The Coverage Issue

REFERENCES

• Boaler , J. 1998 . Open and closed mathematics: Student experiences and understandings . Journal for Research in Mathematics Education , 29 : 41 – 62 .
   Web of Science ®Google Scholar
• Boaler , J. and Staples , M. 2008 . Creating mathematical futures through an equitable teaching approach: The case of Railside School . Teachers College Record , 110 : 608 – 645 .
   Web of Science ®Google Scholar
• Cazden , C. and Mehan , H. 1990 . “ Principles from sociology and anthropology: Context, code, classroom, and culture ” . In The Knowledge Base for Beginning Teachers , Edited by: Reynolds , M. C. 47 – 57 . New York : Pergamon .
   Google Scholar
• Chappell , K. K. 2006 . “ Effects of concept-based instruction on calculus students' acquisition of conceptual understanding and procedural skill ” . In Research in Collegiate Mathematics Education VI , Edited by: Hitt , F. , Harel , G. and Selden , A. 27 – 60 . Providence , RI : American Mathematical Society .
   Google Scholar
• Coppin , C. A. , Mahavier , W. T. May , E. L. 2009 . The Moore Method—A Pathway to Learner-Centered Instruction , Washington , DC : Mathematical Association of America .
   Google Scholar
• Darken , B. , Wynegar , R. and Kuhn , S. 2000 . “ Evaluating calculus reform: A review and a longitudinal study ” . In Research in Collegiate Mathematics Education IV , Edited by: Dubinsky , E. , Schoenfeld , A. H. and Kaput , J. 16 – 41 . Providence , RI : American Mathematical Society .
   Google Scholar
• Harel , G. and Sowder , L. 1998 . “ Students' proof schemes: Results from exploratory studies ” . In Research in Collegiate Mathematics Education III , Edited by: Schoenfeld , A. H. , Kaput , J. and Dubinsky , E. 234 – 283 . Providence , RI : American Mathematical Society .
   Google Scholar
• Housman , D. and Porter , M. 2003 . Proof schemes and learning strategies of above-average mathematics students . Educational Studies in Mathematics , 53 : 139 – 158 .
   Google Scholar
• Kilpatrick , J. , Swafford , J. and Findell , B. 2001 . Adding It up: Helping Children Learn Mathematics , Washington , DC : National Research Council .
   Google Scholar
• Kwon , O.N. , Rasmussen , C. and Allen , K. 2005 . Students' retention of mathematical knowledge and skills in differential equations . School Science and Mathematics , 105 : 227 – 239 .
   Google Scholar
• Mahavier , W.S. 1999 . What is the Moore Method? . PRIMUS , 9 : 339 – 254 .
   Google Scholar
• Mason , J. 2001 . “ Mathematical teaching practices at tertiary level: Working group report ” . In The Teaching and Learning of Mathematics at University Level: An ICMI Study , Edited by: Holton , D.A. 71 – 86 . Hingham , MA : Kluwer .
   Google Scholar
• Moore , R. C. 1994 . Making the transition to formal proof . Educational Studies in Mathematics , 27 : 249 – 266 .
   Google Scholar
• Muis , K. R. 2004 . Personal epistemology and mathematics: A critical review and synthesis of research . Review of Educational Research , 74 : 317 – 377 .
   Web of Science ®Google Scholar
• Rasmussen , C. and Kwon , O. N. 2007 . An inquiry-oriented approach to undergraduate mathematics . Journal of Mathematical Behavior , 26 : 189 – 194 .
   Google Scholar
• Schoenfeld , A. H. 1988 . When good teaching leads to bad results: The disasters of “well-taught” mathematics courses . Educational Psychologist , 23 : 145 – 166 .
   Web of Science ®Google Scholar
• Selden , A. and Selden , J. 2003 . Validation of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? . Journal for Research in Mathematics Education , 34 : 4 – 36 .
   Web of Science ®Google Scholar
• Selden , A. , Selden , J. , Hauk , S. and Mason , A. 2000 . “ Why can't calculus students access their knowledge to solve non-routine problems? ” . In Research in Collegiate Mathematics Education IV , Edited by: Dubinsky , E. , Schoenfeld , A. H. and Kaput , J. 128 – 153 . Providence , RI : American Mathematical Society .
   Google Scholar
• Selden , J. , Selden , A. and Mason , A. 1994 . “ Even good calculus students can't solve nonroutine problems ” . In Research Issues in Undergraduate Mathematics Learning, MAA Notes No. 33 , Edited by: Kaput , J. J. and Dubinsky , E. 19 – 26 . Washington , DC : Mathematical Association of America .
   Google Scholar
• Seymour , E. and Hewitt , N. M. 1997 . Talking about Leaving , Boulder , CO : Westview Press .
   Google Scholar
• Smith , J. C. 2005 . A sense-making approach to proof: Strategies of students in traditional and problem-based number theory courses . Journal of Mathematical Behavior , 25 : 73 – 90 .
   Google Scholar
• Weber , K. 2001 . Student difficulty in constructing proofs: The need for strategic knowledge . Educational Studies in Mathematics , 48 : 101 – 119 .
   Google Scholar