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Articles

Procedural and Conceptual Knowledge: Exploring the Gap Between Knowledge Type and Knowledge Quality

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Pages 169-181 | Published online: 31 May 2013

REFERENCES

  • Bolte , L. A. 1999 . Using concept maps and interpretive essays for assessment in mathematics . School Science and Mathematics , 99 ( 1 ) : 19 – 30 .
  • Brownell , W. A. When is arithmetic meaningful? . Journal of Educational Research , 38 ( 7 ) 1944 – 1945 . 481 – 498 .
  • Byrnes , J. P. and Wasik , B. A. 1991 . Role of conceptual knowledge in mathematical procedural learning . Developmental Psychology , 5 : 777 – 786 .
  • Cramer , K. and Wyberg , T. 2009 . Efficacy of different concrete models for teaching the part–whole construct for fractions . Mathematical Thinking and Learning , 11 ( 4 ) : 226 – 257 .
  • De Jong , T. and Ferguson-Hessler , M. 1996 . Types and qualities of knowledge . Educational Psychologist , 31 ( 2 ) : 105 – 113 .
  • Glaser , R. 1991 . The maturing of the relationship between the science of learning and cognition and educational practice . Learning and Instruction , 1 : 129 – 144 .
  • Gray , E. M. and Tall , D. O. 1994 . Duality, ambiguity, and flexibility: A proceptual view of simple arithmetic . Journal for Research in Mathematics Education , 26 ( 2 ) : 115 – 141 .
  • Hasemann , K. and Mansfield , H. 1995 . Concept mapping in research on mathematical knowledge development: Background, methods, findings and conclusions . Educational Studies in Mathematics , 29 ( 1 ) : 45 – 72 .
  • Hatano , G. and Inagaki , K. 1986 . “ Two courses of expertise ” . In Child development and education in Japan , Edited by: Stevenson , H. , Azuma , H. and Hakuta , K. 262 – 272 . New York , NY : W.H. Freeman and Company .
  • Hazzan , O. and Goldenberg , P. 1997 . Students’ understanding of the notion of function in dynamic geometry environments . International Journal of Computers for Mathematical Learning , 1 : 263 – 291 .
  • Hiebert , J. 1986 . Conceptual and procedural knowledge: The case of mathematics , Hillsdale , NJ : Lawrence Erlbaum .
  • Hiebert , J. and Lefevre , P. 1986 . “ Conceptual and procedural knowledge in mathematics: An introductory analysis ” . In Conceptual and procedural knowledge: The case of mathematics , Edited by: Hiebert , J. 1 – 27 . Hillsdale , NJ : Lawrence Erlbaum .
  • Porter , M. K. and Masingila , J. O. 2000 . Examining the effects of writing on conceptual and procedural knowledge in calculus . Educational Studies in Mathematics , 42 : 165 – 177 .
  • Rittle-Johnson , B. and Alibali , M. W. 1999 . Conceptual and procedural knowledge: Does one lead to the other? . Journal of Educational Psychology , 91 ( 1 ) : 175 – 189 .
  • Rittle-Johnson , B. and Siegler , R. S. 1998 . “ The relation between conceptual and procedural knowledge in learning mathematics: A review ” . In The development of mathematical skills , Edited by: Donlan , C. 75 – 110 . East Sussex , , England : Psychology Press .
  • Rittle-Johnson , B. , Siegler , R. S. and Alibali , M. W. 2001 . Developing conceptual understanding and procedural skill in mathematics: An iterative process . Journal of Educational Psychology , 93 ( 2 ) : 346 – 362 .
  • Rittle-Johnson , B. and Star , J. R. 2007 . Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations . Journal of Educational Psychology , 99 ( 3 ) : 561 – 574 .
  • Roh , K. H. 2008 . Students’ images and their understanding of definitions of the limit of a sequence . Educational Studies in Mathematics , 69 ( 3 ) : 217 – 233 .
  • Rowland , T. and Zazkis , R. 2013 . Contingency in the mathematics classroom: Opportunities taken and opportunities missed . Canadian Journal of Science, Mathematics and Technology Education , 13 ( 2 ) : 137 – 153 .
  • Schneider , M. , Rittle-Johnson , B. and Star , J. R. 2011 . Relations between conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge . Developmental Psychology , 47 ( 6 ) : 1525 – 1538 .
  • Sfard , A. 1991 . On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin . Educational Studies in Mathematics , 22 ( 1 ) : 1 – 36 .
  • Skemp , R. R. 1976 . Relational understanding and instrumental understanding . Mathematics Teaching , 77 : 20 – 26 .
  • Star , J. R. 2005 . Reconceptualizing procedural knowledge . Journal for Research in Mathematics Education , 36 ( 5 ) : 404 – 411 .
  • Star , J. R. 2007 . Foregrounding procedural knowledge . Journal for Research in Mathematics Education , 38 ( 2 ) : 132 – 135 .
  • Stylianides , A. J. 2007 . Proof and proving in school mathematics . Journal for Research in Mathematics Education , 38 : 289 – 321 .
  • Stylianides , G. J. and Stylianides , A. J. 2009 . Facilitating the transition from empirical arguments to proof . Journal for Research in Mathematics Education , 40 : 314 – 352 .
  • Stylianides , G. J. and Stylianides , A. J. 2010 . Mathematics for teaching: A form of applied mathematics . Teaching and Teacher Education , 26 : 161 – 172 .
  • Williams , C. G. 1998 . Using concept maps to assess conceptual knowledge of function . Journal for Research in Mathematics Education , 29 ( 4 ) : 414 – 421 .
  • Wilson , M. R. 1994 . One preservice secondary teacher's understanding of function: The impact of a course integrating mathematical content and pedagogy . Journal for Research in Mathematics Education , 25 ( 4 ) : 346 – 370 .

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