메뉴 건너뛰기




Volumn 15, Issue 1, 2012, Pages 9-33

Implicative relations between strategies used in solving proportional and non-proportional problems;Relaciones implicativas entre las estrategias empleadas en la resolución de situaciones lineales y no lineales

Author keywords

Abusive use of linearity; Implicative relations; Linear situations; Non linear situations; Proportional reasoning

Indexed keywords


EID: 84860333973     PISSN: 16652436     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (3)

References (40)
  • 2
    • 0035729517 scopus 로고    scopus 로고
    • Mapping and development of intuitive proportional thinking
    • Christou, C. & Philippou, G. (2002). Mapping and development of intuitive proportional thinking. Journal of Mathematical Behavior, 20 (3), 321-336.
    • (2002) Journal of Mathematical Behavior , vol.20 , Issue.3 , pp. 321-336
    • Christou, C.1    Philippou, G.2
  • 3
    • 54749155344 scopus 로고
    • Connecting research to teaching proportional reasoning
    • Cramer, K. & Post, T. (1993). Connecting research to teaching proportional reasoning. Mathematics Teacher, 86(5), 404-407.
    • (1993) Mathematics Teacher , vol.86 , Issue.5 , pp. 404-407
    • Cramer, K.1    Post, T.2
  • 4
    • 3843147658 scopus 로고    scopus 로고
    • Improper use of linear reasoning: An in-deph 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-deph study of the nature and the irresistibility of secondary school students' errors. Educational Studies in Mathematics, 50(3), 311-334.
    • (2002) Educational Studies In Mathematics , vol.50 , Issue.3 , pp. 311-334
    • de Bock, D.1    van Dooren, W.2    Janssens, D.3    Verschaffel, L.4
  • 6
    • 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
    • 10.1023/A:1003151011999
    • 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 (1), 65-83. doi: 10.1023/A:1003151011999
    • (1998) Educational Studies In Mathematics , vol.35 , Issue.1 , pp. 65-83
    • de Bock, D.1    Verschaffel, L.2    Janssens, D.3
  • 7
    • 77949380537 scopus 로고    scopus 로고
    • Discriminating nonlinearity from linearity: Its cognitive foundations in five-year-olds
    • doi:10.1080/10986060903465780
    • Ebersbach, M., Van Dooren, W., Goudriaan, M. N. & Verschaffel, L. (2010). Discriminating nonlinearity from linearity: Its cognitive foundations in five-year-olds. Mathematical Thinking and Learing, 12, 4-19. doi:10.1080/10986060903465780
    • (2010) Mathematical Thinking and Learing , vol.12 , pp. 4-19
    • Ebersbach, M.1    van Dooren, W.2    Goudriaan, M.N.3    Verschaffel, L.4
  • 9
    • 79551666616 scopus 로고    scopus 로고
    • De la estructura aditiva a la multiplicativa: Efecto de dos variables en el desarrollo del razonamiento proporcional
    • Fernández, C. y Llinares, S. (2011). De la estructura aditiva a la multiplicativa: efecto de dos variables en el desarrollo del razonamiento proporcional. Infancia Aprendizaje, 34(1), 67-80.
    • (2011) Infancia Aprendizaje , vol.34 , Issue.1 , pp. 67-80
    • Fernández, C.1    Llinares, S.2
  • 10
    • 84860327298 scopus 로고    scopus 로고
    • Características del desarrollo del razonamiento proporcional en la educación primaria y secundaria
    • en prensa
    • Fernández, C. y Llinares, S. (en prensa). Características del desarrollo del razonamiento proporcional en la educación primaria y secundaria. Enseñanza de las Ciencias.
    • Enseñanza De Las Ciencias
    • Fernández, C.1    Llinares, S.2
  • 11
    • 84860320990 scopus 로고    scopus 로고
    • Proportional Reasoning: How task variables influence the development of students' strategies from Primary to secondary School
    • Fernández, C., Llinares, S., Modestou, M. & Gagatsis, A. (2010). Proportional Reasoning: How task variables influence the development of students' strategies from Primary to secondary School. Acta Didactica Universitatis Comenianae Mathematics, 10, 1-18.
    • (2010) Acta Didactica Universitatis Comenianae Mathematics , vol.10 , pp. 1-18
    • Fernández, C.1    Llinares, S.2    Modestou, M.3    Gagatsis, A.4
  • 13
    • 79955808265 scopus 로고    scopus 로고
    • Effect of number structure and nature of quantities on secondary school students' proportional reasoning
    • Fernández, C., Llinares, S., Van Dooren, W., De Bock, D. & Verschaffel, L. (2011). Effect of number structure and nature of quantities on secondary school students' proportional reasoning. Studia psychologica, 53(1), 69-81.
    • (2011) Studia Psychologica , vol.53 , Issue.1 , pp. 69-81
    • Fernández, C.1    Llinares, S.2    van Dooren, W.3    de Bock, D.4    Verschaffel, L.5
  • 16
    • 84860327300 scopus 로고    scopus 로고
    • Structural modelling of development of shifts in grasping proportional relational relations underlying problem solving in area and volume
    • Gagatsis, A., Modestou, M. Elia, I. y Spanoudes, G. (2009). Structural modelling of development of shifts in grasping proportional relational relations underlying problem solving in area and volume. Acta Didactica Universitatis Comenianae, 9, 9-23.
    • (2009) Acta Didactica Universitatis Comenianae , vol.9 , pp. 9-23
    • Gagatsis, A.1    Modestou, M.2    Elia, I.3    Spanoudes, G.4
  • 19
    • 0008772890 scopus 로고
    • Early adolescents' proportional reasoning on 'rate' problems
    • Karplus, R., Pulos, S. & Stage, E. K. (1983). Early adolescents' proportional reasoning on 'rate' problems. Educational Studies in Mathematics 14(3), 219
    • (1983) Educational Studies In Mathematics , vol.14 , Issue.3 , pp. 219
    • Karplus, R.1    Pulos, S.2    Stage, E.K.3
  • 20
    • 0002509359 scopus 로고
    • Ratio and proportion: Children's cognitive and metacognitive processes
    • Th. Carpenter, E. Fennema & Th. Romberg, Hillsdale, NJ: Lawrence Erlbaum Associates, Pub
    • Lamon, S. (1993). Ratio and proportion: Children's cognitive and metacognitive processes. In Th. Carpenter, E. Fennema & Th. Romberg (Eds), Rational Numbers. An Integration of Research (pp. 131-156). Hillsdale, NJ: Lawrence Erlbaum Associates, Pub.
    • (1993) Rational Numbers. An Integration of Research , pp. 131-156
    • Lamon, S.1
  • 22
    • 54949096914 scopus 로고    scopus 로고
    • Rational numbers and proportional reasoning: Toward a theoretical framework for research
    • F. K. Lester, Jr. (ed.), NC: Information Age Publishing
    • Lamon, S. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester, Jr. (ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 629-667). NC: Information Age Publishing.
    • (2007) Second Handbook of Research on Mathematics Teaching and Learning , pp. 629-667
    • Lamon, S.1
  • 23
    • 0002929122 scopus 로고
    • Proportional reasoning
    • J. Hiebert & M. Behr (Eds.), Reston, VA: Lawrence Erlebaum y National Council of Teachers of Mathematics
    • Lesh, R., Post, T. & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number Concepts an Operations in the Middle Grades (pp. 93-118). Reston, VA: Lawrence Erlebaum y National Council of Teachers of Mathematics.
    • (1988) Number Concepts An Operations In the Middle Grades , pp. 93-118
    • Lesh, R.1    Post, T.2    Behr, M.3
  • 24
    • 0041378204 scopus 로고    scopus 로고
    • Diagnostic assessment of children's proportional reasoning
    • Misailidou, C. & Williams, J. (2003). Diagnostic assessment of children's proportional reasoning. Journal of Mathematical Behavior 22(3), 335-368.
    • (2003) Journal of Mathematical Behavior , vol.22 , Issue.3 , pp. 335-368
    • Misailidou, C.1    Williams, J.2
  • 25
    • 70350398211 scopus 로고    scopus 로고
    • Didactical designs for students' proportional reasoning: An "open approach" and a fundamental situation
    • Miyakawa, T. & Winslow, C. (2009). Didactical designs for students' proportional reasoning: an "open approach" and a "fundamental situation". Educational Studies in Mathematics 72(2), 199-218.
    • (2009) Educational Studies in Mathematics , vol.72 , Issue.2 , pp. 199-218
    • Miyakawa, T.1    Winslow, C.2
  • 27
    • 34249108883 scopus 로고    scopus 로고
    • Students' improper proportional reasoning: A result of the epistemological obstacle of inearity
    • Modestou, M. & Gagatsis, A. (2007). Students' improper proportional reasoning: A result of the epistemological obstacle of "linearity". Educational Psychology, 27(1), 75-92.
    • (2007) Educational Psychology , vol.27 , Issue.1 , pp. 75-92
    • Modestou, M.1    Gagatsis, A.2
  • 28
    • 84860317370 scopus 로고    scopus 로고
    • Proportional reasoning reformed
    • A. Gagatsis, A. Kuzniak, E. Deliyianni y L. Vivier (eds.), Nicosia-Paris: University of Cyprus- University Paris Diderot 7
    • Modestou, M. & Gagatsis, A. (2009-a). Proportional reasoning reformed. In A. Gagatsis, A. Kuzniak, E. Deliyianni y L. Vivier (eds.), First French-Cypriot Conference of Mathematics Education (pp. 19-33). Nicosia-Paris: University of Cyprus- University Paris Diderot 7.
    • (2009) First French-Cypriot Conference of Mathematics Education , pp. 19-33
    • Modestou, M.1    Gagatsis, A.2
  • 30
    • 77949419508 scopus 로고    scopus 로고
    • Cognitive and meta-cognitive aspects of proportional reasoning
    • Modestou, M. & Gagatsis, A. (2010). Cognitive and meta-cognitive aspects of proportional reasoning. Mathematical Teaching and Learning 12(1), 36-53.
    • (2010) Mathematical Teaching and Learning , vol.12 , Issue.1 , pp. 36-53
    • Modestou, M.1    Gagatsis, A.2
  • 31
    • 0000112365 scopus 로고
    • Protoquantitative origins of ratio reasoning
    • T. Carpenter, E. Fennema, y T. Romberg (eds.), Hillsdale, NJ: Lawrence Erlbaum Associates, Inc, Publishers
    • Resnick, L. & Singer, J. (1993). Protoquantitative origins of ratio reasoning. In T. Carpenter, E. Fennema, y T. Romberg (eds.), Rational Numbers. An Integration of Research (pp. 107-130). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc, Publishers.
    • (1993) Rational Numbers. An Integration of Research , pp. 107-130
    • Resnick, L.1    Singer, J.2
  • 32
    • 0002528395 scopus 로고
    • Grounded theory methodology: An overview
    • N.K. Denzin y Y. Lincoln, Thousand Oaks: Sage
    • Strauss, A. & Corbin, J. (1994). Grounded theory methodology: An overview. In N.K. Denzin y Y. Lincoln (Eds), Handbook of Qualitative Research (pp. 273-285). Thousand Oaks: Sage.
    • (1994) Handbook of Qualitative Research , pp. 273-285
    • Strauss, A.1    Corbin, J.2
  • 33
    • 84950380367 scopus 로고
    • Proportional reasoning. A review of literature
    • doi: 10.1007/BF02400937
    • Tourniaire, F. & Pulos, S. (1985). Proportional reasoning. A review of literature. Educational Studies in Mathematics 16(2), 181-204. doi: 10.1007/BF02400937
    • (1985) Educational Studies In Mathematics , vol.16 , Issue.2 , pp. 181-204
    • Tourniaire, F.1    Pulos, S.2
  • 34
    • 79551679502 scopus 로고    scopus 로고
    • Los conceptos relevantes en el aprendizaje de la graficación. Un análisis a través de la estadística implicativa
    • Trigueros, M. y Escandón, M.C. (2008). Los conceptos relevantes en el aprendizaje de la graficación. Un análisis a través de la estadística implicativa. Revista Mexicana de Investigación Educativa 13(36), 59-85.
    • (2008) Revista Mexicana De Investigación Educativa , vol.13 , Issue.36 , pp. 59-85
    • Trigueros, M.1    Escandón, M.C.2
  • 35
  • 36
    • 13944269902 scopus 로고    scopus 로고
    • Not everything is proportional: Effects of age and problem type on propensities of 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 of overgeneralization. Cognition and Instruction 23(1), 57-86.
    • (2005) Cognition and Instruction , vol.23 , Issue.1 , pp. 57-86
    • van Dooren, W.1    de Bock, D.2    Hessels, A.3    Janssens, D.4    Verschaffel, L.5
  • 38
    • 77954282542 scopus 로고    scopus 로고
    • From addition to multiplication... and back: The development of students' additive and multiplicative reasoning skills
    • Van Dooren, W., De Bock, D. & Verschaffel, L. (2010). From addition to multiplication... and back: The development of students' additive and multiplicative reasoning skills. Cognition and Instruction 28(3), 360-381.
    • (2010) Cognition and Instruction , vol.28 , Issue.3 , pp. 360-381
    • van Dooren, W.1    de Bock, D.2    Verschaffel, L.3
  • 39
    • 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
  • 40
    • 0000857123 scopus 로고
    • Multiplicative structures
    • R. Lesh & M. Landau (Eds.), London: Academic Press, Inc
    • Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisition of Mathematics Concepts and Processes(pp. 128-175). London: Academic Press, Inc.
    • (1983) Acquisition of Mathematics Concepts and Processes , pp. 128-175
    • Vergnaud, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.