Journey to the Past: Verifying and Modifying the Conceptual Sources of Decimal Fraction Knowledge

REFERENCES

• Behr , M. , Harel , G. , Post , T. and Lesh , R. 1992 . “ Rational number, ratio and proportion ” . In Handbook of research on mathematics teaching and learning , Edited by: Grouws , D. 296 – 333 . New York : Macmillan Publishing .
   Google Scholar
• Kieren , T. 1976 . “ On the mathematical, cognitive, and instructional foundations of rational numbers ” . In Number and measurement: papers from a research workshop , Edited by: Lesh , R. 101 – 144 . Columbus, OH : ERIC/SMEAC .
   Google Scholar
• Markovits , Z. and Sowder , J. T. 1991 . Students' understanding of the relationship between fractions and decimals . Focus on Learning Problems in Mathematics , 13 ( 1 ) : 3 – 11 .
   Google Scholar
• Nesher , P. and Peled , I. 1986 . Shifts in reasoning . Educational Studies in Mathematics , 17 : 67 – 79 .
   Google Scholar
• Olive , J. and Steffe , L. P. 2002 . The construction of an iterative fractional scheme: The case of Joe . Journal of Mathematical Behavior , 20 : 413 – 437 .
   Google Scholar
• Peled , I. 1986 . The development of the decimal number concept , Unpublished doctoral dissertation, The Technion–Israel Institute of Technology, Haifa .
   Google Scholar
• Resnick , L. B. , Nesher , P. , Leonard , F. , Magon , M. , Omanson , S. and Peled , I. 1989 . Conceptual bases of arithmetic errors: The case of decimal fraction . Journal for Research in Mathematics Education , 20 : 8 – 27 .
   Web of Science ®Google Scholar
• Sackure-Grisvard , C. and Leonard , F. 1985 . Intermediate cognitive organization in the process of learning a mathematical concept: The order of positive decimal numbers . Cognition and Instruction , 2 : 157 – 174 .
   Google Scholar
• Stacey , K. 2005 . “ Traveling the road to expertise: A longitudinal study of learning ” . In Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education , Edited by: Chick , H. L. and Vincent , J. L. Vol. 1 , 19 – 36 . Melbourne : PME .
   Google Scholar
• Stacey , K. , Helme , S. and Steinle , V. 2001 . “ Confusions between decimals, fractions and negative numbers: A consequence of the mirror as a conceptual metaphor in three different ways ” . In Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education , Edited by: van den Heuvel-Panhuizen , M. Vol. 4 , 217 – 224 . Utrecht : PME .
   Google Scholar
• Stacey , K. , Helme , S. , Steinle , V. , Baturo , A. , Irwin , K. and Bana , J. 2001 . Teacher's knowledge of difficulties in decimal numeration . Journal of Mathematics Teacher Education , 4 ( 3 ) : 205 – 225 .
   Google Scholar
• Stacey , K. and Steinle , V. 1999 . “ A longitudinal study of children's thinking about decimals: A preliminary analysis ” . In Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education , Edited by: Zaslavsky , O. Vol. 4 , 233 – 240 . Haifa : PME .
   Google Scholar
• Steffe , L. 1988 . “ Children's construction of number sequences and multiplying schemes ” . In Number concepts and operations in the middle grades , Edited by: Hiebert , J. and Behr , M. 119 – 140 . Reston, VA : National Council of Teachers of Mathematics .
   Google Scholar
• Steinle , V. 2004 . Changes with age in students' misconceptions of decimal numbers , Unpublished doctoral dissertation, University of Melbourne, Melbourne .
   Google Scholar
• Steinle , V. and Stacey , K. 2003 . “ Grade-related trends in the prevalence and persistence of decimal misconceptions ” . In Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education , Edited by: Pateman , N. A. , Dougherty , B. J. and Zilliox , J. Vol. 4 , 259 – 266 . Honolulu : PME .
   Google Scholar
• Swan , M. 1983 . Teaching decimal place value: A comprehensive study of “conflict” and “positive only” approaches , Nottingham : Shell Centre for Mathematics Education .
   Google Scholar
• Swan , M. 2001 . “ Dealing with misconceptions in mathematics ” . In Issues in mathematics teaching , Edited by: Gates , P. 147 – 165 . London : Routledge Falmer .
   Google Scholar