Teaching and testing mathematical problem solving by offering optional assistance

Instructional Science

Volumn 30, Issue 3, 2002, Pages 187-220

  Meijer, Joost ^a   Riemersma, Fré ^b  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b Education Council of the Netherlands   (Netherlands)

Author keywords

Assisted assessment; Computer support; Heuristics; Mathematics education; Problem solving; Transfer

Indexed keywords

EID: 0036255082     PISSN: 00204277     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1015129031935     Document Type: Article

References (62)

1. Abels, M.J. & Associates. (1989). Modeme Wiskunde. [Modern Mathematics]. Groningen: Wolters Noordhoff.
2. Anderson, J.R., Reder, L.M. & Simon, H.A. (1996). Situated learning and education. Educational Researcher 25(4): 5-11.
3. Anderson, J.R., Reder, L.M. & Simon, H.A. (1997). Situative versus cognitive perspectives: Form versus substance. Educational Researcher 26(1), 18-21.
4. Badad, E.Y. & Budoff, M. (1974). Sensitivity of learning potential measurement in three levels of ability. Journal of Educational Psychology 3(66): 439-447.
5. Budoff, M. (1987). Measures for assessing learning potential, in C. Schneider Lidz, ed., Dynamic Assessment (pp. 173-195). New York: The Guilford Press.
6. Butterfield, E.C. & Nelson, G.D. (1991). Promoting positive transfer of different types. Cognition and Instruction 8(1), 69-102.
7. Campione, J.C. & Brown, A.L. (1987). Linking dynamic testing with school achievement, in C.S. Lidz, ed., Dynamic Testing (pp. 82-115). New York: Guilford Press.
8. Clements, D.H. & Nastasi, B.K. (1990). Dynamic approach to measurement of children's metacomponential functioning. Intelligence 14(1), 109-125.
9. Cohen, J. (1988). Statistical Power Analysis for the Behavioural Sciences. New York: Academic Press.
10. Couzijn, M. (1995). Observation of Writing and Reading Activities: Effects on Learning and Transfer. Doctoral Dissertation, University of Amsterdam, Amsterdam.
11. Daalen, H. van., Meijer, J., Leeuw, L. de, Beishuizen, J. & Brazier, F. (1987). Teaching arithmetic word problems by distinguisbing between problem states, in C. Schwarzer & B. Seipp (hrsg.), Trends in European Educational Research (Chap. 20, pp. 68-74). Braunschweig: Braunschweiger Studien zur Erziehungs- und Sozialarbeitswissenschaft.
12. Elshout, J.J., Veenman, M.V.J. & Hell, J.G. van (1993). Using the computer as a help tool during learning by doing. Computers in Education; an International Journal 21(1-2), 115-122.
13. Elshout, J.J. & Veenman, M.V.J. (1992). Relation between intellectual ability and working method as predictors of learning. The Journal of Educational Research 85(3).
14. Elshout-Mohr, M., Van Hout-Wolters, B.H.A.M. & Broekkamp, H. (1999). Mapping situations in classroom and research; eight types of instructional-learning episodes. Learning and Instruction 9, 57-75.
15. Emrani, A. & Rijnierse, L. (1994). Kan de computer de leraar vervangen? Unpublished masters thesis. Amsterdam: Graduate School of Education.
16. Evers, A. & Lucassen, W. (1984). DAT '83. Differentiele Aanleg Testserie; voorlopige handleiding [DAT '83. Differential Aptitude Testseries; preliminary guidelines]. Lisse: Swets & Zeitlinger.
17. Freudenthal, H. (1978). Weeding and Sowing. Preface to a Science of Mathematics Education. Dordrecht/Boston: D. Reidel Publishing Co.
18. Gagné, R.M. (1973). The Conditions of Learning. London: Holt, Rinehart & Winston.
19. Greeno, J.G. (1997). On claims that answer the wrong questions. Educational Researcher 26(1), 5-17.
20. Guthke, J.J. (1992). Learning tests: the concept, main research findings, problems and trends. Advances in Cognition and Educational Practice. London: JAI Press Inc.
21. Hagglund, G. (1982) Factor analysis by instrumental variables methods. Psychometrika 47: 209-222.
22. Jong, T. de & Ferguson-Hessler, M.G.M. (1984). Strategiegebruik bij het Oplossen van Problemen in een Semantisch Rijk Domein: Electriciteit en Magnetisme [Strategy usage when solving problems in a semantically rich domain: electricity and magnetism]. Tijdschrift voor Onderwijsresearch 9(1): 3-15.
23. Jöreskog, K.G. & Sörbom, D. (1988). LISREL 7. A Guide to the Program and Applications. Chicago: SPSS Inc.
24. Judd, C.M., Smith, E.R. & Kidder, L.H. (1991). Research Methods in Social Relations. Orlando: Harcourt Brace Jovanovich.
25. Krutetskii, V.A. (1976). The Psychology of Mathematical Abilities in School Children. Chicago: University of Chicago Press.
26. Kuhlemeier, H., Van den Bergh, H. & Teunisse, F. (1990). Interne structuur en constructvaliditeit van belevingsschalen voor wiskunde en Engels [Internal structure and construct validity of instruments for measuring learning experience in mathematics and English]. Tijdschrift voor Onderwijsresearch 15(2): 110-122.
27. Lange, J. de (1987). Mathematics, Insight and Meaning. Unpublished doctoral dissertation, State University of Utrecht, Utrecht.
28. Leeuw, L. de (1979). Leren probleemoplossen. Aanleren van heuristieken en algoritmen in verband met persoonskenmerken [Learning problem solving. Teaching heuristics and algorithms in relation with personality characteristics]. Lisse: Swets & Zeitlinger.
29. Leeuw, L. de, Meijer, J., Perrenet, J. Chr. & Groen, W.E. (1988). De constructie en validering van een transfertest voor wiskunde-onderwijs met gebruikmaking van items met gefaseerde hulp [The construction and validation of a transfertest voor mathematics education using items with help in phases]. Amsterdam: Vrije Universiteit.
30. Leeuw, L. de & Meijer, J. (1989). Coaching students during computer guided transfer problem solving: The construction of a transfer test containing items with incremental help, in P. Span, E. De Corte & B. Van Hout-Wolters, eds, Onderwijsleerprocessen; Strategieën voor de verwerking van informatie [Teaching and learning processes; Strategies for information processing]. Lisse: Swets & Zeitlinger.
31. McLeod, D.B. & Adams, V.M. (1989). Affect and Mathematical Problem Solving. A New Perspective. New York: Springer Verlag.
32. Meijer, J. & Riemersma, F. (1986). Analysis of thinking aloud protocols. Instructional Science 15(1): 3-19.
33. Meijer, J., Perrenet, J. Chr. & Riemersma, F. (1988). Leren probleemoplossen in het wiskundeonderwijs [Learning problemsolving in mathematics education]. Pedagogische Studiën 65(1): 16-31.
34. Meijer, J. (1993). Learning potential, personality characteristics and test performance, in J.H.M. Hamers, K. Sijtsma & A.J.J.M. Ruijssenaars, eds, Learning Potential Assessment; Theoretical, Methodological and Practical Issues (pp. 341-362). Amsterdam/Lisse: Swets & Zeitlinger.
35. Meijer, J. (1996). Learning Potential and Fear of Failure. A study into the Predictive Validity of Learning Potential and the Role of Anxious Tendency. Dissertation University of Amsterdam, Amsterdam.
36. Meijer, J. (1999). Leerpotentieel en intelligentie: voorzetting van een debat over een complexe problematiek, in R. Hamel, M. Elshout-Mohr & M. Milikowski, eds., Meesterschap. Zestien stukken over intelligentie, leren, denken en probleemoplossen voor Jan J. Elshout. Amsterdam: Vossiuspers UAP.
37. Meijer, J. & Elshout, J.J. (2001). The predictive and discriminant validity of the zone of proximal development. British Journal of Educational Psychology 71: 93-113.
38. Mettes, C.T.C.W. & Pilot, A. (1980). Over het leren oplossen van natuurwetenschappelijke problemen [About learning how to solve science problems]. Enschede: Reproductiedienst TH Twente.
39. Nygard, R. & Gjesme, T. (1973). Assessment of achievement motives: Comments and suggestions. Scandinavian Journal of Educational Research 17: 39-46.
40. Perkins, D.N. & Salomon, G. (1988). Teaching for Transfer. Educational Leadership 46(1): 22-32.
41. Perkins, D.N. & Unger, C. (1994). A new look in representations for mathematics and science learning. Instructional Science 22: 1-37.
42. Polya, G. (1954). Induction and Analogy in Mathematics, Vol. I, II. Princeton: Princeton University Press.
43. Polya, G. (1957). How to Solve It. Princeton, NJ: Princeton University Press.
44. Polya, G. (1962). Mathematical Discovery. On Understanding, Learning and Teaching Problem Solving. New York: Wiley.
45. Resing, W. (1990). Intelligentie en Leerpotentieel [Intelligence and Learning Potential]. Amsterdam: Swets & Zeitlinger.
46. Resnick, L.B. (1987). Education and Learning to Think. Washington: National Academy Press.
47. Riemersma, F.S.J. (1991). Leren oplossen van wiskundige problemen in het voortgezet onderwijs [Learning to solve mathematics problems in secundary education]. Dissertation University of Amsterdam, Amsterdam.
48. Riemersma, F.S.J. & Meijer, J. (1995). Wiskundig Probleemoplossen met Zelfgekozen Hulp. Amsterdam: SCO-Kohnstamm Instituut.
49. Riet, N. van't. & Schoemaker, G. (1983). Uit het dagboek van twee loerders. Wiskrant 13(24): 66-67.
50. Saris, W.E. & Stronkhorst, L.H. (1984). Causal Modelling in Non-Experimental Research: An Introduction to the Lisrel Approach. Amsterdam: Sociometric Research Foundation.
51. Schneider-Lidz, C. (1987). Dynamic Assessment: An Interactional Approach to Evaluating Learning Potential. New York: The Guilford Press.
52. Schliemann, A.D. & Acioly, N.M. (1989). Mathematical knowledge developed at work: The contribution of practice versus the contribution of schooling. Cognition and Instruction 6(3): 185-221.
53. Schoenfeld, A.H. (1987). Cognitive Science and Mathematics Education. Hillsdale, N.J.: Erlbaum.
54. Slavin, R.E. (1995). Cooperative Learning. Boston: Allyn and Bacon.
55. Sternberg, R.J. (1985). Beyond IQ: A Triarchic Theory of Human Intelligence. Cambridge: Cambridge University Press.
56. Streun, A. van (1990). Heuristisch Wiskunde-Onderwijs [Heuristic mathematics education]. Dissertation Rijksuniversiteit Groningen, Groningen.
57. Veenman, M.V.J. (1993). Intellectual Ability and Metacognitive Skill: Determinants of Discovery Learning in Computerized Learning Environments. Amsterdam: Dissertation University of Amsterdam.
58. Veenman, M.V.J., Elshout, J.J. & Meijer, J. (1997). The generality vs domain-specificity of metacognitive skills in novice learning across domains. Learning and Instruction 7(2): 187-209.
59. Vygotsky, L.S. (1964). Denken und Sprechen [Thinking and Speaking]. Berlin: Akademie-Verlag.
60. Vygotsky, L.S. (1978). Mind in Society. The Development of Higher Psychological Processes (M. Cole, V. John-Steiner, S. Scribner, & E. Souberman, eds). Cambridge, MA: Harvard University Press.
61. Wang, M.C. & Peverly, S.T. (1986). The self-instructive process in classroom learning contexts. Contemporary Educational Psychology 11: 370-404.
62. Wittrock, M.C. (1987). Models of heuristic teaching, in M.J. Dunkin, ed., The International Encyclopedia of Teaching and Teacher Education. Oxford: Pergamon Press.