Collegiate mathematics teaching: An unexamined practice

Journal of Mathematical Behavior

Volumn 29, Issue 2, 2010, Pages 99-114

  Speer, Natasha M ^a   Smith, John P ^b   Horvath, Aladar ^b  

^a UNIVERSITY OF MAINE   (United States)

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Collegiate mathematics; Teaching practice

Indexed keywords

EID: 77953915817     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2010.02.001     Document Type: Article

References (85)

1. Ahmadi M.H. The impact of cooperative learning in teaching mathematics. Readings in innovative ideas in teaching collegiate mathematics 2002, 3-19. University Press of America, Lanham, MD. M.H. Ahmadi (Ed.).
2. Arcavi A., Meira L., Kessel C., Smith J.P. Teaching mathematical problem solving: An analysis of an emergent classroom community. Research in college mathematics education 1998, Vol. III:1-70. American Mathematical Society, Providence, RI.
3. Asera R. Calculus and community: A history of the Emerging Scholars Program 2001, The College Board, New York.
4. Asiala M., Brown A., DeVries D.J., Dubinsky E., Mathews D., Thomas K. A framework for research and curriculum development in undergraduate mathematics education. Research in collegiate mathematics education II 1996, 1-32. American Mathematical Society, Providence, RI. J. Kaput, A.H. Schoenfeld, E. Dubinsky (Eds.).
5. Ball D.L. Halves, pieces, and twoths: Constructing and using representational contexts in teaching fractions. Rational numbers: An integration of research 1993, 157-195. Lawrence Erlbaum Associates, Hillsdale, NJ. T.P. Carpenter, E. Fennema, T.A. Romberg (Eds.).
6. Ball D.L. With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal 1993, 93:373-397.
7. Ball D.L., Bass H. Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. Multiple perspectives on the teaching and learning of mathematics 2000, Ablex, Westport, CT. J. Boaler (Ed.).
8. Ball D.L., Lubienski S.T., Mewborn D.S. Research on teaching mathematics: The unsolved problem of teachers' mathematical knowledge. Handbook of research on teaching 2001, 433-456. American Educational Research Association, Washington, DC. V. Richardson (Ed.).
9. Bookman J., Friedman C.P. A comparison of the problem solving performance of students in lab based and traditional calculus. Research in Collegiate Mathematics Education I 1994, 101-116. American Mathematical Society, Providence, RI. E. Dubinsky, A.H. Schoenfeld, J. Kaput (Eds.).
10. Bookman J., Friedman C.P. Student attitudes and calculus reform. School Science and Mathematics 1998, 98:117-122.
11. Borko H., Eisenhart M., Brown C.A., Underhill R.G., Jones D., Agard P.C. Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education 1992, 23:194-222.
12. Breidenbach D., Dubinsky Ed., Hawks J., Nichols D. Development of the process conception of function. Educational Studies in Mathematics 1992, 23:247-285.
13. Brown C.A., Borko H. Becoming a mathematics teacher. Handbook of research on mathematics teaching and learning 1996, 209-239. MacMillan Publishing Company, New York. D.A. Grouws (Ed.).
14. Carpenter T., Fennema E., Peterson P., Chiang C., Loef M. Using knowledge of children's mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal 1989, 26:499-531.
15. You're the professor, What next? Ideas and resources for preparing college teachers 1994, Vol. 35. Mathematical Association of America, Washington, DC.
16. Cottrill J., Dubinsky E., Nichols D., Schwingendorf K., Thomas K., Vidakovic D. Understanding the limit concept: Beginning with a coordinated process schema. Journal of Mathematical Behavior 1996, 15:167-192.
17. DeLong M., Winter D. Learning to teach and teaching to learn mathematics: Resources for professional development 2002, Vol. 57. The Mathematical Association of America, Washington, DC.
18. Toward a lean and lively calculus 1986, Mathematics Association of America, Washington, DC. R. Douglas (Ed.).
19. Dubinsky E. Reflective abstraction in advanced mathematical thinking. Advanced mathematical thinking 1991, 95-123. Kluwer Academic Publishers, Boston. D. Tall (Ed.).
20. Dubinsky E., Harel G. The nature of the process conception of function. The concept of function: Aspects of epistemology and pedagogy 1992, 85-107. Mathematical Association of America, Washington, DC. G. Harel, E. Dubinsky (Eds.).
21. Dubinsky E., McDonald M.A. APOS: A constructivist theory of learning in undergraduate mathematics education research. The teaching and learning of mathematics at university level: An ICMI study 2001, 273-280. Kluwer Academic Publishers, Dordrecht, Netherlands. D.A. Holton (Ed.).
22. Dubinsky E., Weller K., McDonald M.A., Brown A. Some historical issues and paradoxes regarding the concept of infinity: An APOS-based analysis: Part 1. Educational Studies in Mathematics 2005, 58:335-359.
23. Dubinsky E., Weller K., McDonald M.A., Brown A. Some historical issues and paradoxes regarding the concept of infinity. An APOS analysis: Part 2. Educational Studies in Mathematics 2005, 60:253-266.
24. Epp S.S. The role of logic in teaching proof. The American Mathematical Monthly 2003, 110:886-899.
25. Ewing J. Towards excellence: Leading a doctoral mathematics department in the 21st century 1999, Report of the AMS Task Force on Excellence, American Mathematical Society, Roanoke, VA.
26. Fennema E., Carpenter T.P., Franke M., Levi L., Jacobs V.R., Empson S.B. A longitudinal study of learning to use children's thinking in mathematics Instruction. Journal for Research in Mathematics Education 1996, 27:403-434.
27. Fravillig J.L., Murphy L.A., Fuson K.C. Advancing children's mathematical thinking in Everyday Mathematics classrooms. Journal for Research in Mathematics Education 1999, 30:148-170.
28. Friedberg S., Ash A., Brown E., Hughes Hallett D., Kasman R., Kenney M., et al. Teaching mathematics in colleges and universities: Case studies for today's classroom: Faculty edition 2001, American Mathematical Society, Providence, RI.
29. Friedberg S., Ash A., Brown E., Hughes Hallett D., Kasman R., Kenney M., et al. Teaching mathematics in colleges and universities: Case studies for today's classroom: Graduate student edition 2001, American Mathematical Society, Providence, RI.
30. Fullilove R.E., Treisman P.U. Mathematics achievement among African American undergraduates at the University of California, Berkeley: An evaluation of the mathematics workshop program. Journal of Negro Education 1990, 59(3):463-478.
31. Fulton, J. D. (Ed.). (2003). Guidelines for programs and departments in undergraduate mathematical sciences, Report of the MAA Guidelines Task Force. Retrieved from (accessed 27.07.10). http://www.maap.org/guidelines/guidelines.html.
32. Ganter S.L. Changing calculus: A report on evaluation efforts and national impact from 1988-1998 2001, Mathematical Association of America, Washington, DC.
33. Halmos P.R. The teaching of problem solving. The American Mathematical Monthly 1975, 82:466-470.
34. Halmos P.R. I want to be a mathematician 1985, Springer-Verlag, New York.
35. Halmos P.R. What is teaching? The American Mathematical Monthly 1994, 101:848-854.
36. Harel G. Two dual assertions: The first on learning and the second on teaching (or vice versa). The American Mathematical Monthly 1998, 105:497-507.
37. The concept of function: Aspects of epistemology and pedagogy 1992, Mathematics Association of America, Washington, DC. G. Harel, E. Dubinsky (Eds.).
38. Henningsen M., Stein M.K. Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education 1997, 28:524-549.
39. Herzig A., Kung D.T. Cooperative learning in calculus reform: What have we learned? Research in collegiate mathematics education 2003, Vol. V:30-55. American Mathematical Society, Providence, RI.
40. Hill H.C., Rowan B., Ball D.L. Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal 2005, 42(2):371-406.
41. Hsu E., Murphy T.J., Treisman P.U. Supporting high minority achievement in introductory collegiate mathematics courses: What We Have Learned from 30 Years of The Emerging Scholars Program. Making the connection: Research and practice in undergraduate mathematics education 2008, 205-220. Mathematical Association of America. M. Carlson, C. Rasmussen (Eds.).
42. Lampert M., Graziani F. Instructional activities as a tool for teachers' and teacher educators' learning. The Elementary School Journal 2009, 109(5):491-509.
43. Leinhardt G., Steele M.D. Seeing the complexity of standing to the side: Instructional dialogues. Cognition and Instruction 2005, 23:87-163.
44. Lobato J., Clarke D., Ellis A.B. Initiating and eliciting in teaching: A reformulation of telling. Journal for Research in Mathematics Education 2005, 36:101-136.
45. Lutzer D.J., Rodi S.B., Kirkman E.E., Maxwell J.W. Statistical abstract of undergraduate programs in the mathematical sciences in the United States: Fall 2005 CBMS survey 2007, American Mathematical Society, Washington, DC.
46. Ma L. Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States 1999, Lawrence Erlbaum Associates, Mahwah, NJ.
47. Mason J. Mathematics teaching practice: A guide for university and college lecturers 2002, Horwood Publishing, Chichester, UK.
48. Mason J., Watson A. Mathematics as constructive activity: Exploiting dimensions of possible variation. Making the connection: Research and practice in undergraduate mathematics 2008, 191-204. Mathematical Association of America, Washington, DC. M. Carlson, C. Rasmussen (Eds.).
49. Michener E.R. Understanding understanding mathematics. Cognitive Science 1978, 2:361-383.
50. National Council of Teachers of Mathematics Professional teaching standards for school mathematics 1991, Author, Reston, VA.
51. National Council of Teachers of Mathematics Mathematics teaching today: Improving practice, improving student learning 2007, Author, Reston, VA. 2nd ed.
52. National Research Council Moving beyond myths: Revitalizing undergraduate mathematics 1991, National Academy Press, Washington, DC.
53. Post T.R., Wahsmith I., Lesh R., Behr M.J. Order and equivalence of rational numbers: A cognitive analysis. Journal for Research in Mathematics Education 1985, 16:18-36.
54. Rasmussen C.L. New directions in differential equations: A framework for interpreting students' understandings and difficulties. Journal of Mathematical Behavior 2001, 20:55-87.
55. Rasmussen C., King K. Locating starting points in differential equations: A realistic mathematics approach. International Journal of Mathematical Education in Science and Technology 2000, 31:161-172.
56. Rasmussen C., Marrongelle K. Pedagogical content tools: Integrating student reasoning and mathematics in instruction. Journal for Research in Mathematical Education 2006, 37:388-420.
57. Ramussen C., Yackel E., King K. Social and sociomathematical norms in the mathematics classroom. Teaching mathematics through problem solving: Grades 6-12 2003, 143-154. National Council of Teachers of Mathematics, Reston, VA. H. Schoen, R. Charles (Eds.).
58. Rishel T. Teaching first: A guide for new mathematicians 2000, Vol. 54. Mathematical Association of America, Washington, DC.
59. Rittenhouse P.S. The teacher's role in mathematical conversation: Stepping in and stepping out. Talking mathematics in school 1998, 163-189. Cambridge University Press, Cambridge, UK. M. Lampert, M.L. Blunk (Eds.).
60. Robert A., Speer N. Research on the teaching and learning of calculus/elementary analysis. The teaching and learning of mathematics at university level: An ICMI study 2001, 283-299. Kluwer Academic Publishers, Dordrecht, Holland. D. Holmes (Ed.).
61. Roskam A., Morris A., Hiebert J., Suzuka K., Lewis J., Cole Y., et al. Improving mathematics teaching and teacher education through " specification." Presentation at the national council of teachers of mathematics research presession 2009.
62. Rowe M.B. Relation of wait-time and rewards to the development of language, logic, and fate control: Part II-Rewards. Journal of Research in Science Teaching 1974, 11:291-308.
63. Rowe M.B. Wait time: Slowing down may be a way of speeding up!. Journal of Teacher Education 1986, 37:43-50.
64. Schoenfeld A.H. Mathematical problem solving 1985, Academic Press, Orlando, FL.
65. Schoenfeld A.H. On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. Informal reasoning and education 1991, 311-343. Lawrence Erlbaum Associates, Hillsdale, NJ. J.F. Voss, D.N. Perkins, J.W. Segal (Eds.).
66. Schoenfeld A.H. Reflections on doing and teaching problem solving. Mathematics thinking and problem solving 1994, 53-70. Lawrence Erlbaum Associates, Hillsdale, NJ. A.H. Schoenfeld (Ed.).
67. Schoenfeld A.H. Reflections on a course in mathematical problem solving. Research in college mathematics education 1998, Vol. III:81-113. American Mathematical Society, Providence, RI.
68. Selden A., Selden J. Collegiate mathematics education research: What would that be like? The College Mathematics Journal 1998, 24:431-445.
69. Smith J.P., Star J.R. Expanding the notion of impact in K-12 standards-based and reform calculus programs. Journal for Research in Mathematics Education 2007, 38:3-34.
70. Speer N. Collections of beliefs and their relationship to mathematics teachers' instructional practices. Cognition and Instruction 2008, 26:218-267.
71. Speer N., Wagner J. Knowledge needed by a teacher to provide analytic scaffolding during undergraduate mathematics classroom discussions. Journal for Research in Mathematics Education 2009, 40(5):530-565.
72. Speer N., Gutmann T., Murphy T.J. Educational research on mathematics graduate student teaching assistants: A decade of substantial progress. Studies in Graduate and Professional Student Development 2009, 12:1-10.
73. Stephan M., Rasmussen C. Classroom mathematical practices in differential equations. Journal of Mathematical Behavior 2002, 21:459-490.
74. Stigler J.W., Hiebert J. The teaching gap 1999, Free Press, New York.
75. Thompson P.W. Students, functions, and curriculum. Research in collegiate mathematics education 1994, Vol. I:21-44. American Mathematical Society, Providence, RI.
76. Triesman, P. U. (1985). A study of the mathematics performance of black students at the University of California, Berkeley. Unpublished doctoral dissertation, University of California, Berkeley.
77. Triesman U. Studying students studying calculus: A look at the lives of minority mathematics students in college. The College Mathematics Journal 1992, 23:362-372.
78. Priming the calculus pump: Innovations and resources 1990, Mathematics Association of America, Washington, DC. T.W. Tucker (Ed.).
79. van Zee E., Minstrell J. Using questioning to guide student thinking. Journal of the Learning Sciences 1997, 6:227-269.
80. Wagner J., Speer N., Rossa B. Beyond mathematical content knowledge: A mathematician's knowledge needed for teaching an inquiry-oriented differential equations course. Journal of Mathematical Behavior 2007, 26:247-266.
81. Weber K. Traditional instruction in advanced mathematics courses: A case study of one professor's lectures and proofs in an introductory real analysis course. Journal of Mathematical Behavior 2004, 23:115-133.
82. Weller K., Clark J.M., Dubinsky E., Loch S., McDonald M.A., Merkovsky R.R. Performance and attitudes in courses based on APOS theory. Research in collegiate mathematics V 2003, 97-131. American Mathematical Society, Providence, RI. A. Selden, E. Dubinsky, G. Harel, F. Hitt (Eds.).
83. Yackel E., Ramussen C., King K. Social and socio-mathematical norms in an advanced undergraduate mathematics course. Journal of Mathematical Behavior 2000, 19:275-287.
84. Zitarelli D.E. The origin and early impact of the Moore method. The American Mathematical Monthly 2004, 111:465-486.
85. Zodik I., Zaslasky O. Characteristics of teachers' choice of examples in and for the mathematics classroom. Educational Studies in Mathematics 2008, 69:165-182.