The case of the Case of Benny: Elucidating the influence of a landmark study in mathematics education

Journal of Mathematical Behavior

Volumn 35, Issue , 2014, Pages 101-109

  Leatham, Keith R ^a   Winiecke, Tyler ^a  

^a BRIGHAM YOUNG UNIVERSITY   (United States)

Author keywords

Case study; Curriculum; Erlwanger; Qualitative research; Student mathematical beliefs; Student mathematical conceptions

Indexed keywords

EID: 84904568195     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2014.06.001     Document Type: Article

References (45)

1. Anderson L.M., Brubaker N.L., Alleman-Brooks J., Duffy G.G. A qualitative study of seatwork in first-grade classrooms. Elementary School Journal 1985, 86:123-140. 10.1086/461438.
2. Au W. Teaching under the new Taylorism: High-stakes testing and the standardization of the 21st century curriculum. Journal of Curriculum Studies 2011, 43:25-45. 10.1080/00220272.2010.521261.
3. Ball D.L. Working on the inside: Using one's own practice as a site for studying teaching and learning. Handbook of research design in mathematics and science education 2000, 365-402. Lawrence Erlbaum Associates, Mahwah, NJ. A.E. Kelly, R.A. Lesh (Eds.).
4. Becker J.P., Selter C. Elementary school practices. International handbook of mathematics education 1996, 511-564. Kluwer Academic, Dordrecht, The Netherlands. A.J. Bishop, K. Clements, K. Christine, J. Kilpatrick, C. Laborde (Eds.).
5. Blumenfeld H.L. Students' reinvention of straight-line solutions to systems of linear ordinary differential equations 2006, (Master's thesis), San Diego State University, Retrieved from http://www.howardblumenfeld.com/thesis.pdf.
6. Boaler J. When politics took the place of inquiry: A response to the national mathematics advisory panel's review of instructional practices. Educational Researcher 2008, 37:588-594. 10.3102/0013189X08327998.
7. Brophy J. Successful teaching strategies for the inner-city child. Phi Delta Kappan 1982, 63:527-530.
8. Brousseau G., Davis R.B., Werner T. Observing students at work. Perspectives on mathematics education 1986, 205-241. D. Reidel, Dordrecht, The Netherlands. B. Christiansen, A.G. Howson, M. Otte (Eds.).
9. Brown A.L., Campione J.C., Reeve R.A., Ferrara R.A., Palincsar A.S. Interactive learning and individual understanding: The case of reading and mathematics. Culture, schooling, and psychological development 1991, 136-170. Ablex, Norwood, NJ. L.T. Landsmann (Ed.).
10. Classics in mathematics education research 2004, National Council of Teachers of Mathematics, Reston, VA. T.P. Carpenter, J.A. Dossey, J.L. Koehler (Eds.).
11. Carpenter T.P., Dossey J.A., Koehler J.L. Preface. Classics in mathematics education research 2004, vii-viii. National Council of Teachers of Mathematics, Reston, VA. T.P. Carpenter, J.A. Dossey, J.L. Koehler (Eds.).
12. Clarke D., Breed M., Fraser S. The consequences of a problem-based mathematics curriculum. Mathematics Educator 2004, 14(2):7-16.
13. Clements M. Statistical significance testing: Providing historical perspective for Menon's paper. Mathematics Education Research Journal 1993, 5(1):23-27. 10.1007/BF03217250.
14. Cobb P., Steffe L.P. The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education 1983, 14:83-94. 10.2307/748576.
15. Cooney T.J. Stories and the challenge for JMTE. Journal of Mathematics Teacher Education 1999, 2:1-2. 10.1023/A:1009925721141.
16. Davis R.B. Conceptual and procedural knowledge in mathematics: A summary analysis. Conceptual and procedural knowledge: The case of mathematics 1986, 265-300. Lawrence Erlbaum Associates, Hillsdale, NJ. J. Hiebert (Ed.).
17. Davis R.B., Ginsburg H. Explanation of this journal. Journal of Children's Mathematical Behavior 1972, 1(1):5.
18. Davis R.B., Ginsburg H. Explanation of this issue. Journal of Children's Mathematical Behavior 1975, 1(3):5.
19. Erlwanger S.H. Benny's conception of rules and answers in IPI mathematics. Journal of Children's Mathematical Behavior 1973, 1(2):7-26.
20. Erlwanger S.H. Benny's conception of rules and answers in IPI mathematics. Classics in mathematics education research 1973/2004, 49-58. National Council of Teachers of Mathematics, Reston, VA, (Reprinted from Journal of Children's Mathematical Behavior, 1(2), 7-26, 1973). T.P. Carpenter, J.A. Dossey, J.L. Koehler (Eds.).
21. Erlwanger S.H. Case studies of children's conceptions of mathematics 1974, (Doctoral dissertation), University of Illinois at Urbana-Champaign.
22. Erlwanger S.H. Case studies of children's conceptions of mathematics: I. Journal of Children's Mathematical Behavior 1975, 1(3):157-283.
23. Ernest P. Popularization: Myths, massmedia and modernism. International handbook of mathematics education 1996, 785-817. Kluwer Academic, Dordrecht, The Netherlands. A.J. Bishop, K. Clements, K. Christine, J. Kilpatrick, C. Laborde (Eds.).
24. Goldin G.A. Developing complex understandings: On the relation of mathematics education research to mathematics. Educational Studies in Mathematics 2003, 54:171-202. 10.1023/B:EDUC.0000006180.20493.3c.
25. Hiebert J. The constantly underestimated challenge of improving mathematics instruction. Vital directions for mathematics education research 2013, 45-56. Springer, New York. K.R. Leatham (Ed.).
26. Hoyles C., Noss R. Synthesizing mathematical conceptions and their formalization through the construction of a logo-based school mathematics curriculum. International Journal of Mathematical Education in Science and Technology 1987, 18:581-595. 10.1080/0020739870180411.
27. Lappan G., Ferrini-Mundy J. Knowing and doing mathematics: A new vision for middle grades students. Elementary School Journal 1993, 93:625-641. 10.1086/461744.
28. Leatham K.R. Observations on citation practices in mathematics education research. Journal for Research in Mathematics Education 2014, (in press).
29. Linchevski L., Livneh D. Structure sense: The relationship between algebraic and numerical contexts. Educational Studies in Mathematics 1999, 40:173-196. 10.1023/A:1003606308064.
30. Macmillan A. Children thinking mathematically beyond authoritative identities. Mathematics Education Research Journal 1995, 7:111-131. 10.1007/BF03217280.
31. Mueller M., Yankelewitz D., Maher C. Rules without reason: Allowing students to rethink previous conceptions. Montana Mathematics Enthusiast 2010, 7:307-320.
32. Neyland J. Beliefs and values in mathematics education: An outline of Ernest's model. Mathematics education: A handbook for teachers 1995, Vol. 2:139-149. Wellington College of Education, Wellington, New Zealand.
33. Niss M. Key issues and trends in research on mathematical education. Proceedings of the ninth international congress on mathematical education 2004, 37-57. Springer, Roskilde, Denmark. H. Fujita, Y. Hashimoto, B. Hodgson, P. Lee, S. Lerman, T. Sawada (Eds.).
34. Schoenfeld A.H. Method. Second handbook of research on mathematics teaching and learning 2007, Vol. 1:69-107. Information Age Publishing, Charlotte, NC.
35. Standards-based school mathematics curricula: What are they? What do students learn? 2003, Lawrence Erlbaum, Mahwah, NJ. S.L. Senk, D.R. Thompson (Eds.).
36. Shulman L.S. On teaching problem solving and solving the problems of teaching. Teaching and learning mathematical problem solving: Multiple research perspectives 1985, 439-450. Lawrence Erlbaum Associates, Hillsdale, NJ. E.A. Silver (Ed.).
37. Shulman L.S. Knowledge and teaching: Foundations of the new reform. Harvard Educational Review 1987, 57:1-23.
38. Speiser B., Walter C. Remembering Stanley Erlwanger. For the Learning of Mathematics 2004, 24(3):33-39.
39. Stewart V. Making sense of students' understanding of fractions: An exploratory study of sixth graders' construction of fraction concepts through the use of physical referents and real world representations 2005, (Doctoral dissertation), Florida State University, Retrieved from http://etd.lib.fsu.edu/theses/available/etd-10302005-024424/.
40. Stigler J.W., Hiebert J. The teaching gap: Best ideas from the world's teachers for improving education in the classroom 2009, Free Press, New York, NY.
41. Strickland T.K. The effects of blended instruction and visual representations on area problems involving quadratic expressions for secondary students with mathematics learning difficulties 2011, (Doctoral dissertation), University of Maryland, Retrieved from http://drum.lib.umd.edu/handle/1903/11905.
42. Stylianides A.J., Stylianides G.J. Learning mathematics with understanding: A critical consideration of the learning principle in the principles and standards for school mathematics. Montana Mathematics Enthusiast 2007, 4:103-114.
43. Tytler R., Osborne J., Williams G., Tytler K., Clark J.C. Opening up pathways: Engagement in STEM across the primary-secondary school transition 2008, Australian Department of Education, Employment and Workplace Relations, Canberra, Australia.
44. Wheatley G.H. The role of reflection in mathematics learning. Educational Studies in Mathematics 1992, 23:529-541. 10.1007/BF00571471.
45. Yager R.E. Priorities for research in science education: A study committee report. Journal of Research in Science Teaching 1978, 15:99-107. 10.1002/tea.3660150204.