Students' Improper Proportional Reasoning: A result of the epistemological obstacle of “linearity”

References

• Behr , J. 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: Grows , D. A. 296 – 333 . New York : Macmillan .
   Google Scholar
• Bodin , A. , Coutourier , R. and Gras , R. 2000 . CHIC: Classification Hierarchique Implicative et Cohesitive‐Version sous Windows – CHIC 1.2 , Rennes, , France : Association pour le Recherche en Didactique des Mathematiques .
   Google Scholar
• Brousseau , G. 1997 . Theory of didactical situations in mathematics , Edited by: Balacheff , N. , Cooper , M. , Sutherland , R. and Warfielf , V. Dordrecht, , The Netherlands : Kluwer .
   Google Scholar
• De Bock , D. , Van Dooren , W. , Janssens , D. and Verschaffel , L. 2004 . “ The illusion of linearity: A literature review from a conceptual perspective ” . In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education , Edited by: Hoines , M. J. and Fuglestad , A. B. Vol. 1 , 373 Norway : Bergen University College .
   Google Scholar
• De Bock , D. , Van Dooren , W. , Janssens , D. and Verschaffel , L. 2002 . Improper use of linear reasoning: An in‐depth study of the nature and the irresistibility of secondary school students' errors . Educational Studies in Mathematics , 50 : 311 – 314 .
   Google Scholar
• De Bock , D. , Verschaffel , L. and Janssens , D. 1998 . The predominance of the linear model in secondary school students' solutions of word problems involving length and area of similar plane figures . Educational Studies in Mathematics , 35 : 65 – 85 .
   Google Scholar
• De Bock , D. , Verschaffel , L. and Janssens , D. 2002 . The effects of different problem presentations and formulations on the illusion of linearity in secondary school students . Mathematical Thinking and Learning , 4 : 65 – 89 .
   Google Scholar
• De Bock , D. , Verschaffel , L. , Janssens , D. , Van Dooren , W. and Claes , K. 2003 . Do realistic contexts and graphical representations always have a beneficial impact on students' performance? Negative evidence from a study on modelling non‐linear geometry problems . Learning and Instruction , 13 : 441 – 463 .
   Web of Science ®Google Scholar
• Duroux , A. 1982 . La valeur absolue: Difficultés majeures pour une notion mineure [The absolute value: Major difficulties related to a minor concept] . Petit X , 3 : 43 – 67 .
   Google Scholar
• Fragkos , P. C. 1983 . Παιδαγωγικές έρϵυνϵς και ϵϕαρµογές [Pedagogical research and implementation] , Thessalonica, , Greece : University Studio Press .
   Google Scholar
• Freudenthal , H. 1973 . Mathematics as an educational task , Dordrecht, , The Netherlands : Reidel .
   Google Scholar
• Freudenthal , H. 1983 . Didactical phenomenology of mathematical structures , Dordrecht, , The Netherlands : Reidel .
   Google Scholar
• Gagatsis , A. and Kyriakides , L. 2000 . Teachers' attitudes towards their pupils' mathematical errors . Educational Research and Evaluation , 6 : 24 – 58 .
   Google Scholar
• Gagatsis , A. , Sriraman , B. , Elia , I. and Modestou , M. 2006 . Exploring young children's geometrical strategies . Nordic Studies in Mathematics Education , 11 : 25 – 52 .
   Google Scholar
• Greer , B. 1997 . Modeling reality in the mathematics classroom: The case of word problems . Learning and Instruction , 7 : 293 – 307 .
   Web of Science ®Google Scholar
• Lerman , I. C. 1981 . Classification et analyse ordinale des données , Paris : Dunod .
   Google Scholar
• Modestou , M. and Gagatsis , A. 2004 . “ Students' improper proportional reasoning: A multidimensional statistical analysis ” . In Proceedings of ICME 10 – Topic Study Group 2: New developments and trends in secondary mathematics education , Edited by: De Bock , D. , Isoda , M. , Cruz , J. A. G. , Gagatsis , A. and Simmt , E. 87 – 94 . Copenhagen : Denmark .
   Google Scholar
• Modestou , M. , Gagatsis , A. and Pitta‐Pantazi , D. 2004 . “ Students' improper proportional reasoning: The case of area and volume of rectangular figures ” . In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education , Edited by: Hoines , M. J. and Fuglestad , A. B. Vol. 3 , 345 – 352 . Norway : Bergen University College .
   Google Scholar
• Radford , L. , Boero , P. and Vasco , C. 2000 . “ Epistemological assumptions framing interpretations of students' understanding of mathematics ” . In History in mathematics education: The ICMI study , Edited by: Fauvel , J. and Maanen , J. V. 162 – 167 . Dordrecht, , The Netherlands : Kluwer .
   Google Scholar
• Rouchier , A. 1999 . “ Recent trends in the theory of didactical situations ” . In Proceedings of the First Conference of the European Society for Research in Mathematics Education , Edited by: Schwank , I. Vol. 2 , 275 – 284 . Osnabrueck, , Germany : Research Institute for Mathematics Education .
   Google Scholar
• Sierpinska , A. 1987 . Humanities students and epistemological obstacles related to limits . Educational Studies in Mathematics , 18 : 371 – 397 .
   Google Scholar
• Stavy , R. and Tirosh , D. 2000 . How students (mis‐)understand science and mathematics: Intuitive rules , New York : Teachers College Press .
   Google Scholar
• Van Dooren , W. , De Bock , D. , Hessels , A. , Janssens , D. and Verschaffel , L. 2004 . Remedying secondary school students' illusion of linearity: A teaching experiment aiming at conceptual change . Learning and Instruction , 14 : 485 – 501 .
   Web of Science ®Google Scholar
• Van Dooren , W. , De Bock , D. , Hessels , A. , Janssens , D. and Verschaffel , L. 2005 . Not everything is proportional: Effects of age and problem type on propensities for overgeneralization . Cognition and Instruction , 23 : 57 – 86 .
   Web of Science ®Google Scholar
• Van Dooren , W. , De Bock , D. , Janssens , D. and Verschaffel , L. in press . Students' over‐reliance on linearity: A scholastic effect . British Journal for Educational Psychology ,
   Google Scholar
• Van Dooren , W. , De Bock , D. , Janssens , D. and Verschaffel , L. in press . Students' over‐use of linearity: A quest for its roots and an evaluation of its impact .
   Google Scholar
• Van Dooren , W. , De Bock , D. , Weyers , D. and Verschaffel , L. 2004 . The predictive power of intuitive rules: A critical analysis of the impact of “More A – more B” and “Same A – same B” . Educational Studies in Mathematics , 56 : 179 – 207 .
   Google Scholar
• Vergnaud , G. 1997 . “ The nature of mathematical concepts ” . In Learning and teaching mathematics: An international perspective , Edited by: Nunes , T. and Bryant , P. 5 – 28 . Hove : Psychology Press .
   Google Scholar
• Verschaffel , L. , De Corte , E. and Lasure , S. 1994 . Realistic considerations in mathematical modeling of school arithmetic problems . Learning and Instruction , 4 : 273 – 294 .
   Google Scholar
• Verschaffel , L. , Greer , B. and De Corte , E. 2000 . Making sense of word problems , Lisse, , Netherlands : Swets & Zeitlinger .
   Google Scholar