Learning trajectories in teacher education: Supporting teachers' understandings of students' mathematical thinking

Journal of Mathematical Behavior

Volumn 32, Issue 2, 2013, Pages 103-121

  Wilson, P Holt ^a   Mojica, Gemma F ^b   Confrey, Jere ^c  

^a UNIVERSITY OF NORTH CAROLINA AT GREENSBORO   (United States)

^b UNIVERSITY OF NORTH CAROLINA   (United States)

^c NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Learning trajectories; Professional development; Teacher education; Teacher Learning rational numbers

Indexed keywords

EID: 84872540404     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2012.12.003     Document Type: Article

References (67)

1. Ball D. Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education 1990, 21:132-146.
2. Ball D.L., Thames M.H., Phelps G. Content knowledge for teaching: What makes it special?. Journal of Teacher Education 2008, 59(5):389-407.
3. Battista M. Applying cognition-based assessment to elementary school students' development of understanding of area and volume measurement. Mathematical Thinking and Learning 2004, 6(2):185-204.
4. Black M. Models and metaphors: Studies in language and philosophy 1962, Cornell University Press, Ithaca, NY.
5. Bobis J., Clarke B., Clarke D., Thomas G., Wright R., Young-Loveridge J. Supporting teachers in the development of young children's mathematical thinking: Three large scale cases. Mathematics Education Research Journal 2005, 6(3):27-57.
6. Carpenter T., Fennema E., Peterson P., Carey D. Teachers' pedagogical content knowledge of students' problem solving in elementary arithmetic. Journal for Research in Mathematics Education 1988, 19:385-401.
7. Carpenter T., Fennema E., Peterson P., Chaing C., Loef M. Using knowledge of children's mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal 1989, 26(4):499-531.
8. Carpenter T., Fennema E., Franke M. Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. The Elementary School Journal 1996, 97(1):3-20.
9. Carpenter T., Franke M., Jacobs V., Fennema E. A longitudinal study of invention and understanding in children's multidigit addition and subtraction. Journal for Research in Mathematics Education 1998, 29(3):3-20.
10. Council of Chief State School Officers & National Governor's Association Common core state standards initiative standards-setting criteria 2010, Retrieved from http://www.corestandards.org/Files/Criteria.pdf.
11. Clements D., Sarama J. Learning trajectories in mathematics education. Mathematical Thinking and Learning 2004, 6(2):81-89.
12. Clements D., Sarama J. Building blocks 2007, SRA/McGraw-Hill, Columbus, OH.
13. Clements D., Wilson D., Sarama J. Young children's composition of geometric figures: A learning trajectory. Mathematical Thinking and Learning 2004, 6(2):163-184.
14. Cobb P., Steffe L.P. The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education 1983, 14:83-94.
15. Cobb P., Confrey J., diSessa A., Lehrer R., Schauble L. Design experiments in educational research. Educational Researcher 2003, 32(1):9-13.
16. Confrey J. Lear to see children's mathematics: Crucial challenges in constructivist reform. Constructivist perspectives in science and mathematics 1993, 299-321. American Association for the Advancement of Science, Washington, DC. K. Tobin (Ed.).
17. Confrey J. Voice and perspective: Hearing epistemological innovations in student words. Constructivism and education 1998, 152-170. Cambridge University Press, Boston, MA, [English]. M. Larochelle, N. Bednarz, J. Garrison (Eds.).
18. Confrey J. The evolution of design studies as methodology. The Cambridge handbook of the learning sciences 2006, 135-152. Cambridge University Press, New York. R.K. Sawyer (Ed.).
19. Confrey J. A synthesis of the research on rational number reasoning: A learning progressions approach to synthesis. Presentation at the 11th international congress of mathematics instruction 2008.
20. Confrey J. Better measurement of higher-cognitive processes through learning trajectories and diagnostic assessments in mathematics: The challenge in adolescence. The adolescent brain: Learning, reasoning, and decision making 2012, 155-182. American Psychological Association, Washington, DC. V. Reyna, M. Dougherty, S.B. Chapman, J. Confrey (Eds.).
21. Confrey J., Lachance A. Transformative teaching experiments through conjecture-driven research design. Handbook of research design in mathematics and science education 2000, 231-265. Lawrence Erlbaum Associates, Mahwah, NJ. A. Kelly, R. Lesh (Eds.).
22. Confrey, J., & Maloney, A. (in press). Linking mathematics standards to LTs: A case study from North Carolina, 2008-9. In J. Confrey, A. Maloney, & K. Nguyen (Eds.), Learning over time: Learning trajectories in mathematics education. Charlotte, NC: Information Age Publications.
23. Confrey J., Maloney A. Next-generation digital classroom assessment based on learning trajectories. Digital Teaching Platforms: Customizing Classroom Learning for Each Student 2012, 134-152. New York, NY, Teacher's College Press. C. Dede, J. Richards (Eds.).
24. Confrey J., Maloney A., Nguyen K., Mojica G., Myers M. Equipartitioning/splitting as a foundation of rational number reasoning using LTs. Proceedings of the 33rd conference of the International Group for the Psychology of Mathematics Education 2009, Vol. 2:345-352. PME, Thessaloniki, Greece.
25. Confrey J., Maloney A.P., Wilson P.H., Nguyen K.H. Understanding over time: The cognitive underpinnings of learning trajectories. Paper presented at the annual meeting of the American Education Research Association 2010.
26. Confrey, J., Hasse, E., Maloney, A., Nguyen, K. H., & Varela, S. (2011). A summary report from the conference designing technology-enabled diagnostic assessments for K-12 mathematics. Designing technology-enabled diagnostic assessments for K-12 mathematics. Raleigh, NC.
27. Corcoran T., Mosher F.A., Rogat A. Learning progressions in science: An evidence-based approach to reform 2009, Retrieved from http://www.cpre.org/images/stories/cpre_pdfs/lp_science_rr63.pdf.
28. Cramer K., Lesh R. Rational number knowledge of pre-service elementary education teachers. Proceedings of the tenth annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education 1998, M. Behr (Ed.).
29. D'Ambrosio B.S., Campos T.M. Pre-service teachers' representations of children's understanding of mathematical concepts: Conflicts and conflict resolution. Educational Studies in Mathematics 1992, 23(9):213-230.
30. Darling-Hammond L., Wei R., Andree A., Richardson N., Orphanos S. Professional Learning in the Learning Profession: A Status Report on Teacher Development in the United States and Abroad 2009, National Staff Development Council, Washington, DC.
31. Fennema E., Carpenter T., Franke M., Levi L., Jacobs V., Empson S. Learning to use children's thinking in mathematics instruction: A longitudinal study. Journal for Research in Mathematics Education 1996, 27:403-434.
32. Franke M.L., Carpenter T.P., Levi L., Fennema E. Capturing teachers' generative change: A follow-up study of professional development in mathematics. American Educational Research Journal 2001, 38(3):653-689.
33. Furtak Toward learning progressions as teacher development tools. Paper presented at the learning progressions in science (LeaPS) conference 2009, Retrieved from http://www.education.uiowa.edu/projects/leaps/proceedings/Default.aspx.
34. Glaser B. Basics of grounded theory analysis 1992, Sociology Press, Mill Valley, CA.
35. Graeber A., Tirosh D., Glover R. Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education 1989, 20(1):95-102.
36. Greer B. Nonconservation of multiplication and division involving decimals. Journal for Research in Mathematics Education 1987, 18:37-45.
37. Grossman P., Compton C., Igra D., Ronfeldt M., Shahan E., Williamson P.W. Teaching practice: A cross-professional perspective. Teachers College Record 2009, 11(9):2055-2100.
38. Hammerness K., Darling-Hammond L., Grossman P., Rust F., Shulman L. The design of teacher education programs. Preparing teachers for a changing world: What teachers should learn and be able to do 2005, 390-441. Jossey-Bass, San Francisco, CA. J. Bransford, L. Darling-Hammond (Eds.).
39. Haydar, H. (2002). The effect of clinical assessment training on teachers' instructional efficacy. Unpublished doctoral dissertation. Columbia University.
40. Horvath J., Lehrer R. The design of a case-based hypermedia teaching tool. International Journal of Computers for Mathematical Learning 2000, 5:115-141.
41. Izsak I. Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction 2008, 26:95-143.
42. Jacobs V., Lamb L., Philipp R. Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education 2010, 41(2):169-202.
43. Krebs A. Analyzing student work as a professional development activity. School Science and Mathematics 2005, 105(8):402-411.
44. Lamon S. Rational numbers and proportional reasoning. Second handbook of research on mathematics teaching and learning 2007, 629-666. Information Age Publishing, Charlotte, NC. F. Lester (Ed.).
45. Lesh R., Post T., Behr M. Proportional reasoning. Number concepts and operations in the middle grades 1988, 93-118. Lawrence Erlbaum Associates, Mahwah, NJ. M. Behr, J. Hiebert (Eds.).
46. Loucks-Horsley S., Hewson P., Love N., Stiles K. Designing professional development for teachers of science and mathematics 1998, Sage, Thousand Oaks, CA.
47. Ma L. Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States 1999, Lawrence Erlbaum Associates, Mahwah, NJ.
48. Maher C. Video recordings as pedagogical tools in mathematics teacher education. The international handbook of mathematics teacher education 2008, 65-84. Sense Publishers, Boston, MA. D. Tirosh, T. Wood (Eds.).
49. Maloney A.P., Confrey J. The construction, refinement, and early validation of the equipartitioning learning trajectory. 9th International conference of the learning sciences 2010.
50. McDonough A., Clarke B., Clarke D.M. Understanding, assessing and developing children's mathematical thinking: The power of a one-to-one interview for pre-service teachers in providing insights into appropriate pedagogical practices. International Journal of Educational Research 2002, 37(11):211-226.
51. Moss J., Case R. Developing children's understanding of the rational numbers: A new model and an experimental curriculum. Journal for Research in Mathematics Education 1999, 30:122-147.
52. National Assessment of Educational Progress Nation's report card: Mathematics 2008, Retrieved from http://nationsreportcard.gov/math_2007/.
53. National Mathematics Advisory Panel Foundations for success: The final report of the National Mathematics Advisory Panel 2008, Retrieved from http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf.
54. National Research Council Adding it up: Helping children learn mathematics 2003, National Academies Pres, Washington, DC.
55. National Council of Teachers of Mathematics Principles and standards for school mathematics 2000, NCTM, Reston, VA.
56. National Council of Teachers of Mathematics Curriculum focal points: A quest for coherence 2006, NCTM, Reston, VA.
57. Philipp R.A., Ambrose R., Lamb L.L.C., Sowder J.T., Schappelle B.P., Sowder L., et al. Effects of early field experiences on the mathematical content knowledge and beliefs of prospective elementary school teachers: An experimental study. Journal for Research in Mathematics Education 2007, 38:438-476.
58. Piaget J., Inhelder B., Szeminski A. The child's conception of geometry 1960, Routledge & Kegan Paul, London.
59. Powell A.B., Francisco J.M., Maher C.A. An analytic model for studying the development of learners' mathematical ideas and reasoning using videotape data. Journal of Mathematical Behavior 2003, 22:405-435.
60. Sherin M., van Es E.A. Using video to support teachers' ability to notice classroom interactions. Journal of Technology and Teacher Education 2005, 13(3):475-491.
61. Simon M.A. Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education 1995, 26:114-145.
62. Sztajn P., Confrey J., Wilson P.H., Edgington C. Learning trajectory based instruction: Toward a theory of teaching. Educational Researcher 2012, 41(5):147-156.
63. TERC Investigations in number, data, and space 2007/1998, Pearson-Scott Foresman, Glenview, IL. 2nd ed.
64. Tirosh D. Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education 2000, 31:5-25.
65. Wilson P.H., Edgington C., Nguyen K.H., Pescosolido R., Confrey J. Fractions: How to share fair. Mathematics Teaching in the Middle School 2011, 17(4):230-237.
66. Wilson P.H., Lee H.S., Hollebrands K.F. Understanding prospective mathematics teachers' processes for making sense of students' work with technology. Journal for Research in Mathematics Education 2011, 41:39-64.
67. Wilson P.H., Myers M., Edgington C., Confrey J. Fair shares, matey, or walk the plank. Teaching Children Mathematics 2012, 18(8):482-489.