Students’ reflections on their learning experiences: lessons from a longitudinal study on the development of mathematical ideas and reasoning

Balacheff, N. (1988, April). A study of pupil's proving processes at junior high school level. Paper presented at the Joint International Conference 66th NCTM and UCSMP Project, Chicago, IL. Case, 1992, Neo-Piagetian theories of child development Cole, 1992, Context, modularity, and the cultural constitution of human development, 5 Creswell, 1998 Davis, 1990, Suggestions for the improvement of mathematics education De Corte, 2002, “Knowing what to believe”: The relevance of students’ mathematical beliefs for mathematics education Dörfler, 2000, Means for meaning Dweck, 1988, A social-cognitive approach to motivation and personality, Psychological Review, 95, 256, 10.1037/0033-295X.95.2.256 Erickson, 1992, The interface between ethnography and microanalysis, 201 Ernest, 1998, The epistemological basis of qualitative research in mathematics: A postmodern perspective, 22 Francisco, J. M. (2004a). Students’ views on mathematical learning: Insights from a longitudinal study. Paper presented at the ICME-10, Copenhagen, Denmark. Francisco, J. M. (2004b). Students’ reflections on mathematical learning: Results from a longitudinal study. Unpublished doctoral dissertation, Rutgers University, New Brunswick, NJ. 1985 Hammer, 2002, On the form of a personal epistemology Hanna, 1990, Some pedagogical aspects of proof, Interchange, 21, 6, 10.1007/BF01809605 Hofer, B. K. (1994). Epistemological beliefs and first-year college students: Motivation and cognition in different instructional contexts. Paper presented at the annual meeting of the American Psychological Association, Los Angeles. Hofer, 1997, The development of epistemological theories: Beliefs about knowledge and knowing and their relation to learning, Review of Educational Research, 67, 88, 10.3102/00346543067001088 Kiczek, R. D. (2000). Tracing the development of probabilistic thinking: Profiles from a longitudinal study. Unpublished doctoral dissertation, Rutgers University, New Brunswick, NJ. Kiczek, R. D., & Maher, C. A. (2002). Long term building of mathematical ideas related to proof making. Paper presented at the ICME9 TSG12, Tokyo, Japan. Kiczek, 2001, Tracing the origins and extensions of Michael's representation, 201 Lave, 1988 Lave, 1991 Lyons, 1990, Dilemmas of knowing: Ethical and epistemological dimensions of teachers’ work and development, Harvard Educational Review, 60, 159, 10.17763/haer.60.2.v71123u7768r47w6 Maher, 1987, The teacher as designer, implementer, and evaluator of children's mathematical learning environments, The Journal of Mathematical Behaviour, 6, 295 Maher, 2002, How students structure their own investigations and educate us: What we’ve learned from a fourteen-year study Maher, 1992, Teachers building on students’ thinking, Arithmetic Teacher, 32, 10.5951/AT.39.7.0032 Maher, 1992, Individual thinking and the integration of the ideas of others in problem solving situations, 72 Maher, 1993, Conditions contributing to conceptual change in the building of the idea of mathematical proof Maher, 1996, The development of the idea of mathematical proof: A 5-Year case study, Journal for Research in Mathematics Education, 27, 194, 10.2307/749600 Markee, 2000 Martino, A. M. (1992). Elementary students’ construction of mathematical knowledge. Unpublished doctoral dissertation, Rutgers University, New Brunswick, NJ. Moustakas, 1994 Muter, E. M. (1999). Tracing the development of student ideas in combination and proof. Unpublished doctoral dissertation, Rutgers University, New Brunswick, NJ. Pehkonen, E., & Hannula, M. S. (2004). Mathematical belief research in Finland. Nordisk Matematikk Didaktikk [Nordic Studies in Mathematics Education], 9(2), 23–38. Pintrich, 2002, Future challenges and directions for theory and research on personal epistemology Pintrich, 1993, Beyond cold conceptual: The role of motivational beliefs and classroom contextual factors in the process of conceptual change, Review of Educational Research, 63, 167, 10.3102/00346543063002167 Pirie, 1992, Creating constructivist environments and constructing creative mathematics, Educational Studies in Mathematics, 23, 505, 10.1007/BF00571470 Powell, A. B. (2003). “So Let's prove it”: Emergent and elaborated mathematical ideas and reasoning in the discourse and inscriptions of learners engaged in a combinatorial task. Unpublished doctoral dissertation, Rutgers University, New Brunswick. Powell, A. B., Francisco, J. M., & Maher, C. A. (2001). An evolving analytical model for understanding the development of mathematical thinking using videotape data. Paper presented at the Seventh Annual Meeting of the American Educational Research Association, Seattle, WA. Powell, 2003, An evolving analytical model for understanding the development of mathematical thinking using videotape data, The Journal of Mathematical Behavior, 22, 405, 10.1016/j.jmathb.2003.09.002 Power, 1997 Roth, 1994, Physics students’ epistemologies and views about knowing and learning, Journal of Research in Science Education, 31, 5 Schoenfeld, 1985 Schoenfeld, 1989, Explorations of students’ mathematical beliefs and behavior, Journal of Research in Mathematics Education, 20, 338, 10.2307/749440 Schommer, 1990, Effects of beliefs about the nature of knowledge and comprehension, Journal of Educational Studies, 82, 498 Schommer, 1993, Comparisons of beliefs about the nature of knowledge and learning among postsecondary students, Research in Higher Education, 34, 355, 10.1007/BF00991849 Schommer, 1993, Epistemological development and academic performance among secondary students, Journal of Educational Psychology, 85, 406, 10.1037/0022-0663.85.3.406 Schommer, 2002, An evolving theoretical framework for an epistemological belief system Schommer, 1995, Are epistemological beliefs similar across domains?, Journal of Educational Psychology, 87, 424, 10.1037/0022-0663.87.3.424 Steencken, E. P. (2001). Tracing the growth in understanding of fraction ideas: A fourth grade case study. Unpublished doctoral dissertation, Rutgers University, New Brunswick, NJ. Steiner, 1987, Philosophical and epistemological aspects of mathematics and their interaction with theory and practice in mathematics education, For the Learning of Mathematics, 7, 7 Sternberg, 1989, Domain-generality versus domain-specificity: The life and impending death of a false dichotomy, Merril-Palmer Quarterly, 35, 115 Wilson, 1977, The use of ethnographic techniques in educational research, Review of Educational Research, 47, 245, 10.3102/00346543047002245