메뉴 건너뛰기




Volumn 39, Issue 3, 2008, Pages 311-342

The linear imperative: An inventory and conceptual analysis of students' overuse of linearity

Author keywords

All school levels; Mathematical modeling; Problem solving; Ratio, proportion, percent; Review of research

Indexed keywords


EID: 44249113592     PISSN: 00218251     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review
Times cited : (71)

References (103)
  • 1
    • 44249125856 scopus 로고    scopus 로고
    • Mathematical dimensions of students' use of proportional reasoning in high school physics
    • Akatufba, A. H., & Wallace, J. (1999). Mathematical dimensions of students' use of proportional reasoning in high school physics. School Science & Mathematics, 99, 31-41.
    • (1999) School Science & Mathematics , vol.99 , pp. 31-41
    • Akatufba, A.H.1    Wallace, J.2
  • 2
    • 85131478181 scopus 로고
    • Intuitive physics: Understanding and learning of physical relations
    • T. J. Tighe & B. E. Shepp Eds, Hillsdale, NJ: Lawrence Erlbaum Associates
    • Anderson, N. H. (1983). Intuitive physics: Understanding and learning of physical relations. In T. J. Tighe & B. E. Shepp (Eds.), Perception, cognition and development: Interactional analyses (pp. 231-265). Hillsdale, NJ: Lawrence Erlbaum Associates.
    • (1983) Perception, cognition and development: Interactional analyses , pp. 231-265
    • Anderson, N.H.1
  • 3
    • 0011769472 scopus 로고    scopus 로고
    • Spurious correlations in mathematical thinking
    • Ben-Zeev, T., & Star, J. R. (2001). Spurious correlations in mathematical thinking. Cognition and Instruction, 19, 253-275.
    • (2001) Cognition and Instruction , vol.19 , pp. 253-275
    • Ben-Zeev, T.1    Star, J.R.2
  • 6
    • 44249086777 scopus 로고    scopus 로고
    • Des grandeurs aux espaces vectoriels: La linéarité comme fil conducteur [From quantities to vector spaces: Linearity as a general guiding principle]
    • Centre de Recherche sur l'Enseignement des Mathématiques, Belgium: Author
    • Centre de Recherche sur l'Enseignement des Mathématiques. (2002). Des grandeurs aux espaces vectoriels: La linéarité comme fil conducteur [From quantities to vector spaces: Linearity as a general guiding principle]. Nivelles, Belgium: Author.
    • (2002) Nivelles
  • 8
    • 0009980501 scopus 로고
    • Learning and teaching ratio and proportion: Research implications
    • D. T. Owens Ed, New York: Macmillan
    • Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. T. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 159-178). New York: Macmillan.
    • (1993) Research ideas for the classroom: Middle grades mathematics , pp. 159-178
    • Cramer, K.1    Post, T.2    Currier, S.3
  • 9
    • 44249092421 scopus 로고
    • Epistemological comparative analysis of two approaches to plane geometry on the age of twelve, Unpublished doctoral dissertation, Faculté des Sciences, Université Catholique de Louvain, Louvain-la-Neuve, Belgium
    • De Block-Docq, C. (1992). Analyse épistémologique comparative de deux enseignements de la géométrie plane vers l'age de douze ans [Epistemological comparative analysis of two approaches to plane geometry on the age of twelve]. Unpublished doctoral dissertation, Faculté des Sciences, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.
    • (1992) Analyse épistémologique comparative de deux enseignements de la géométrie plane vers l'age de douze ans
    • De Block-Docq, C.1
  • 10
    • 3843147658 scopus 로고    scopus 로고
    • Improper use of linear reasoning: An in-depth study of the nature and the irresistibility of secondary school students' errors
    • De Bock, D., Van Dooren, W., Janssens, D., & 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, 311-334.
    • (2002) Educational Studies in Mathematics , vol.50 , pp. 311-334
    • De Bock, D.1    Van Dooren, W.2    Janssens, D.3    Verschaffel, L.4
  • 12
    • 54549127983 scopus 로고    scopus 로고
    • The predominance of the linear model in secondary school students' solutions of word problems involving length and area of similar plane figures
    • De Bock, D., Verschaffel, L., & 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, 65-83.
    • (1998) Educational Studies in Mathematics , vol.35 , pp. 65-83
    • De Bock, D.1    Verschaffel, L.2    Janssens, D.3
  • 13
    • 0012169671 scopus 로고    scopus 로고
    • The effects of different problem presentations and formulations on the illusion of linearity in secondary school students
    • De Bock, D., Verschaffel, L., & 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.
    • (2002) Mathematical Thinking and Learning , vol.4 , pp. 65-89
    • De Bock, D.1    Verschaffel, L.2    Janssens, D.3
  • 14
    • 0037411652 scopus 로고    scopus 로고
    • 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
    • De Bock, D., Verschaffel, L., Janssens, D., Van Dooren, W., & 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.
    • (2003) Learning and Instruction , vol.13 , pp. 441-463
    • De Bock, D.1    Verschaffel, L.2    Janssens, D.3    Van Dooren, W.4    Claes, K.5
  • 15
    • 0009299656 scopus 로고    scopus 로고
    • A division problem with a remainder embedded across two contexts: Children's solutions in restrictive versus real-world settings
    • DeFranco, T. C., & Curcio, F. R. (1997). A division problem with a remainder embedded across two contexts: Children's solutions in restrictive versus real-world settings. Focus on Learning Problems in Mathematics, 19(2), 58-72.
    • (1997) Focus on Learning Problems in Mathematics , vol.19 , Issue.2 , pp. 58-72
    • DeFranco, T.C.1    Curcio, F.R.2
  • 16
    • 44249088689 scopus 로고    scopus 로고
    • Ebersbach, M., & Resing, W. C. M. (2006). Reasoning about non-linearity in 6- to 9-year-olds: The role of task presentation. In J. Novotná, H. Moraová, M. Kràtká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (3, pp. 9-16). Prague, Czech Republic: International Group for the Psychology of Mathematics Education.
    • Ebersbach, M., & Resing, W. C. M. (2006). Reasoning about non-linearity in 6- to 9-year-olds: The role of task presentation. In J. Novotná, H. Moraová, M. Kràtká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 9-16). Prague, Czech Republic: International Group for the Psychology of Mathematics Education.
  • 17
    • 33847379311 scopus 로고    scopus 로고
    • Children's intuitive mathematics: The development of knowledge about non-linear growth
    • Ebersbach, M., & Wilkening, F. (2007). Children's intuitive mathematics: The development of knowledge about non-linear growth. Child Development, 78, 296-308.
    • (2007) Child Development , vol.78 , pp. 296-308
    • Ebersbach, M.1    Wilkening, F.2
  • 18
    • 0040709388 scopus 로고
    • Newtonian in mind, but Aristotelian at heart
    • Ebison, M. G. (1993). Newtonian in mind, but Aristotelian at heart. Science and Education, 2, 345-362.
    • (1993) Science and Education , vol.2 , pp. 345-362
    • Ebison, M.G.1
  • 19
    • 34249982820 scopus 로고    scopus 로고
    • Extending linear models to non-linear contexts: An in-depth study about two university students' mathematical productions
    • M. J. Høines & A. B. Fuglestad Eds, Bergen, Norway: International Group for the Psychology of Mathematics Education
    • Esteley, C., Villarreal, M., & Alagia, H. (2004). Extending linear models to non-linear contexts: An in-depth study about two university students' mathematical productions. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 343-350). Bergen, Norway: International Group for the Psychology of Mathematics Education.
    • (2004) Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education , vol.2 , pp. 343-350
    • Esteley, C.1    Villarreal, M.2    Alagia, H.3
  • 20
    • 0141867846 scopus 로고    scopus 로고
    • In two minds: Dual process accounts of reasoning
    • Evans, J. S. B. T. (2003). In two minds: Dual process accounts of reasoning. Trends in Cognitive Sciences, 7, 454-459.
    • (2003) Trends in Cognitive Sciences , vol.7 , pp. 454-459
    • Evans, J.S.B.T.1
  • 22
    • 0008785255 scopus 로고    scopus 로고
    • Intuitions and schemata in mathematical reasoning
    • Fischbein, E. (1999). Intuitions and schemata in mathematical reasoning. Educational Studies in Mathematics, 38, 11-50.
    • (1999) Educational Studies in Mathematics , vol.38 , pp. 11-50
    • Fischbein, E.1
  • 23
    • 0041417052 scopus 로고
    • Does the teaching of probability improve probabilistic intuitions?
    • Fischbein, E., & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? Educational Studies in Mathematics, 15, 1-24.
    • (1984) Educational Studies in Mathematics , vol.15 , pp. 1-24
    • Fischbein, E.1    Gazit, A.2
  • 24
    • 21444456108 scopus 로고    scopus 로고
    • The evolution with age of probabilistic, intuitively based misconceptions
    • Fischbein, E., & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education, 28, 96-105.
    • (1997) Journal for Research in Mathematics Education , vol.28 , pp. 96-105
    • Fischbein, E.1    Schnarch, D.2
  • 27
    • 0012202558 scopus 로고    scopus 로고
    • Teachers' attitudes towards their pupils' mathematical errors
    • Gagatsis, A., & Kyriakides, L. (2000). Teachers' attitudes towards their pupils' mathematical errors. Educational Research and Evaluation, 6, 24-58.
    • (2000) Educational Research and Evaluation , vol.6 , pp. 24-58
    • Gagatsis, A.1    Kyriakides, L.2
  • 28
    • 0003954555 scopus 로고
    • H. Crew & A. deSalvio, Trans, New York: Dover, Original work published 1638
    • Galilei, G. (1990). Dialogues concerning two new sciences (H. Crew & A. deSalvio, Trans.). New York: Dover. (Original work published 1638)
    • (1990) Dialogues concerning two new sciences
    • Galilei, G.1
  • 29
    • 0011493292 scopus 로고
    • Understanding of arithmetical operations as models of situations
    • J. A. Sloboda & D. Rogers Eds, Oxford, United Kingdom: Clarendon
    • Greer, B. (1987). Understanding of arithmetical operations as models of situations. In J. A. Sloboda & D. Rogers (Eds.), Cognitive processes in mathematics (pp. 60-80). Oxford, United Kingdom: Clarendon.
    • (1987) Cognitive processes in mathematics , pp. 60-80
    • Greer, B.1
  • 30
    • 0000683216 scopus 로고
    • The mathematical modelling perspective on word problems
    • Greer, B. (1993). The mathematical modelling perspective on word problems. Journal of Mathematical Behavior, 12, 239-250.
    • (1993) Journal of Mathematical Behavior , vol.12 , pp. 239-250
    • Greer, B.1
  • 32
    • 3242702754 scopus 로고    scopus 로고
    • Teachers' pedagogical content knowledge: Graphs, from a cognitivist to a situated perspective
    • A. D. Cockburn & E. Nardi Eds, Norwich, United Kingdom: International Group for the Psychology of Mathematics Education
    • Hadjidemetriou, C., & Williams, J. S. (2002b). Teachers' pedagogical content knowledge: Graphs, from a cognitivist to a situated perspective. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 57-64). Norwich, United Kingdom: International Group for the Psychology of Mathematics Education.
    • (2002) Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education , vol.3 , pp. 57-64
    • Hadjidemetriou, C.1    Williams, J.S.2
  • 33
    • 84917516270 scopus 로고    scopus 로고
    • Foreword
    • A. J. Baroody & A. Dowker Eds, Mahwah, NJ: Lawrence Erlbaum Associates
    • Hatano, G. (2003). Foreword. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills (pp. xi-xiii). Mahwah, NJ: Lawrence Erlbaum Associates.
    • (2003) The development of arithmetic concepts and skills
    • Hatano, G.1
  • 34
    • 0013341649 scopus 로고
    • Children's conceptions of probability - A psychological and pedagogical review
    • Hawkins, A. S., & Kapadia, R. (1984). Children's conceptions of probability - A psychological and pedagogical review. Educational Studies in Mathematics, 15, 349-377.
    • (1984) Educational Studies in Mathematics , vol.15 , pp. 349-377
    • Hawkins, A.S.1    Kapadia, R.2
  • 35
    • 0002686468 scopus 로고
    • From words to equations, meaning and representation in algebra word problems
    • M. A. Just & P. A. Carpenter Eds, Hillsdale, NJ: Lawrence Erlbaum Associates
    • Hinsley, D., Hayes, J., & Simon, H. (1977). From words to equations, meaning and representation in algebra word problems. In M. A. Just & P. A. Carpenter (Eds.), Cognitive processes in comprehension (pp. 89-108). Hillsdale, NJ: Lawrence Erlbaum Associates.
    • (1977) Cognitive processes in comprehension , pp. 89-108
    • Hinsley, D.1    Hayes, J.2    Simon, H.3
  • 38
    • 49649138413 scopus 로고
    • Subjective probability: A judgement of representativeness
    • Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgement of representativeness. Cognitive Psychology, 3, 430-454.
    • (1972) Cognitive Psychology , vol.3 , pp. 430-454
    • Kahneman, D.1    Tversky, A.2
  • 39
    • 0002351467 scopus 로고
    • Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns
    • G. Harel & J. Confrey Eds, New York: State University of New York Press
    • Kaput, J. J., & West, M. M. (1994). Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 235-287). New York: State University of New York Press.
    • (1994) The development of multiplicative reasoning in the learning of mathematics , pp. 235-287
    • Kaput, J.J.1    West, M.M.2
  • 40
    • 0010168088 scopus 로고
    • Continuous functions: Students' viewpoints
    • Karplus, R. (1979). Continuous functions: Students' viewpoints. European Journal of Science Education, 1, 397-413.
    • (1979) European Journal of Science Education , vol.1 , pp. 397-413
    • Karplus, R.1
  • 41
    • 0017794370 scopus 로고
    • The representation of children's knowledge
    • H. Reese & L. P. Lipsitt Eds, New York: Academic Press
    • Klahr, D., & Siegler, R. (1978). The representation of children's knowledge. In H. Reese & L. P. Lipsitt (Eds.), Advances in child development and behavior (Vol. 12, pp. 62-116). New York: Academic Press.
    • (1978) Advances in child development and behavior , vol.12 , pp. 62-116
    • Klahr, D.1    Siegler, R.2
  • 42
    • 84963254759 scopus 로고
    • Informal conceptions of probability
    • Konoid, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6, 59-98.
    • (1989) Cognition and Instruction , vol.6 , pp. 59-98
    • Konoid, C.1
  • 43
    • 44249104838 scopus 로고    scopus 로고
    • Investigating factors that influence students' mathematical reasoning
    • M. van den Heuvel-Panhuizen Ed, Utrecht, The Netherlands: International Group for the Psychology of Mathematics Education
    • Kuchemann, D., & Hoyles, C. (2001). Investigating factors that influence students' mathematical reasoning. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 85-92). Utrecht, The Netherlands: International Group for the Psychology of Mathematics Education.
    • (2001) Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education , vol.3 , pp. 85-92
    • Kuchemann, D.1    Hoyles, C.2
  • 44
    • 3843086571 scopus 로고    scopus 로고
    • The nature of pupils' probabilistic thinking in primary school pupils in Cyprus
    • A. D. Cockburn & E. Nardi Eds, Norwich, United Kingdom: International Group for the Psychology of Mathematics Education
    • Lamprianou, I., & Lamprianou, T. A. (2002). The nature of pupils' probabilistic thinking in primary school pupils in Cyprus. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 273-280). Norwich, United Kingdom: International Group for the Psychology of Mathematics Education.
    • (2002) Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education , vol.3 , pp. 273-280
    • Lamprianou, I.1    Lamprianou, T.A.2
  • 45
    • 3843082192 scopus 로고    scopus 로고
    • A developmental scale for assessing probabilistic thinking and the tendency to use a representativeness heuristic
    • A. D. Cockburn & E. Nardi Eds, Norwich, United Kingdom: International Group for the Psychology of Mathematics Education
    • Lamprianou, T. A., & Williams, J. (2002). A developmental scale for assessing probabilistic thinking and the tendency to use a representativeness heuristic. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 9-16). Norwich, United Kingdom: International Group for the Psychology of Mathematics Education.
    • (2002) Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education , vol.3 , pp. 9-16
    • Lamprianou, T.A.1    Williams, J.2
  • 46
    • 0004064564 scopus 로고
    • Cambridge, United Kingdom: University Press
    • Lave, J. (1988). Cognition in practice. Cambridge, United Kingdom: University Press.
    • (1988) Cognition in practice
    • Lave, J.1
  • 47
    • 85066269882 scopus 로고
    • Word problems: A microcosm of theories of learning
    • P. Light & G. Butterworth Eds, New York: Harvester Wheatsheaf
    • Lave, J. (1992). Word problems: A microcosm of theories of learning. In P. Light & G. Butterworth (Eds.), Context and cognition: Ways of learning and knowing (pp. 74-92). New York: Harvester Wheatsheaf.
    • (1992) Context and cognition: Ways of learning and knowing , pp. 74-92
    • Lave, J.1
  • 50
    • 3843100860 scopus 로고    scopus 로고
    • Models and modeling perspectives on the development of students and teachers
    • Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5, 109-129.
    • (2003) Mathematical Thinking and Learning , vol.5 , pp. 109-129
    • Lesh, R.1    Lehrer, R.2
  • 51
    • 13944275726 scopus 로고    scopus 로고
    • A models and modeling perspective on metacognitive functioning in everyday situations where problem solvers develop mathematical constructs
    • R. Lesh & H. Doerr Eds, Mahwah, NJ: Lawrence Erlbaum Associates
    • Lesh, R., Lester, F. K., & Hjalmarson, M. (2003). A models and modeling perspective on metacognitive functioning in everyday situations where problem solvers develop mathematical constructs. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching (pp. 383-404). Mahwah, NJ: Lawrence Erlbaum Associates.
    • (2003) Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching , pp. 383-404
    • Lesh, R.1    Lester, F.K.2    Hjalmarson, M.3
  • 52
    • 44249109357 scopus 로고    scopus 로고
    • Differentiation of students' reasoning on linear and quadratic geometric number patterns
    • M. J. Høines & A. B. Fuglestad Eds, Bergen, Norway: International Group for the Psychology of Mathematics Education
    • Lin, F.-L., & Yang, K.-L. (2004). Differentiation of students' reasoning on linear and quadratic geometric number patterns. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 457-464). Bergen, Norway: International Group for the Psychology of Mathematics Education.
    • (2004) Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education , vol.4 , pp. 457-464
    • Lin, F.-L.1    Yang, K.-L.2
  • 54
    • 44249124620 scopus 로고    scopus 로고
    • Livne, T. (1996). Examination of high school students' difficulties in understanding the change in surface area, and surface area/with the change in size and/or shape of a body. Unpublished master's thesis, Tel-Aviv University, Tel-Aviv, Israel (In Hebrew).
    • Livne, T. (1996). Examination of high school students' difficulties in understanding the change in surface area, volume and surface area/volume with the change in size and/or shape of a body. Unpublished master's thesis, Tel-Aviv University, Tel-Aviv, Israel (In Hebrew).
  • 56
    • 0003098859 scopus 로고
    • Towards a process model for high school algebra errors
    • D. Sleeman & J. S. Brown Eds, London: Academic Press
    • Matz, M. (1982). Towards a process model for high school algebra errors. In D. Sleeman & J. S. Brown (Eds.), Intelligent tutoring systems (pp. 25-50). London: Academic Press.
    • (1982) Intelligent tutoring systems , pp. 25-50
    • Matz, M.1
  • 57
    • 44249108200 scopus 로고
    • Perceptual reasoning and proportion
    • Müller, D. (1979). Perceptual reasoning and proportion. Mathematics Teaching, 87, 20-22.
    • (1979) Mathematics Teaching , vol.87 , pp. 20-22
    • Müller, D.1
  • 59
    • 0003865799 scopus 로고    scopus 로고
    • National Council of Teachers of Mathematics, Reston, VA: Author
    • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
    • (2000) Principles and standards for school mathematics
  • 60
    • 33746831717 scopus 로고    scopus 로고
    • School stereotype word problems and the open nature of applications
    • C. Alsina, J. M. Alvarez, B. Hodgson, C. Laborde, & A. Pérez Eds, Sevilla, Spain: Doble Cero
    • Nesher, P. (1996). School stereotype word problems and the open nature of applications. In C. Alsina, J. M. Alvarez, B. Hodgson, C. Laborde, & A. Pérez (Eds.), Selected lectures from the 8th International Congress on Mathematical Education (pp. 335-343). Sevilla, Spain: Doble Cero.
    • (1996) Selected lectures from the 8th International Congress on Mathematical Education , pp. 335-343
    • Nesher, P.1
  • 62
    • 1842717611 scopus 로고
    • Students' perception and use of pattern and generalization
    • J. P. da Ponte & J. F. Matos Eds, Lisbon, Portugal: International Group for the Psychology of Mathematics Education
    • Orton, J., & Orton, A. (1994). Students' perception and use of pattern and generalization. In J. P. da Ponte & J. F. Matos (Eds.), Proceedings of the 18th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 407-414). Lisbon, Portugal: International Group for the Psychology of Mathematics Education.
    • (1994) Proceedings of the 18th Conference of the International Group for the Psychology of Mathematics Education , vol.3 , pp. 407-414
    • Orton, J.1    Orton, A.2
  • 65
    • 44249101514 scopus 로고    scopus 로고
    • Post, T., Behr, M., & Lesh, R. (1988). Proportionality and the development of pre-algebra understanding. In A. Coxford (Ed.), Algebraic concepts in the curriculum K-12 (1988 Yearbook) (pp. 78-90). Reston, VA: National Council of Teachers of Mathematics.
    • Post, T., Behr, M., & Lesh, R. (1988). Proportionality and the development of pre-algebra understanding. In A. Coxford (Ed.), Algebraic concepts in the curriculum K-12 (1988 Yearbook) (pp. 78-90). Reston, VA: National Council of Teachers of Mathematics.
  • 66
    • 0000112365 scopus 로고
    • Protoquantitative origins of ratio reasoning
    • T. P. Carpenter, E. Fennema, & T. A. Romberg Eds, Hillsdale, NJ: Lawrence Erlbaum Associates
    • Resnick, L. B., & Singer, J. A. (1993). Protoquantitative origins of ratio reasoning. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 107-130). Hillsdale, NJ: Lawrence Erlbaum Associates.
    • (1993) Rational numbers: An integration of research , pp. 107-130
    • Resnick, L.B.1    Singer, J.A.2
  • 67
    • 0031497221 scopus 로고    scopus 로고
    • Every word problem has a solution: The suspension of reality and sense-making in the culture of school mathematics
    • Reusser, K., & Stebler, R. (1997). Every word problem has a solution: The suspension of reality and sense-making in the culture of school mathematics. Learning and Instruction, 7, 309-328.
    • (1997) Learning and Instruction , vol.7 , pp. 309-328
    • Reusser, K.1    Stebler, R.2
  • 68
    • 44249121158 scopus 로고
    • Acquisition de notions relatives à la dimensionalité des mesures spatiales (longueur, surface) [Acquisition of notions relative to the dimensionality of spatial measures (length, area)]
    • Rogalski, J. (1982). Acquisition de notions relatives à la dimensionalité des mesures spatiales (longueur, surface) [Acquisition of notions relative to the dimensionality of spatial measures (length, area)]. Recherches en Didactique des Mathématiques, 3, 343-396.
    • (1982) Recherches en Didactique des Mathématiques , vol.3 , pp. 343-396
    • Rogalski, J.1
  • 69
    • 44249087273 scopus 로고    scopus 로고
    • Rouche, N. (1989). Prouver: Amener à l'évidence ou contrôler des implications? [Proving: Bringing back to evidence or verifying the implications?]. In Commission inter-IREM Histoire et Epistémologie des Mathématiques (Ed.), La démonstration dans l'histoire [Demonstration in history] (pp. 8-38). Lyon, France: IREM.
    • Rouche, N. (1989). Prouver: Amener à l'évidence ou contrôler des implications? [Proving: Bringing back to evidence or verifying the implications?]. In Commission inter-IREM Histoire et Epistémologie des Mathématiques (Ed.), La démonstration dans l'histoire [Demonstration in history] (pp. 8-38). Lyon, France: IREM.
  • 71
    • 44249118188 scopus 로고
    • The sense of measurement, Bruxelles, Belgium: Didier Hatier
    • Rouche, N. (1992b). Le sens de la mesure [The sense of measurement]. Bruxelles, Belgium: Didier Hatier.
    • (1992) Le sens de la mesure
    • Rouche, N.1
  • 72
    • 78651241383 scopus 로고
    • When good teaching leads to bad results: The disasters of "well-taught" mathematics courses
    • Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of "well-taught" mathematics courses. Educational Psychologist, 23, 145-166.
    • (1988) Educational Psychologist , vol.23 , pp. 145-166
    • Schoenfeld, A.H.1
  • 73
    • 85068096396 scopus 로고
    • On mathematics as sense-making. An informal attack on the unfortunate divorce of formal and informal mathematics
    • J. F. Voss, D. N. Perkins, & J. W. Segal Eds, Hillsdale, NJ: Lawrence Erlbaum Associates
    • Schoenfeld, A. H. (1991). On mathematics as sense-making. An informal attack on the unfortunate divorce of formal and informal mathematics. In J. F. Voss, D. N. Perkins, & J. W. Segal (Eds.), Informal reasoning and education (pp. 311-343). Hillsdale, NJ: Lawrence Erlbaum Associates.
    • (1991) Informal reasoning and education , pp. 311-343
    • Schoenfeld, A.H.1
  • 74
    • 0002855588 scopus 로고
    • Research in probability and statistics: Reflections and directions
    • D. A. Grouws Ed, New York: Macmillan
    • Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D. A. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 465-494). New York: Macmillan.
    • (1992) Handbook of research in mathematics teaching and learning , pp. 465-494
    • Shaughnessy, J.M.1
  • 75
    • 21844524057 scopus 로고
    • Building and understanding multiplicative relationships: A study of prospective elementary teachers
    • Simon, M. A., & Blume, G. W. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers. Journal for Research in Mathematics Education, 25, 472-494.
    • (1994) Journal for Research in Mathematics Education , vol.25 , pp. 472-494
    • Simon, M.A.1    Blume, G.W.2
  • 76
    • 0000406266 scopus 로고    scopus 로고
    • Knowing about proportions in different contexts
    • T. Nunes & P. Bryant Eds, Hove, United Kingdom: Lawrence Erlbaum Associates
    • Singer, J. A., Kohn, A. S., & Resnick, L. B. (1997). Knowing about proportions in different contexts. In T. Nunes & P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 115-132). Hove, United Kingdom: Lawrence Erlbaum Associates.
    • (1997) Learning and teaching mathematics: An international perspective , pp. 115-132
    • Singer, J.A.1    Kohn, A.S.2    Resnick, L.B.3
  • 77
    • 0011055627 scopus 로고
    • Representations of proportional relationships: Are children part-part or part-whole reasoners?
    • Singer, J. A., & Resnick, L. B. (1992). Representations of proportional relationships: Are children part-part or part-whole reasoners? Educational Studies in Mathematics, 23, 132-246.
    • (1992) Educational Studies in Mathematics , vol.23 , pp. 132-246
    • Singer, J.A.1    Resnick, L.B.2
  • 78
    • 77954557633 scopus 로고    scopus 로고
    • The empirical case for two systems of reasoning
    • Sloman, S. A. (1996). The empirical case for two systems of reasoning. Psychological Bulletin, 119, 3-22.
    • (1996) Psychological Bulletin , vol.119 , pp. 3-22
    • Sloman, S.A.1
  • 79
    • 0031514345 scopus 로고    scopus 로고
    • Proportional reasoning in young children: The parts and the whole of it
    • Sophian, C., & Wood, A. (1997). Proportional reasoning in young children: The parts and the whole of it. Journal of Educational Psychology, 89, 309-317.
    • (1997) Journal of Educational Psychology , vol.89 , pp. 309-317
    • Sophian, C.1    Wood, A.2
  • 80
    • 84989491909 scopus 로고
    • Children's proportional judgements: The importance of a half
    • Spinillo, A. G., & Bryant, P. E. (1991). Children's proportional judgements: The importance of a half. Child Development, 62, 427-440.
    • (1991) Child Development , vol.62 , pp. 427-440
    • Spinillo, A.G.1    Bryant, P.E.2
  • 81
    • 0011025448 scopus 로고    scopus 로고
    • Proportional reasoning in young children: Part-part comparisons about continuous and discontinuous quantity
    • Spinillo, A. G., & Bryant, P. E. (1999). Proportional reasoning in young children: Part-part comparisons about continuous and discontinuous quantity. Mathematical Cognition, 5, 181-197.
    • (1999) Mathematical Cognition , vol.5 , pp. 181-197
    • Spinillo, A.G.1    Bryant, P.E.2
  • 82
    • 1842768042 scopus 로고
    • Finding and using patterns in linear generalising problems
    • Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20, 147-164.
    • (1989) Educational Studies in Mathematics , vol.20 , pp. 147-164
    • Stacey, K.1
  • 84
    • 3843113716 scopus 로고
    • Prospective primary teachers' conceptions of area
    • G. Booker, P. Cobb, & T. N. de Mendicuti Eds, Oaxtepex, Mexico: International Group for the Psychology of Mathematics Education
    • Tierney, C., Boyd, C., & Davis, G. (1990). Prospective primary teachers' conceptions of area. In G. Booker, P. Cobb, & T. N. de Mendicuti (Eds.), Proceedings of the 14th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 307-314). Oaxtepex, Mexico: International Group for the Psychology of Mathematics Education.
    • (1990) Proceedings of the 14th Conference of the International Group for the Psychology of Mathematics Education , vol.2 , pp. 307-314
    • Tierney, C.1    Boyd, C.2    Davis, G.3
  • 85
    • 0041579531 scopus 로고    scopus 로고
    • Intuitive rules: A way to explain and predict students' reasoning
    • Tirosh, D., & Stavy, R. (1999a). Intuitive rules: A way to explain and predict students' reasoning. Educational Studies in Mathematics, 38, 51-66.
    • (1999) Educational Studies in Mathematics , vol.38 , pp. 51-66
    • Tirosh, D.1    Stavy, R.2
  • 87
    • 3843150849 scopus 로고
    • Examination of a relationship between children's estimation of probabilities and their understanding of proportion
    • J. da Ponte & J. F. Matos Eds, Lisbon, Portugal: International Group for the Psychology of Mathematics Education
    • Truran, J. M. (1994). Examination of a relationship between children's estimation of probabilities and their understanding of proportion. In J. da Ponte & J. F. Matos (Eds.), Proceedings of the 18th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 337-344). Lisbon, Portugal: International Group for the Psychology of Mathematics Education.
    • (1994) Proceedings of the 18th Conference of the International Group for the Psychology of Mathematics Education , vol.4 , pp. 337-344
    • Truran, J.M.1
  • 92
    • 13944269902 scopus 로고    scopus 로고
    • Not everything is proportional: Effects of age and problem type on propensities for overgeneralization
    • Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005). Not everything is proportional: Effects of age and problem type on propensities for overgeneralization. Cognition and Instruction, 23, 57-86.
    • (2005) Cognition and Instruction , vol.23 , pp. 57-86
    • Van Dooren, W.1    De Bock, D.2    Hessels, A.3    Janssens, D.4    Verschaffel, L.5
  • 94
    • 4544268394 scopus 로고    scopus 로고
    • Challenging the predictive power of intuitive rules: A replication and extension study on the impact of 'more A-more B' and 'same A-same B
    • Van Dooren, W., De Bock, D., Weyers, D., & Verschaffel, L. (2004). Challenging the predictive power of intuitive rules: A replication and extension study on the impact of 'more A-more B' and 'same A-same B.' Educational Studies in Mathematics, 56, 179-207.
    • (2004) Educational Studies in Mathematics , vol.56 , pp. 179-207
    • Van Dooren, W.1    De Bock, D.2    Weyers, D.3    Verschaffel, L.4
  • 95
    • 44249122470 scopus 로고    scopus 로고
    • Modelling for life: Developing adaptive expertise in mathematical modelling from an early age
    • L. Verschaffel, F. Dochy, M. Boekaerts, & S. Vosniadou Eds, Oxford, United Kingdom: Elsevier
    • Van Dooren, W., Verschaffel, L., Greer, B., & De Bock, D. (2006). Modelling for life: Developing adaptive expertise in mathematical modelling from an early age. In L. Verschaffel, F. Dochy, M. Boekaerts, & S. Vosniadou (Eds.), Instructional psychology: Past, present, and future trends (pp. 91-109). Oxford, United Kingdom: Elsevier.
    • (2006) Instructional psychology: Past, present, and future trends , pp. 91-109
    • Van Dooren, W.1    Verschaffel, L.2    Greer, B.3    De Bock, D.4
  • 96
    • 0000857123 scopus 로고
    • Multiplicative structures
    • R. Lesh & M. Landau Eds, New York: Academic Press
    • Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 127-174). New York: Academic Press.
    • (1983) Acquisition of mathematics concepts and processes , pp. 127-174
    • Vergnaud, G.1
  • 97
    • 33746708117 scopus 로고    scopus 로고
    • Taking the modelling perspective seriously at the elementary school level: Promises and pitfalls
    • A. D. Cockburn & E. Nardi Eds, Norwich, United Kingdom: International Group for the Psychology of Mathematics Education
    • Verschaffel, L. (2002). Taking the modelling perspective seriously at the elementary school level: Promises and pitfalls. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 64-80). Norwich, United Kingdom: International Group for the Psychology of Mathematics Education.
    • (2002) Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education , vol.1 , pp. 64-80
    • Verschaffel, L.1
  • 98
    • 0000523545 scopus 로고
    • Realistic considerations in mathematical modelling of school arithmetic word problems
    • Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modelling of school arithmetic word problems. Learning and Instruction, 4, 273-294.
    • (1994) Learning and Instruction , vol.4 , pp. 273-294
    • Verschaffel, L.1    De Corte, E.2    Lasure, S.3
  • 101
    • 44249117952 scopus 로고    scopus 로고
    • Villarreal, M., Esteley, C., & Alagia, H. (2004). University students' extension of linear models to non-linear situations. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (1, p. 364). Bergen, Norway: International Group for the Psychology of Mathematics Education.
    • Villarreal, M., Esteley, C., & Alagia, H. (2004). University students' extension of linear models to non-linear situations. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, p. 364). Bergen, Norway: International Group for the Psychology of Mathematics Education.
  • 102
    • 84989125373 scopus 로고
    • Diagnosing and altering three Aristotelian alternative conceptions in dynamics: Microcomputer simulations of scientific models
    • Weiler, H. G. (1995). Diagnosing and altering three Aristotelian alternative conceptions in dynamics: Microcomputer simulations of scientific models. Journal of Research in Science Teaching, 32, 271-290.
    • (1995) Journal of Research in Science Teaching , vol.32 , pp. 271-290
    • Weiler, H.G.1
  • 103
    • 0031498027 scopus 로고    scopus 로고
    • Word problems and mathematical reasoning: A study of children's mastery of reference and meaning in textual realities
    • Wyndhamn, J., & Säljö, R. (1997). Word problems and mathematical reasoning: A study of children's mastery of reference and meaning in textual realities. Learning and Instruction, 7, 361-382.
    • (1997) Learning and Instruction , vol.7 , pp. 361-382
    • Wyndhamn, J.1    Säljö, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.