. 2, pp. 107–125, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. D. Teuscher, K. R. Leathan, and B. Peterson, “From a framework to a lens: learning to notice students mathematical thinking,” in Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks, O. Schack, M. H. Fisher, and J. A. Wilhelm, Eds., Springer International Publishing AG, Basel, Switzerland, 2017. View at Google Scholar
  18. L. S. Shulman, “Those who understand teaching: knowledge growth in teaching,” Educational Researcher, vol. 57, no. 1, pp. 1–22, 1986. View at Google Scholar
  19. R. Marks, “Pedagogical content knowledge: from a mathematical case to a modified conception,” Journal of Teacher Education, vol. 41, no. 3, pp. 3–11, 1990. View at Publisher · View at Google Scholar · View at Scopus
  20. T. Carpenter, E. Fennema, and M. Franke, “Cognitively guided instruction: a knowledge base for reform in primary mathematics instruction,” Elementary School Journal, vol. 97, no. 1, pp. 3–20, 1996. View at Google Scholar
  21. V. R. Jacobs, L. C. Lamb, and R. A. Philipp, “Professional noticing of children’s mathematical thinking,” Journal of Research in Mathematics Education, vol. 41, no. 2, pp. 169–202, 2010. View at Google Scholar
  22. M. L. Franke, E. Kazemi, and D. Battey, “Understanding teaching and classroom practice in mathematics,” in Second Handbook of Research on Mathematics Teaching and Learning, F. Lester Jr., Ed., pp. 225–256, Information Age, Charlotte, NC, USA, 2007. View at Google Scholar
  23. M. Franke and E. Kazemi, “Learning to teach mathematics: focus on students thinking,” Theory into Practice, vol. 40, no. 2, pp. 102–109, 2001. View at Publisher · View at Google Scholar · View at Scopus
  24. V. R. Jacobs, M. L. Franke, T. P. Carpenter, L. Levi, and D. Battey, “Professional development focused on children’s algebraic reasoning in elementary schools,” Journal for Research in Mathematics Education, vol. 38, no. 3, pp. 258–288, 2007. View at Google Scholar
  25. A. Sfard and C. Kieran, “Cognition as communication: rethinking learning-by-talking through multi-faceted analysis of students’ mathematical interactions,” Mind, Culture, and Activity, vol. 8, no. 1, pp. 42–76, 2001. View at Publisher · View at Google Scholar · View at Scopus
  26. J. Fraivillig, “Strategies for advancing children’s mathematics understanding,” Teaching Children Mathematics, vol. 7, no. 8, pp. 1–6, 2001. View at Google Scholar
  27. T. Barnhart and E. Van Es, “Studying teacher noticing: examining the relationship among pre-service science teachers’ ability to attend, analyze and respond to student thinking,” Teaching and Teacher Education, vol. 45, pp. 83–93, 2015. View at Publisher · View at Google Scholar · View at Scopus
  28. P. Grossman, C. Compton, D. Igra, M. Ronfeldt, E. Shahan, and P. W. Williamson, “Teaching practice: a cross-professional perspective,” Teachers College Record, vol. 111, no. 9, pp. 2055–2100, 2009. View at Google Scholar
  29. J. Mason, Researching Your Own Practice: The Discipline of Noticing, Routledge-Falmer, London, UK, 2002.
  30. V. R. Jacobs and R. C. Ambrose, “Making the most of the story problems,” Teaching Children Mathematics, vol. 15, pp. 260–266, 2008. View at Google Scholar
  31. M. Sherin and E. Van Es, “Using videos to support teachers’ ability to notice teachers’ interactions,” Journal of Technology and Teacher Education, vol. 13, no. 3, 2005. View at Google Scholar
  32. E. Van Es and M. Sherin, “How different video club designs support teachers in learning ‘to notice’,” Journal of Computing in Teacher Education, vol. 22, pp. 571–596, 2007. View at Google Scholar
  33. J. Kaste, “Scaffolding through cases: diverse constructivist teaching in the literacy methods course,” Teaching and Teacher Education, vol. 20, Article ID 31e45, 2004. View at Publisher · View at Google Scholar · View at Scopus
  34. L. S. Vygotsky, Mind in Society, Harvard University Press, Cambridge, MA, USA, 1978.
  35. D. Wood, J. S. Bruner, and G. Ross, “The role of tutoring in problem solving,” Journal of Psychology and Psychiatry, vol. 17, no. 2, pp. 89–100, 1976. View at Publisher · View at Google Scholar · View at Scopus
  36. L. Sleep and T. Boerst, “Preparing beginning teachers to elicit and interpret students’ mathematical thinking,” Teaching and Teacher Education, vol. 28, no. 7, pp. 1038–1048, 2011. View at Publisher · View at Google Scholar · View at Scopus
  37. L. Van Zoest and S. Stockero, “Synergistic scaffolds as a means to support pre-service teacher learning,” Teaching and Teacher Education, vol. 23, no. 8, pp. 2038–2048, 2008. View at Publisher · View at Google Scholar · View at Scopus
  38. D. Holton and D. Clarke, “Scaffolding and metacognition,” International Journal of Mathematical Education in Science and Technology, vol. 37, no. 2, pp. 127–143, 2006. View at Publisher · View at Google Scholar · View at Scopus
  39. I. Tabak, “Synergy: a complement to emerging patterns of distributed scaffolding,” Journal of the Learning Sciences, vol. 13, no. 3, pp. 305–335, 2004. View at Publisher · View at Google Scholar · View at Scopus
  40. S. Empson, “Responsive teaching from the inside out: teaching base ten to younger children,” Investigations in Mathematics Learning, vol. 7, no. 1, pp. 23–53, 2014. View at Publisher · View at Google Scholar
  41. N. Golafshani, “Understanding reliability and validity in qualitative research,” Qualitative Report, vol. 8, no. 4, pp. 597–607, 2003. View at Google Scholar
  42. H. K. Klein and M. D. Myers, “A set of principles for conducting and evaluating interpretive field studies in information systems,” MIS Quarterly, vol. 23, no. 1, pp. 67–94, 1999. View at Publisher · View at Google Scholar
  43. G. Walsham, “Interpretive case studies in IS research: nature and method,” European Journal of Information Systems, vol. 4, no. 2, pp. 74–81, 1995. View at Publisher · View at Google Scholar · View at Scopus
  44. M. T. H. Chi, “Quantifying qualitative analyses of verbal data: a practical guide,” Journal of the Learning Sciences, vol. 6, no. 3, pp. 271–315, 1997. View at Publisher · View at Google Scholar · View at Scopus
  45. M. Miles and A. M. Huberman, Qualitative Data Analysis, SAGE, Thousand Oaks, CA, USA, 2nd edition, 1994.
  46. M. S. Smith and M. K. Stein, “Selecting and creating mathematical tasks: from research to practice,” Mathematics Teaching in Middle School, vol. 3, pp. 344–350, 1998. View at Google Scholar
  47. M. K. Stein and M. S. Smith, “Mathematical tasks as a framework for reflection: from research to practice,” Mathematics Teaching in the Middle School, vol. 3, no. 4, pp. 268–275, 1998. View at Google Scholar
  48. J. Creswell and D. Miller, “Determining validity of qualitative research,” Theory into Practice, vol. 39, no. 1, 2000. View at Publisher · View at Google Scholar
  49. T. P. Carpenter, E. Fennema, M. L. Franke, L. Levi, and S. B. Empson, Children’s Mathematics: Cognitively Guided Instruction, Heinemann, Portsmouth, NH, USA, 1999.
  50. National Mathematics Advisory Panel, Foundations for Success: The Final Report of the National Mathematics Advisory Panel, U.S. Department of Education, Washington, DC, USA, 2008.
  51. P. Grossman, K. Hammerness, and M. McDonald, “Redefining teaching, re-imagining teacher education,” Teachers and Teaching, vol. 15, no. 2, pp. 273–289, 2009. View at Publisher · View at Google Scholar · View at Scopus
  52. M. Henningsen and M. K. Stein, “Mathematical tasks and student cognition: classroom-based factors that support and inhibit high-level mathematical thinking and reasoning,” Journal for Research in Mathematics Education, vol. 28, no. 5, pp. 524–549, 1997. View at Publisher · View at Google Scholar · View at Scopus
  53. J. Hiebert, T. P. Carpenter, E. Fennema et al., Making Sense: Teaching and Learning Mathematics with Understanding, vol. 361, Heinemann, Portsmouth, NH, USA, 1997.
  54. J. Hiebert and D. Wearne, “Instructional tasks, classroom discourse, and students’ learning in second-grade Arithmetic,” American Educational Research Journal, vol. 30, no. 2, pp. 393–425, 1993. View at Publisher · View at Google Scholar
  55. J. Houssart, “Simplification and repetition of mathematical tasks: a recipe for success or failure?” Journal of Mathematical Behavior, vol. 21, no. 2, pp. 191–202, 2002. View at Publisher · View at Google Scholar · View at Scopus
  56. National Council for Teachers of Mathematics, Principals and Standards for School Mathematics, Reston, VA, USA, 2000.
  57. M. K. Stein, M. S. Smith, M. A. Henningsen, and E. A. Silver, Implementing Standards Based Mathematics Instruction: A Casebook for Professional Development, Teachers College Press, New York, NY, USA, 2000.
  58. A. J. Stylianides and G. J. Stylianides, “Studying the classroom implementation of tasks: high-level mathematical tasks embedded in ‘real-life’ contexts,” Teaching and Teacher Education, vol. 24, no. 4, pp. 859–875, 2008. View at Publisher · View at Google Scholar · View at Scopus
  59. S. Crespo, “Learning to pose mathematical problems: exploring changes in pre-service teachers practices,” Educational Studies in Mathematics, vol. 52, no. 3, pp. 243–270, 2003. View at Publisher · View at Google Scholar · View at Scopus
  60. A. Norton and Z. Rutledge, “Measuring task posing cycles: mathematical letter writing between algebra students and pre-service teachers,” Mathematics Teacher Educator, vol. 19, no. 1, pp. 32–45, 2006. View at Google Scholar
  61. Z. Rutledge and N. Norton, “Pre-service teachers mathematical task posing: an opportunity for coordination of perspectives,” Mathematics Educator, vol. 18, no. 1, pp. 31–40, 2008. View at Google Scholar