메뉴 건너뛰기




Volumn 1, Issue , 2011, Pages 15-30

Can Modelling Be Taught and Learnt? Some Answers from Empirical Research

Author keywords

Mathematical Competency; Modelling Competency; Modelling Task; Solution Plan; Word Problem

Indexed keywords


EID: 85102015745     PISSN: 22114920     EISSN: 22114939     Source Type: Book Series    
DOI: 10.1007/978-94-007-0910-2_3     Document Type: Chapter
Times cited : (150)

References (74)
  • 1
    • 84904256151 scopus 로고
    • Project work in school mathematics
    • J. De Lange et al. (Eds.), (pp. , Chichester: Horwood
    • Abrantes, P. (1993). Project work in school mathematics. In J. De Lange et al. (Eds.), Innovation in maths education by modelling and applications (pp. 355–364). Chichester: Horwood.
    • (1993) Innovation in Maths Education by Modelling and Applications , pp. 355-364
    • Abrantes, P.1
  • 3
    • 85045948835 scopus 로고    scopus 로고
    • Less chalk, less words, less symbols … More objects, more context, more actions
    • W. Blum et al. (Eds.), (pp. , New York: Springer
    • Alsina, C. (2007). Less chalk, less words, less symbols … More objects, more context, more actions. In W. Blum et al. (Eds.), Modelling and applications in mathematics education (pp. 35–44). New York: Springer.
    • (2007) Modelling and Applications in Mathematics Education , pp. 35-44
    • Alsina, C.1
  • 4
    • 84886436088 scopus 로고    scopus 로고
    • Classroom activities and the teacher
    • W. Blum et al. (Eds.), (pp. , New York: Springer
    • Antonius, S., et al. (2007). Classroom activities and the teacher. In W. Blum et al. (Eds.), Modelling and applications in mathematics education (pp. 295–308). New York: Springer.
    • (2007) Modelling and Applications in Mathematics Education , pp. 295-308
    • Antonius, S.1
  • 6
    • 85067994749 scopus 로고    scopus 로고
    • What’s all the fuss about competencies?
    • W. Blum et al. (Eds.), (pp. , New York: Springer
    • Blomhøj, M., & Jensen, T. H. (2007). What’s all the fuss about competencies? In W. Blum et al. (Eds.), Modelling and applications in mathematics education (pp. 45–56). New York: Springer.
    • (2007) Modelling and Applications in Mathematics Education , pp. 45-56
    • Blomhøj, M.1    Jensen, T.H.2
  • 7
    • 84867424054 scopus 로고    scopus 로고
    • On the role of “Grundvorstellungen” for reality-related proofs – Examples and reflections
    • P. Galbraith et al. (Eds.), (pp. , Chichester: Horwood
    • Blum, W. (1998). On the role of “Grundvorstellungen” for reality-related proofs – Examples and reflections. In P. Galbraith et al. (Eds.), Mathematical modelling – Teaching and assessment in a technology-rich world (pp. 63–74). Chichester: Horwood.
    • (1998) Mathematical Modelling – Teaching and Assessment in a Technology-Rich World , pp. 63-74
    • Blum, W.1
  • 8
    • 85101991278 scopus 로고    scopus 로고
    • Filling up – In the problem of independence-preserving teacher interventions in lessons with demanding modelling tasks. In M. Bosch (Ed.), CERME-4 – Proceedings of the Fourth Conference of the European Society for Research in Mathematics Education
    • Blum, W., & Leiß, D. (2006). Filling up – In the problem of independence-preserving teacher interventions in lessons with demanding modelling tasks. In M. Bosch (Ed.), CERME-4 – Proceedings of the Fourth Conference of the European Society for Research in Mathematics Education, Guixol.
    • (2006) Guixol
    • Blum, W.1    Leiß, D.2
  • 9
    • 84869443635 scopus 로고    scopus 로고
    • How do students and teachers deal with modelling problems?
    • C. Haines et al. (Eds.), (pp. , Chichester: Horwood
    • Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines et al. (Eds.), Mathematical modelling: Education, engineering and economic (pp. 222–231). Chichester: Horwood.
    • (2007) Mathematical Modelling: Education, Engineering and Economic , pp. 222-231
    • Blum, W.1    Leiß, D.2
  • 10
    • 84911022556 scopus 로고    scopus 로고
    • Investigating quality mathematics teaching – The DISUM project
    • C. Bergsten et al. (Eds.), Malmö
    • Blum, W., & Leiß, D. (2008). Investigating quality mathematics teaching – The DISUM project. In C. Bergsten et al. (Eds.), Proceedings of MADIF-5, Malmö.
    • (2008) Proceedings of MADIF-5
    • Blum, W.1    Leiß, D.2
  • 11
    • 0010187979 scopus 로고
    • Applied mathematical problem solving, modelling, applications, and links to other subjects – State, trends and issues in mathematics instruction
    • Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects – State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68.
    • (1991) Educational Studies in Mathematics , vol.22 , Issue.1 , pp. 37-68
    • Blum, W.1    Niss, M.2
  • 12
    • 13944270039 scopus 로고    scopus 로고
    • ICMI study 14: Applications and modelling in mathematics education – Discussion document
    • Blum, W., et al. (2002). ICMI study 14: Applications and modelling in mathematics education – Discussion document. Educational Studies in Mathematics, 51(1/2), 149–171.
    • (2002) Educational Studies in Mathematics , vol.51 , Issue.1-2 , pp. 149-171
    • Blum, W.1
  • 14
    • 84867424919 scopus 로고    scopus 로고
    • Theoretical and empirical differentiations of phases in the modelling process
    • Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 86–95.
    • (2006) Zentralblatt für Didaktik Der Mathematik , vol.38 , Issue.2 , pp. 86-95
    • Borromeo Ferri, R.1
  • 15
    • 77957551687 scopus 로고    scopus 로고
    • Modelling problems from a cognitive perspective
    • C. Haines et al. (Eds.), (pp. , Chichester: Horwood
    • Borromeo Ferri, R. (2007). Modelling problems from a cognitive perspective. In C. Haines et al. (Eds.), Mathematical modelling: Education, engineering and economics (pp. 260–270). Chichester: Horwood.
    • (2007) Mathematical Modelling: Education, Engineering and Economics , pp. 260-270
    • Borromeo Ferri, R.1
  • 16
    • 80053059285 scopus 로고    scopus 로고
    • Insights into teachers’ unconscious behaviour in modeling contexts
    • R. Lesh et al. (Eds.), (pp. , New York: Springer
    • Borromeo Ferri, R., & Blum, W. (2010). Insights into teachers’ unconscious behaviour in modeling contexts. In R. Lesh et al. (Eds.), Modeling students’ mathematical modeling competencies (pp. 423–432). New York: Springer.
    • (2010) Modeling students’ Mathematical Modeling Competencies , pp. 423-432
    • Borromeo Ferri, R.1    Blum, W.2
  • 17
    • 84965520752 scopus 로고
    • Situated cognition and the culture of learning
    • Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18, 32–42.
    • (1989) Educational Researcher , vol.18 , pp. 32-42
    • Brown, J.S.1    Collins, A.2    Duguid, P.3
  • 18
    • 85025900646 scopus 로고
    • Mathematical modelling – Are we heading in the right direction?
    • J. Berry et al. (Eds.), (pp. , Chichester: Horwood
    • Burghes, D. (1986). Mathematical modelling – Are we heading in the right direction? In J. Berry et al. (Eds.), Mathematical modelling methodology, models and micros (pp. 11–23). Chichester: Horwood.
    • (1986) Mathematical Modelling Methodology, Models and Micros , pp. 11-23
    • Burghes, D.1
  • 20
    • 84892321645 scopus 로고    scopus 로고
    • Functional mathematics and teaching modelling
    • C. Haines et al. (Eds.), (pp. , Chichester: Horwood
    • Burkhardt, H. (2006). Functional mathematics and teaching modelling. In C. Haines et al. (Eds.), Mathematical modelling: Education, engineering and economics (pp. 177–186). Chichester: Horwood.
    • (2006) Mathematical Modelling: Education, Engineering and Economics , pp. 177-186
    • Burkhardt, H.1
  • 21
    • 79952797094 scopus 로고    scopus 로고
    • Modelling in mathematics classrooms: Reflections on past developments and the future
    • Burkhardt, H., & Pollak, H. O. (2006). Modelling in mathematics classrooms: Reflections on past developments and the future. Zentralblatt für Didaktik der Mathematik, 38(2), 178–195.
    • (2006) Zentralblatt für Didaktik Der Mathematik , vol.38 , Issue.2 , pp. 178-195
    • Burkhardt, H.1    Pollak, H.O.2
  • 22
    • 85101970646 scopus 로고
    • T. Breiteig et al. (Eds.), Teaching and learning mathematics in context (pp. , Chichester: Horwoood
    • DaPonte, J. P. (1993). Necessary research in mathematical modelling and applications. In T. Breiteig et al. (Eds.), Teaching and learning mathematics in context (pp. 219–227). Chichester: Horwoood.
    • (1993) Necessary Research in Mathematical Modelling and Applications , pp. 219-227
    • Daponte, J.P.1
  • 23
    • 85084876530 scopus 로고    scopus 로고
    • Mathematics teaching and learning
    • D. C. Berliner & R. C. Calfee (Eds.), (pp. , New York: Macmillan
    • De Corte, E., Greer, B., & Verschaffel, L. (1996). Mathematics teaching and learning. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 491–549). New York: Macmillan.
    • (1996) Handbook of Educational Psychology , pp. 491-549
    • de Corte, E.1    Greer, B.2    Verschaffel, L.3
  • 24
    • 85101984709 scopus 로고    scopus 로고
    • DeLange, J. (1987). Mathematics, insight and meaning. Utrecht: CD-Press.
    • DeLange, J. (1987). Mathematics, insight and meaning. Utrecht: CD-Press.
  • 25
    • 84994833591 scopus 로고    scopus 로고
    • What knowledge do teachers need for teaching mathematics through applications and modelling?
    • W. Blum et al. (Eds.), (pp. , New York: Springer
    • Doerr, H. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum et al. (Eds.), Modelling and applications in mathematics education (pp. 69–78). New York: Springer.
    • (2007) Modelling and Applications in Mathematics Education , pp. 69-78
    • Doerr, H.1
  • 26
    • 0003734127 scopus 로고
    • Mathematics as an educational task
    • Dordrecht
    • Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: Reidel.
    • (1973) Reidel
    • Freudenthal, H.1
  • 27
    • 17444410406 scopus 로고
    • Beyond standard models – Meeting the challenge of modelling
    • Galbraith, P., & Clathworthy, N. (1990). Beyond standard models – Meeting the challenge of modelling. Educational Studies in Mathematics, 21(2), 137–163.
    • (1990) Educational Studies in Mathematics , vol.21 , Issue.2 , pp. 137-163
    • Galbraith, P.1    Clathworthy, N.2
  • 28
    • 84855340908 scopus 로고    scopus 로고
    • A framework for identifying student blockages during transitions in the modelling process
    • Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 143–162.
    • (2006) Zentralblatt für Didaktik Der Mathematik , vol.38 , Issue.2 , pp. 143-162
    • Galbraith, P.1    Stillman, G.2
  • 29
    • 52249123856 scopus 로고    scopus 로고
    • Recognizing constructs within mathematical modelling
    • Haines, C., & Crouch, R. (2001). Recognizing constructs within mathematical modelling. Teaching Mathematics and Its Applications, 20(3), 129–138.
    • (2001) Teaching Mathematics and Its Applications , vol.20 , Issue.3 , pp. 129-138
    • Haines, C.1    Crouch, R.2
  • 30
    • 84991105803 scopus 로고    scopus 로고
    • Modelling pedagogy – Overview
    • W. Blum et al. (Eds.), (pp. , New York: Springer
    • Henn, H.-W. (2007). Modelling pedagogy – Overview. In W. Blum et al. (Eds.), Modelling and applications in mathematics education (pp. 321–324). New York: Springer.
    • (2007) Modelling and Applications in Mathematics Education , pp. 321-324
    • Henn, H.-W.1
  • 32
    • 33644539021 scopus 로고    scopus 로고
    • On the generation of basic ideas and individual images: Normative, descriptive and constructive aspects
    • J. Kilpatrick & A. Sierpinska (Eds.), (pp. , Dordrecht: Kluwer
    • Hofe, R. V. (1998). On the generation of basic ideas and individual images: Normative, descriptive and constructive aspects. In J. Kilpatrick & A. Sierpinska (Eds.), Mathematics education as a research domain: A search for identity (pp. 317–331). Dordrecht: Kluwer.
    • (1998) Mathematics Education as A Research Domain: A Search for Identity , pp. 317-331
    • Hofe, R.V.1
  • 33
    • 84873526627 scopus 로고    scopus 로고
    • Assessing the “phases” of mathematical modelling
    • W. Blum et al. (Eds.), (pp. , New York: Springer
    • Houston, K. (2007). Assessing the “phases” of mathematical modelling. In W. Blum et al. (Eds.), Modelling and applications in mathematics education (pp. 249–256). New York: Springer.
    • (2007) Modelling and Applications in Mathematics Education , pp. 249-256
    • Houston, K.1
  • 34
    • 85067934774 scopus 로고    scopus 로고
    • Possibilities for, and obstacles to teaching applications and modelling in the lower secondary levels
    • W. Blum et al. (Eds.), (pp. , New York: Springer
    • Ikeda, T. (2007). Possibilities for, and obstacles to teaching applications and modelling in the lower secondary levels. In W. Blum et al. (Eds.), Modelling and applications in mathematics education (pp. 457–462). New York: Springer.
    • (2007) Modelling and Applications in Mathematics Education , pp. 457-462
    • Ikeda, T.1
  • 35
    • 84873275791 scopus 로고    scopus 로고
    • Assessing mathematical modelling competencies
    • C. Haines et al. (Eds.), (pp. , Chichester: Horwood
    • Jensen, T. H. (2007). Assessing mathematical modelling competencies. In C. Haines et al. (Eds.), Mathematical modelling: Education, engineering and economics (pp. 141–148). Chichester: Horwood.
    • (2007) Mathematical Modelling: Education, Engineering and Economics , pp. 141-148
    • Jensen, T.H.1
  • 36
    • 84873272588 scopus 로고    scopus 로고
    • Modelling and modelling competencies in school
    • C. Haines et al. (Eds.), (pp. , Chichester: Horwood
    • Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines et al. (Eds.), Mathematical modelling: Education, engineering and economics (pp. 110–119). Chichester: Horwood.
    • (2007) Mathematical Modelling: Education, Engineering and Economics , pp. 110-119
    • Kaiser, G.1
  • 37
    • 84873244337 scopus 로고    scopus 로고
    • Modelling in lower secondary mathematics classroom – Problems and opportunities
    • W. Blum et al. (Eds.), (pp. , New York: Springer
    • Kaiser, G., & Maaß, K. (2007). Modelling in lower secondary mathematics classroom – Problems and opportunities. In W. Blum et al. (Eds.), Modelling and applications in mathematics education (pp. 99–108). New York: Springer.
    • (2007) Modelling and Applications in Mathematics Education , pp. 99-108
    • Kaiser, G.1    Maaß, K.2
  • 38
    • 84867418726 scopus 로고    scopus 로고
    • Mathematical modelling as bridge between school and university
    • Kaiser, G., & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. Zentralblatt für Didaktik der Mathematik, 38(2), 196–208.
    • (2006) Zentralblatt für Didaktik Der Mathematik , vol.38 , Issue.2 , pp. 196-208
    • Kaiser, G.1    Schwarz, B.2
  • 39
    • 84873277039 scopus 로고    scopus 로고
    • Authentic modelling problems in mathematics education – Examples and experiences
    • Kaiser, G., & Schwarz, B. (2010). Authentic modelling problems in mathematics education – Examples and experiences. Journal für Mathematik-Didaktik, 31, 51–76.
    • (2010) Journal für Mathematik-Didaktik , vol.31 , pp. 51-76
    • Kaiser, G.1    Schwarz, B.2
  • 40
    • 84873526740 scopus 로고    scopus 로고
    • Mathematical modelling and applications: Empirical and theoretical perspectives
    • Kaiser, G., Blomhøj, M., & Sriraman, B. (2006). Mathematical modelling and applications: Empirical and theoretical perspectives. Zentralblatt für Didaktik der Mathematik, 38(2), 178–195.
    • (2006) Zentralblatt für Didaktik Der Mathematik , vol.38 , Issue.2 , pp. 178-195
    • Kaiser, G.1    Blomhøj, M.2    Sriraman, B.3
  • 42
    • 0021907853 scopus 로고
    • Understanding word arithmetic problems
    • Kintsch, W., & Greeno, J. (1985). Understanding word arithmetic problems. Psychological Review, 92(1), 109–129.
    • (1985) Psychological Review , vol.92 , Issue.1 , pp. 109-129
    • Kintsch, W.1    Greeno, J.2
  • 43
    • 2942533330 scopus 로고
    • Powerful tasks: A contribution to a high level of acting and reflecting in mathematics instruction
    • Krainer, K. (1993). Powerful tasks: A contribution to a high level of acting and reflecting in mathematics instruction. Educational Studies in Mathematics, 24, 65–93.
    • (1993) Educational Studies in Mathematics , vol.24 , pp. 65-93
    • Krainer, K.1
  • 44
    • 0345706880 scopus 로고    scopus 로고
    • The effects of metacognitive instruction on solving mathematical authentic tasks
    • Kramarski, B., Mevarech, Z. R., & Arami, V. (2002). The effects of metacognitive instruction on solving mathematical authentic tasks. Educational Studies in Mathematics, 49(2), 225–250.
    • (2002) Educational Studies in Mathematics , vol.49 , Issue.2 , pp. 225-250
    • Kramarski, B.1    Mevarech, Z.R.2    Arami, V.3
  • 45
    • 77951460526 scopus 로고    scopus 로고
    • Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: Validation of the COACTIV constructs
    • Krauss, S., Baumert, J., & Blum, W. (2008). Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: Validation of the COACTIV constructs. Zentralblatt für Didaktik der Mathematik, 40(5), 873–892.
    • (2008) Zentralblatt für Didaktik Der Mathematik , vol.40 , Issue.5 , pp. 873-892
    • Krauss, S.1    Baumert, J.2    Blum, W.3
  • 47
    • 34548495342 scopus 로고    scopus 로고
    • Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks
    • Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics, 66, 349–371.
    • (2007) Educational Studies in Mathematics , vol.66 , pp. 349-371
    • Leikin, R.1    Levav-Waynberg, A.2
  • 48
    • 3042514325 scopus 로고    scopus 로고
    • Beyond constructivism: A models and modelling perspective on teaching, learning
    • Mahwah: Lawrence Erlbaum
    • Lesh, R. A., & Doerr, H. M. (2003). Beyond constructivism: A models and modelling perspective on teaching, learning, and problem solving in mathematics education. Mahwah: Lawrence Erlbaum.
    • (2003) And Problem Solving in Mathematics Education
    • Lesh, R.A.1    Doerr, H.M.2
  • 49
    • 85101961924 scopus 로고    scopus 로고
    • Modelling in teacher education
    • W. Blum et al. (Eds.), (pp. , New York: Springer
    • Lingefjaerd, T. (2007). Modelling in teacher education. In W. Blum et al. (Eds.), Modelling and applications in mathematics education (pp. 475–482). New York: Springer.
    • (2007) Modelling and Applications in Mathematics Education , pp. 475-482
    • Lingefjaerd, T.1
  • 50
    • 33744733352 scopus 로고    scopus 로고
    • Auf den Lehrer kommt es an
    • (pp. , Beiheft. Weinheim: Beltz
    • Lipowsky, F. (2006). Auf den Lehrer kommt es an. In Beiheft der Zeitschrift für Pädagogik, 51 (pp. 47–70). Beiheft. Weinheim: Beltz.
    • (2006) Beiheft Der Zeitschrift für Pädagogik , vol.51 , pp. 47-70
    • Lipowsky, F.1
  • 52
    • 45849108212 scopus 로고    scopus 로고
    • Modelling in class: What do we want the students to learn?
    • C. Haines et al. (Eds.), (pp. , Chichester: Horwood
    • Maaß, K. (2007). Modelling in class: What do we want the students to learn? In C. Haines et al. (Eds.), Mathematical modelling: Education, engineering and economics (pp. 63–78). Chichester: Horwood.
    • (2007) Mathematical Modelling: Education, Engineering and Economics , pp. 63-78
    • Maaß, K.1
  • 53
    • 84873248816 scopus 로고    scopus 로고
    • The quest for meaning in students’ mathematical modelling activity
    • S. K. Houston et al. (Eds.), (pp. , Chichester: Horwood
    • Matos, J. F., & Carreira, S. (1997). The quest for meaning in students’ mathematical modelling activity. In S. K. Houston et al. (Eds.), Teaching & leaning mathematical modelling (pp. 63–75). Chichester: Horwood.
    • (1997) Teaching & Leaning Mathematical Modelling , pp. 63-75
    • Matos, J.F.1    Carreira, S.2
  • 55
    • 10844269326 scopus 로고    scopus 로고
    • Goals of mathematics teaching
    • A. Bishop et al. (Eds.), (pp. , Dordrecht: Kluwer
    • Niss, M. (1996). Goals of mathematics teaching. In A. Bishop et al. (Eds.), International handbook of mathematical education (pp. 11–47). Dordrecht: Kluwer.
    • (1996) International Handbook of Mathematical Education , pp. 11-47
    • Niss, M.1
  • 56
    • 0040001856 scopus 로고    scopus 로고
    • Aspects of the nature and state of research in mathematics education
    • Niss, M. (1999). Aspects of the nature and state of research in mathematics education. Educational Studies in Mathematics, 40, 1–24.
    • (1999) Educational Studies in Mathematics , vol.40 , pp. 1-24
    • Niss, M.1
  • 57
    • 72149111251 scopus 로고    scopus 로고
    • Issues and problems of research on the teaching and learning of applications and modelling
    • J. F. Matos et al. (Eds.), (pp. , Chichester: Ellis Horwood
    • Niss, M. (2001). Issues and problems of research on the teaching and learning of applications and modelling. In J. F. Matos et al. (Eds.), Modelling and mathematics education: ICTMA-9 (pp. 72–88). Chichester: Ellis Horwood.
    • (2001) Modelling and Mathematics Education: ICTMA-9 , pp. 72-88
    • Niss, M.1
  • 58
    • 33846156319 scopus 로고    scopus 로고
    • Mathematical competencies and the learning of mathematics: The Danish KOM project
    • A. Gagatsis & S. Papastavridis (Eds.), (pp. , Athens: The Hellenic Mathematical Society
    • Niss, M. (2003). Mathematical competencies and the learning of mathematics: The Danish KOM project. In A. Gagatsis & S. Papastavridis (Eds.), 3rd Mediterranean Conference on Mathematical Education (pp. 115–124). Athens: The Hellenic Mathematical Society.
    • (2003) 3Rd Mediterranean Conference on Mathematical Education , pp. 115-124
    • Niss, M.1
  • 60
    • 0003610530 scopus 로고    scopus 로고
    • Paris: OECD
    • OECD. (2005). PISA 2003 technical report. Paris: OECD.
    • (2003) Technical Report
  • 62
    • 84873270879 scopus 로고    scopus 로고
    • Features and impact of the authenticity of applied mathematical school tasks
    • W. Blum et al. (Eds.), (pp. , New York: Springer
    • Palm, T. (2007). Features and impact of the authenticity of applied mathematical school tasks. In W. Blum et al. (Eds.), Modelling and applications in mathematics education (pp. 201–208). New York: Springer.
    • (2007) Modelling and Applications in Mathematics Education , pp. 201-208
    • Palm, T.1
  • 64
    • 84867410262 scopus 로고
    • The interaction between mathematics and other school subjects
    • UNESCO (Ed.), (Vol. , pp. , UNESCO: Paris
    • Pollak, H. O. (1979). The interaction between mathematics and other school subjects. In UNESCO (Ed.), New trends in mathematics teaching (Vol. IV pp. 232–248). UNESCO: Paris.
    • (1979) New Trends in Mathematics Teaching , vol.4 , pp. 232-248
    • Pollak, H.O.1
  • 65
    • 0004235832 scopus 로고
    • Princeton: Princeton University Press
    • Polya, G. (1957). How to solve it. Princeton: Princeton University Press.
    • (1957) How to Solve It
    • Polya, G.1
  • 66
    • 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
  • 68
    • 0003036905 scopus 로고
    • The role of presentational structures in understanding and solving mathematical word problems
    • C. A. Weaver, S. Mannes, & C. R. Fletcher (Eds.), (pp. , Hillsdale: Lawrence Erlbaum
    • Staub, F. C., & Reusser, K. (1995). The role of presentational structures in understanding and solving mathematical word problems. In C. A. Weaver, S. Mannes, & C. R. Fletcher (Eds.), Discourse comprehension. Essays in honor of Walter Kintsch (pp. 285–305). Hillsdale: Lawrence Erlbaum.
    • (1995) Discourse Comprehension. Essays in Honor of Walter Kintsch , pp. 285-305
    • Staub, F.C.1    Reusser, K.2
  • 69
    • 54649083588 scopus 로고    scopus 로고
    • Applying mathematics with real world connections: Metacognitive characteristic of secondary students
    • Stillman, G., & Galbraith, P. (1998). Applying mathematics with real world connections: Metacognitive characteristic of secondary students. Educational Studies in Mathematics, 36(2), 157–195.
    • (1998) Educational Studies in Mathematics , vol.36 , Issue.2 , pp. 157-195
    • Stillman, G.1    Galbraith, P.2
  • 70
    • 85055714932 scopus 로고
    • Developing metacognition through peer and self assessment
    • T. Breiteig et al. (Eds.), (pp. , Chichester: Horwoood
    • Tanner, H., & Jones, S. (1993). Developing metacognition through peer and self assessment. In T. Breiteig et al. (Eds.), Teaching and learning mathematics in context (pp. 228–240). Chichester: Horwoood.
    • (1993) Teaching and Learning Mathematics in Context , pp. 228-240
    • Tanner, H.1    Jones, S.2
  • 71
    • 85101963350 scopus 로고    scopus 로고
    • Turner, R. et al. (in press). Using mathematical competencies to predict item difficulty in PISA: A MEG study 2003–2009. To appear in Proceedings of the PISA Research Conference, Kiel, 2009.
    • Turner, R. et al. (in press). Using mathematical competencies to predict item difficulty in PISA: A MEG study 2003–2009. To appear in Proceedings of the PISA Research Conference, Kiel, 2009.
  • 73
    • 84885676365 scopus 로고    scopus 로고
    • Assessment of applied mathematics and modelling: Using a laboratory-like environment
    • W. Blum et al. (Eds.), (pp. , New York: Springer
    • Vos, P. (2007). Assessment of applied mathematics and modelling: Using a laboratory-like environment. In W. Blum et al. (Eds.), Modelling and applications in mathematics education (pp. 441–448). New York: Springer.
    • (2007) Modelling and Applications in Mathematics Education , pp. 441-448
    • Vos, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.