The role of local theories: teacher knowledge and its impact on engaging students with challenging tasks
 Jeffrey Choppin
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
This study explores the extent to which a teacher elicited students’ mathematical reasoning through the use of challenging tasks and the role her knowledge played in doing so. I characterised the teacher’s knowledge in terms of a local theory of instruction, a form of pedagogical content knowledge that involves an empirically tested set of conjectures situated within a mathematical domain. Video data were collected and analysed and used to stimulate the teacher’s reflection on her enactments of an instructional sequence. The teacher, chosen for how she consistently elicited student reasoning, showed evidence of possessing a local theory in that she articulated the ways student thinking developed over time, the processes by which that thinking developed, and the resources that facilitated the development of student thinking. Her knowledge informed how she revised and enacted challenging tasks in ways that elicited and refined student thinking around integer addition and subtraction. Furthermore, her knowledge and practices emphasised the progressive formalisation of students’ ideas as a key learning process. A key implication of this study is that teachers are able to develop robust knowledge from enacting challenging tasks, knowledge that organises how they elicit and refine student reasoning from those tasks.
Inside
Within this Article
 Introduction
 Research questions
 Framework
 Context
 Methods
 Results
 Discussion
 Implications
 References
 References
Other actions
 Cai, J., Moyer, J. C., Wang, N., & Nie, B. (2009). Learning from classroom instruction in a curricular content: An analysis of instructional tasks. Paper presented at the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Atlanta, GA: Georgia State University.
 Carpenter, T. P., Blanton, M. L., Cobb, P., Franke, M. L., Kaput, J., & McClain, K. (2004). Scaling up innovative practices in mathematics and science (Research report). Madison: National Center for Improving Student Learning and Achievement in Mathematics and Science.
 Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in education research. Educational Researcher, 32(1), 9–13. CrossRef
 Cobb, P., Zhao, Q., & Dean, C. (2009). Conducting design experiments to support teachers' learning: A reflection from the field. Journal of the Learning Sciences, 18(2), 165–199.
 Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected two teachers' learning. The Elementary School Journal, 103(3), 287–311.
 Confrey, J., Strutchens, M. E., Battista, M., Smith, M. S., King, K. D., Sutton, J. T., et al. (2008). Situating research on curricular change. Journal for Research in Mathematics Education, 39(2), 102–112.
 diSessa, A., & Cobb, P. (2004). Ontological innovation and the role of theory in design experiments. Journal of the Learning Sciences, 13(1), 77–103. CrossRef
 GessNewsome, J. (1999). Pedagogical content knowledge: An introduction and orientation. In J. GessNewsome & N. G. Lederman (Eds.), Examining pedagogical content knowledge: The construct and its implications for science education (pp. 3–17). Boston: Kluwer Academic Publishers.
 Gravemeijer, K. (1994). Educational development and developmental research in mathematics education. Journal for Research in Mathematics Education, 25(5), 443–471. CrossRef
 Gravemeijer, K. (2004). Local instruction theories as means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105–128. CrossRef
 Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
 Hiebert, J., Gallimore, R., Garnier, H., Givvin, K. B., Hollingsworth, H., Jacobs, J., et al. (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 Video Study. Washington: National Centre for Education Statistics, U.S. Department of Education.
 Hill, H., Ball, D. L., & Schilling, S. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topicspecific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.
 Hill, H., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406. CrossRef
 Lampert, M. (1990). When the problem is not the question and the solution is not the answer: mathematical knowing and teaching. American Educational Research Journal, 27(1), 29–63.
 Lappan, G., & Phillips, E. (2009). A designer speaks. Educational Designer, 1(3). Retrieved from http://www.educationaldesigner.org/ed/volume1/issue3/article11
 Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (1998). Connected Mathematics. Palo Alto: Dale Seymour Publications.
 Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2006). Connected mathematics 2. Boston: Prentice Hall.
 Lewis, C., Perry, R., & Murata, A. (2006). How should research contribute to instructional improvement? The case of lesson study. Educational Researcher, 35(3), 3–14. CrossRef
 Magnusson, S., Krajcik, J., & Borko, H. (1999). Nature, sources and development of pedagogical content knowledge for science teaching. In J. GessNewsome & N. G. Lederman (Eds.), Examining pedagogical content knowledge: The construct and its implications for science education (pp. 133–144). Boston: Kluwer Academic Publishers.
 Remillard, J. T., & Bryans, M. B. (2004). Teachers’ orientations toward mathematics curriculum materials: Implications for teacher learning. Journal for Research in Mathematics Education, 35(5), 352–388. CrossRef
 Schoenfeld, A. (2006). What doesn’t work: The challenge and failure of the What Works Clearinghouse to conduct meaningful reviews of studies of mathematics curricula. Educational Researcher, 35(2), 13–21. CrossRef
 Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
 Simon, M., & Tzur, R. (1999). Explicating the teachers’ perspective from the researcher’ perspectives: Generating accounts of mathematics teachers’ practice. Journal for Research in Mathematics Education, 30(3), 252–264. CrossRef
 Stein, M. K., Grover, B. W., & Henningsen, M. A. (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.
 Stylianides, G. J. (2009). Reasoningandproving in school mathematics textbooks. Mathematical Thinking and Learning, 11(4), 258–288. CrossRef
 Sullivan, P., Clarke, D., & Clarke, B. (2009). Converting mathematics tasks to learning opportunities: An important aspect of knowledge for mathematics teaching. Mathematics Education Research Journal, 21(1), 85–105.
 TERC. (1998). Investigations in Number, Data, and Space. Menlo Park: Dale Seymour.
 Van den HeuvelPanhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54, 9–35. CrossRef
 Van den HeuvelPanhuizen, M. (2008). Learning from “Didactikids:” An impetus for revisiting the empty number line. Mathematics Education Research Journal, 20(3), 6–31.
 Vincent, J., & Stacey, K. (2008). Do mathematics textbooks cultivate shallow teaching? Applying the TIMSS video study criteria to Australian eighthgrade textbooks. Mathematics Education Research Journal, 20(1), 82–107.
 Title
 The role of local theories: teacher knowledge and its impact on engaging students with challenging tasks
 Journal

Mathematics Education Research Journal
Volume 23, Issue 1 , pp 525
 Cover Date
 20110301
 DOI
 10.1007/s1339401100018
 Print ISSN
 10332170
 Online ISSN
 2211050X
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Curriculum
 Local theory
 Challenging tasks
 Teacher knowledge
 Instructional practices
 Authors

 Jeffrey Choppin ^{(1)}
 Author Affiliations

 1. Department of Teaching and Curriculum, The University of Rochester, Dewey Hall 1160K, Box 270425, Rochester, NY, 14627, USA