Skip to main content

Central Role of Students’ Reasoning

  • Chapter
A Love of Discovery

Abstract

In this chapter, the focus of Robert Karplus’s work on students’ reasoning will be revisited. The emphasis on exploring and understanding students’ reasoning in multiplicative conceptual domains, beyond the elementary school, is central in the mathematics and science education-related work of Robert Karplus. About 30 years ago, at a time when the emphasis in mathematics and science education research was on students’ achievement test scores and related statistical group averages, Robert Karplus launched a sequence of studies focusing on identifying and classifying students’ reasoning as they attempted to solve a variety of well-designed problems (or at times they were referred to as puzzles) that purposefully embedded key mathematical concepts such as proportions, control of variables, probability, correlations and others. It is the quality of students’ thinking and how they had reasoned that Karplus and his colleagues focused on, rather than the correct/incorrect answers students may have given.

AESOP (Advancement of Education in Sceince-Oriented Programs) is supported by a grant from the National Science Foundation.

Supported by a grant from the National Science Foundation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adi, H., Karplus, R., Lawson, A., and Pulos, S., 1978, Intellectual development beyond elementary school VI: Correlational reasoning. School Science and Mathematics, 78(8):675–683.

    Article  Google Scholar 

  2. Adi, H., Karplus, R., and Lawson, A., 1980, Conditional logic abilities on the four-card problem: Assessment of behavioral and reasoning performances. Educational Studies in Mathematics 11:479–496.

    Article  Google Scholar 

  3. Behr, M., Harel, G., Post, T., and Lesh, R., 1992, Rational number, ratio, and proportion. In Handbook of Research in Mathematics Teaching and Learning, D. Grouws, ed., Macmillan Publishing Co., New York.

    Google Scholar 

  4. Billings, E., 1998, Qualitative-based Reasoning of Preservice Elementary School Teachers in Proportional Situations, Unpublished doctoral dissertation, Northern Illinois University, DeKalb, Illinois.

    Google Scholar 

  5. Harel, G., and Confrey, J. (Eds.), 1994, The development of multiplicative reasoning in the learning of mathematics, SUNY Press, New York.

    Google Scholar 

  6. Hart, K., Brown, M., Kerslake, D., Kuchemann, D., and Ruddock, G., 1985, Chelsea Diagnostic Mathematics Tests: Ratio and Proportion, NFER-NELSON, Berkshire, Great Britain.

    Google Scholar 

  7. Hines, E., 1998, Analysis of Processes Used by Middle School Students to Interpret Functions Embedded in Dynamic Physical Models and Represented in Tables, Equations, and Graphs, Unpublished doctoral dissertation, Northern Illinois University, DeKalb, Illinois.

    Google Scholar 

  8. Karplus, E., 1980, Classroom Research: Valuing Students Errors, A paper presented at the 4th annual MERGA conference in Hobart, Australia.

    Google Scholar 

  9. Karplus, E., and Karplus, R., 1970, Intellectual development beyond elementary school I: Deductive logic, School Science and Mathematics, 70(5):398–406.

    Article  Google Scholar 

  10. Karplus, E., Karplus, R., and Wollman, W., 1974, Intellectual development beyond elementary school IV: Ratio, the influence of cognitive style, School Science and Mathematics, 74(6):476–482.

    Article  Google Scholar 

  11. Karplus, R., May, 1978, Final Report: Advancing Education Through Science-Oriented Programs (AESOP); Pre-college Components, NSF funded projects to Lawrence Hall of Science, University of California, Berkeley, California.

    Google Scholar 

  12. Karplus, R., Adi, H., and Lawson, A., 1980, Intellectual development beyond elementary school VIII: Proportional, probabilistic, and correlational reasoning, School Science and Mathematics, 80(8):673–683.

    Article  Google Scholar 

  13. Karplus, R., and Karplus, B., 1979, Student Attitudes Toward Research in the Classroom, Unpublished research report, AESOP Project: Lawrence Hall of Science, University of California, Berkeley.

    Google Scholar 

  14. Karplus, R., and Karplus, E., 1972, Intellectual development beyond elementary school III: Ratio, a longitudinal study. School Science and Mathematics, 72(8):735–742.

    Article  Google Scholar 

  15. Karplus, R., Karplus, E., Formisano, M., and Paulson, A. G, 1977, A survey of proportional reasoning and control of variables in seven countries. Journal of Research in Science Teaching, 74(5):411–417.

    Article  Google Scholar 

  16. Karplus, R., and Peterson, R., 1970, Intellectual development beyond elementary school II: Ratio, a survey. School Science and Mathematics, 70(9):813–820.

    Article  Google Scholar 

  17. Khoury, H., 1997, Measuring Up: A Middle School Experience, An Eisenhower professional development project, Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois.

    Google Scholar 

  18. Kurtz, B., and Karplus, R., 1979, Intellectual development beyond elementary school VII: Teaching for proportional reasoning. School Science and Mathematics, 79(5):387–398.

    Article  Google Scholar 

  19. Monk, S., 1992, Students’ understanding of a function given by a physical model, in G Harel, and E. Dubinsky. eds.,The concept of a function: Aspects of epistemology and pedagogy. MAA Notes, 25:175–194.

    Google Scholar 

  20. National Council of Teachers of Mathematics, 1989, Curriculum and Evaluation Standards for School Mathematics, NCTM, Reston, VA.

    Google Scholar 

  21. National Council of Teachers of Mathematics, 2000, Principles and Standards or School Mathematics, NCTM, Reston, VA.

    Google Scholar 

  22. Silver, E., 1977, Algebra for all: Increasing students’ access to algebraic ideas, not just algebra courses Mathematics Teaching in the Middle School, 2(4):204–207.

    Google Scholar 

  23. Thrun, J., 1999, College Students’ Rational Number as Operator Strategies: A Focus on Students’ Coordination of Units and Distributivity of Operators in Problem-solving Situations, Unpublished doctoral dissertation, Northern Illinois University, DeKalb, IL.

    Google Scholar 

  24. Wollman, W., and Karplus, R., 1974, Intellectual development beyond elementary school V: Using ratio in differing tasks. School Science and Mathematics, 74(11):593–613.

    Article  Google Scholar 

  25. Elizabeth F. Karplus and Robert Karplus. “Intellectual Development Beyond Elementary School. I. Deductive Logic.” School Science and Mathematics, LXX (May 1970), 398–406.

    Google Scholar 

  26. B. Inhelder and J. Piaget. The Growth of Logical Thinking from Childhood to Adolescence. Basic Books, New York, 1958.

    Book  Google Scholar 

  27. “Intellectual Development Beyond Elementary School II: Ratio, A Survey,” by Robert Karplus and Rita W. Peterson, School Science and Mathematics, December, 1970, pp. 813–820.

    Google Scholar 

  28. B. Inhelder and J. Piaget, The Growth of Logical Thinking from Childhood to Adolescence, Basic Books, New York, 1958.

    Book  Google Scholar 

  29. Robert Karplus and Rita W. Peterson, School Science and Mathematics Vol. 70, pp. 813–820 (December 1970).

    Article  Google Scholar 

  30. Robert Karplus and Elizabeth F. Karplus, School Science and Mathematics Vol. 72, pp. 735–742 (November 1972).

    Article  Google Scholar 

  31. H. F. Witkin, Psychological Differentiation, New York: John Wiley, 1962.

    Google Scholar 

  32. B. Inhelder and J. Piaget, The Growth of Logical Thinking from Childhood to Adolescence, New York: Basic Books, 1958.

    Book  Google Scholar 

  33. Robert Karplus and Elizabeth F. Karplus, School Science and Mathematics Vol. 70, pp. 398–406 (May 1970).

    Article  Google Scholar 

  34. Robert Karplus and Rita W. Peterson, “Intellectual Development Beyond Elementary School II: Ratio, A Survey,” School Science and Mathematics, 70 (December 1970): 813–820.

    Article  Google Scholar 

  35. Robert Karplus and Elizabeth F. Karplus, “Intellectual Development Beyond Elementary School III—Ratio: A Longitudinal Study,” School Science and Mathematics, 72 (November 1972): 735–742.

    Article  Google Scholar 

  36. Elizabeth F. Karplus, Robert Karplus, and Warren Wollman, “Intellectual Development Beyond Elementary School IV: Ratio, The Influence of Cognitive Style,” School Science and Mathematics (in press).

    Google Scholar 

  37. B. Inhelder and J. Piaget, The Growth of Logical Thinking from Childhood to Adolescence (New York: Basic Books, 1958).

    Book  Google Scholar 

  38. E. A. Lunzer and P. D. Pumfrey, “Understanding Proportionality,” Mathematics Teaching, 34 (1966): 7–12.

    Google Scholar 

  39. E. A. Lunzer, “Problems of Formal Reasoning in Test Situations,” in European Research in Cognitive Development, edited by P. Mussen, Monograph of the Society for Research in Cognitive Development, Vol. 30, No. 2 (1965): 19–41.

    Google Scholar 

  40. K. Lovell and I. B. Butterworth, “Abilities Underlying the Understanding of Proportionality,” Mathematics Teaching, 35 (1966): 5–9.

    Google Scholar 

  41. C. Gattegno, A Teacher’s Introduction to the Cuisenaire-Gattegno Method of Teaching Arithmetic (New York: Cuisenaire Company of America, Inc., 1960).

    Google Scholar 

  42. E. A. Lunzer, C. Harrison, and M. Davey, “The Four-Card Problem and the Generality of Formal Reasoning,” Quarterly Journal of Psychology, 24 (August 1972): 326–339.

    Article  Google Scholar 

  43. Inhelder, B., & Piaget, J. The growth of logical thinking from childhood to adolescence. New York: Basic Books, 1958.

    Book  Google Scholar 

  44. Karplus, R., Karplus, E. F., Formisano, M., & Paulsen, A. C. Proportional reasoning and control of variables in seven countries. Berkeley: Lawrence Hall of Science, 1975.

    Google Scholar 

  45. Karplus, R., Karplus, E. F., & Wollman, W. T. Intellectual development beyond elementary school IV: Ratio, the influence of cognitive style. School Science and Mathematics, 1974, 74, 476–482.

    Article  Google Scholar 

  46. Karplus, R., Lawson, A. E., Wollman, W. T., Appel, M., Bernoff, R., Howe, A., Rusch, J. J., & Sullivan, F. L. Workshop on science teaching and the development of reasoning Berkeley: Lawrence Hall of Science, 1977.

    Google Scholar 

  47. Karplus, R., & Peterson, R. W. Intellectual development beyond elementary school II: Ratio, a survey. School Science and Mathematics, 1970, 70, 813–820.

    Article  Google Scholar 

  48. Karplus, R., & Wollman, W. T. Intellectual development beyond elementary school V: Using ratio in differing tasks. School Science and Mathematics, 1974, 74, 593–711.

    Article  Google Scholar 

  49. Kurtz, B. A study of teaching for proportional reasoning. Doctoral Dissertation, University of California, Berkeley, 1976.

    Google Scholar 

  50. Lawson, A. E. Sex differences in concrete and formal reasoning ability as measured by manipulative tasks and written tasks. Science Education, 1975, 59, 387–396.

    Article  Google Scholar 

  51. Lawson, A. E., & Wollman, W. T. Encouraging the transition from concrete to formal cognitive functioning—An experiment. Journal of Research in Science Teaching, 1976, 13, 413–430.

    Article  Google Scholar 

  52. Levine, D., & Linn, M. C. Scientific reasoning ability in adolescence: Theoretical viewpoints and educational implications. Journal of Research in Science Teaching, 1977, 14, 371–384.

    Article  Google Scholar 

  53. Lovell, K., & Butterworth, I. B. Abilities underlying the understanding of proportionality. Mathematics Teaching, 1966, 37, 5–9.

    Google Scholar 

  54. Lunzer, A. E., & Pumfrey, P. D. Understanding proportionality. Mathematics Teaching, 1966, 34, 7–12.

    Google Scholar 

  55. Suarez, A. Die Entwicklung der Denkoperation beim Verständnis Funktionaler Zusammenhänge. Doctoral Dissertation. Eidgenössische Technische Hochschule, Zürich, 1974.

    Google Scholar 

  56. Wollman, W. T. Intellectual development beyond elementary school IV: Controlling variables, a survey. Berkeley: Lawrence Hall of Science, 1975.

    Google Scholar 

  57. Blasi, A., and Hoeffel, E. C., “Adolescence and formal operations.” Human Development, 17, 344–363, 1974.

    Article  Google Scholar 

  58. Inhelder, B., and Piaget, J., The Growth of Logical Thinking from Childhood to Adolescence. New York: Basic Books, 1958.

    Book  Google Scholar 

  59. Karplus, R., and Peterson, R., “Intellectual development beyond elementary school II: ratio, a survey.” School Science and Mathematics, 70(9), 813–820, 1970.

    Article  Google Scholar 

  60. Lawson, A., and Renner, J., “A quantitative analysis of responses to Piagetian tasks and its implications for curriculum.” Science Education, 58(4), 545–559, 1974.

    Article  Google Scholar 

  61. Neimark, E., “Intellectual development during adolescence.” In F. Degan (Ed.) Review of Child Development Research Vol. 4. Chicago: University of Chicago Press, 1975.

    Google Scholar 

  62. Piaget, J., “Intellectual evolution from adolescence to adulthood.” Human Development, 15, 1–12, 1972.

    Article  Google Scholar 

  63. USMES Guide, Newton, Massachusetts: Education Development Center, 1974.

    Google Scholar 

  64. Biggs, E. “Investigations and Problem-Solving in Mathemetical Education.” In A. G. Howson, Ed. Proceedings of the Second International Congress on Mathematical Education. London: Cambridge University Press, 1973.

    Google Scholar 

  65. Inhelder, B., & Piaget, J. The Growth of Logical Thinking from Childhood to Adolescene. New York: Basic Books, 1958.

    Book  Google Scholar 

  66. Karplus, R., Karplus, E., Formisano, M., & Paulsen, A. C. “A Survey of Proportional Reasoning and Control of Variables in Seven Countries.” Journal of Research in Science Teaching, 1977(a), 14, 411–417.

    Article  Google Scholar 

  67. Karplus, R., Lawson, A. E., Wollman, W., Appel, M., Bernoff, R., Howe, A., Rusch, J. J., & Sullivan, F. Science Teaching and the Development of Reasoning. Berkeley, CA: Lawrence Hall of Science, University of California, 1977(b).

    Google Scholar 

  68. Karplus, R., & Lawson, C. A. SCIS Teachers Handbook. Berkeley, CA: Lawrence Hall of Science, University of California, 1974.

    Google Scholar 

  69. Karplus, R., & Peterson, R. W. “Intellectual Development Beyond Elementary School II: Ratio, a Survey.” School Science and Mathematics, 1970, 70, 813–820.

    Article  Google Scholar 

  70. Kurtz, G., “A Study of Teaching for Proportional Reasoning.” Doctoral Dissertation, University of California, Berkeley, 1976.

    Google Scholar 

  71. Lovell, K., & Butterworth, I. B. “Abilities Underlying the Understanding of Proportionality.” Mathematics Teaching, 1966, 37, 5–9.

    Google Scholar 

  72. Lunzer, E. A., & Pumfrey, P. D. “Understanding Proportionality.” Mathematics Teaching, 1966, 34, 7–12.

    Google Scholar 

  73. Siegel, S. Nonparametric Statistics for the Behavioral Sciences. New York: McGraw Hill Book Co., Inc., 1956.

    Google Scholar 

  74. Suarez, A. “Die Entwicklung der Denkoperation Beim Verständnis Funktionaler Zusammenhänge.” Doctoral Dissertation. Eidgenössische Technische Hochschule, Zürich, 1974.

    Google Scholar 

  75. Wollman, W., & Karplus, R. “Intellectual Development Beyond Elementary School V: Using Ratio in Differing Tasks,” School Science and Mathematics, 1974, 74, 593–613.

    Article  Google Scholar 

  76. Wollman, W. T., & Lawson, A. E. “The Influence of Instruction on Proportional Reasoning in Seventh Graders,” Journal of Research in Science Teaching, 1978, 75, 227–232.

    Article  Google Scholar 

  77. Adi, H., Karplus, R. Lawson, A. E., and Pulos, S., Intellectual Development Beyond Elementary School VI: Correlational Reasoning. School Science and Mathematics 78(8), 675–683, 1978.

    Article  Google Scholar 

  78. Arons, A. B. Cultivating the Capacity for Formal Reasoning: Objectives and Procedures in an Introductory Physical Science Course. American Journal of Physics, 44(9), 834–838, 1976.

    Article  Google Scholar 

  79. Bauman, R. P. Applicability of Piagetian Theory to College Teaching. Journal of College Science Teaching, 6, 94–96, 1976.

    Google Scholar 

  80. Griffiths, D. Physics Teaching, Does It Hinder Intellectual Development? American Journal of Physics, 44(1), 81–86, 1976.

    Article  Google Scholar 

  81. Herron, J. D. Piaget for Chemists. Journal of Chemical Education, 52, 146–150, 1975.

    Article  Google Scholar 

  82. Karplus, E. F., Karplus, R., and Wollman, W. Intellectual Development Beyond Elementary School IV: The Influence of Cognitive Style. School Science and Mathematics, 74(6), 476–482, 1974.

    Article  Google Scholar 

  83. Karplus, R. Opportunities for Concrete and Formal Thinking of Science Tasks. In Presseisen, B. Z., Goldstein, D., and Appel, M. H. (eds.) Topics in Cognitive Development. New York: Plenum Press, 1978.

    Google Scholar 

  84. Karplus, R., Karplus, E. F., Formisano, M., and Paulsen, A. C. A Survey of Proportional Reasoning and Control of Variables in Seven Countries. Journal of Research in Science Teaching, 14(5), 411–417, 1977.

    Article  Google Scholar 

  85. Karplus, R., Karplus, E., Formisano, M., and Paulsen, A. C. Proportional Reasoning and Control of Variables in Seven Countries. Berkeley, CA: Lawrence Hall of Science, 1975.

    Google Scholar 

  86. Karplus, R., Lawson, A. E., Wollman, W. T., Appel, M., Bernoff, R., Howe, A., Rusch, J. J., and Sullivan, F. Science Teaching and the Development of Reasoning. Berkeley, CA: Lawrence Hall of Science, 1977.

    Google Scholar 

  87. Karplus, R. and Peterson, R. W. Intellectual Development Beyond Elementary School II: Ratio, A Survey. School Science and Mathematics, 70(9), 813–820, 1970.

    Article  Google Scholar 

  88. Kolodyi, G.The Cognitive Development of High School and College Science Students. Journal of College Science Teaching, 5, 20–22, 1975.

    Google Scholar 

  89. Kurtz, B. A Study for Teaching for Proportional Reasoning. Doctoral Dissertation, University of California, Berkeley, 1976.

    Google Scholar 

  90. Kurtz, B. and Karplus, R. Intellectual Development Beyond Elementary School VII: Teaching for Proportional Reasoning. School Science and Mathematics, 79(5), 387–398, 1979.

    Article  Google Scholar 

  91. Lawson, A. E. Developing Formal Thought through Biology Teaching. The American Biology Teacher, 37(7), 411–420, 1975.

    Article  Google Scholar 

  92. Lawson, A. E. The Development and Validation of a Classroom Test of Formal Reasoning. Journal of Research in Science Teaching, 15(1), 11–24, 1978.

    Article  Google Scholar 

  93. Lawson, A. E., Karplus, R., and Adi, H. The Acquisition of Propositional Logic and Formal OperationalSchemata During the Secondary School Years. Journal of Research in Science Teaching, 15(6), 465–478, 1978.

    Article  Google Scholar 

  94. Lawson, A. E. and Renner, J. W. Relationship of Science Subject Matter and Developmental Levels of Learning. Journal of Research in Science Teaching, 12(4), 347–358, 1975.

    Article  Google Scholar 

  95. Lovell, K. Some Aspects of the Growth of the Concept of a Function. In M. Rosskopf, L. Steffe, and S. Tabac, Eds. Piagetian Cognitive Development Research and Mathematical Education, Reston, VA: National Council of Teachers of Mathematics, 1971, page 12.

    Google Scholar 

  96. Sayre, S. A. and Ball, D. W. Piagetian Development in Students. Journal of College Science Teachings, 5, 23, 1975.

    Google Scholar 

  97. Shayer, M. Conceptual Demands in the Nuffield O-Level Physics Course. School Science Review, 51, 186, 1972.

    Google Scholar 

  98. Shayer, M. Conceptual Demands of Nuffield O-Lovel Chemistry. Education in Chemistry, 8, 8, 1973.

    Google Scholar 

  99. Shayer, M. Conceptual Demands in the Nuffield O-Lovel Biology Course. School Science Review, 56, 381, 1974.

    Google Scholar 

  100. Suarez, A. Formales Denken und Funktionsbegriff bei Jugendlichen. Bern, Switzerland: Hans Huber, 1977.

    Google Scholar 

  101. Suarez, A. and Rhonheimer, M. Lineare Funktion. Zurich, Switzerland: Limmat Stiftung, 1974.

    Google Scholar 

  102. Wollman, W. and Lawson, A. E. The Influence of Instruction on Proportional Reasoning in Seventh Graders. Journal of Research in Science Teaching, 15(3), 227–232, 1978.

    Article  Google Scholar 

  103. Adi, H., Karplus, R., Lawson, A., and Pulos, S.: 1978, “Intellectual development beyond elementary school VI: Correlational reasoning”, School Science and Mathematics 78, 675–638.

    Article  Google Scholar 

  104. Bell, A. W.: 1976, “A study of pupils” proof-explanations in mathematical situations’, Educational Studies in Mathematics 7, 23–40.

    Article  Google Scholar 

  105. Carroll, C. A.: 1975, “Low achievers” understanding of logical inference forms’, in M. Rosskopf (ed.), Children’s Mathematical Concepts, Teachers College Press, New York.

    Google Scholar 

  106. Copi, I. M.: 1978, Introduction to Logic (4th ed.), Macmillan, New York.

    Google Scholar 

  107. Ennis, R. H.: 1976, “An alternation to Piaget’s conceptualization of logical competence”, Child Development 47, 903–919.

    Article  Google Scholar 

  108. Ennis, R. H., and Paulus, D. H.: 1965, Critical Thinking Readiness in Grades 1–12 (Phase 1: Deductive Reasoning in Adolescence), Cornell Critical Thinking Project, Ithaca, New York.

    Google Scholar 

  109. Falmagne, R. J.: “The development of logical competence: A psycholinguistic perspective”, in R. Kluwe and H. Spada (eds.), Development Models of Thinking. Academic Press, New York (in press).

    Google Scholar 

  110. Jansson, L.: 1978, “A comparison of two approaches to the assessment of conditional reasoning abilities”, Journal for Research in Mathematics Education 9, 175–188.

    Article  Google Scholar 

  111. Johnson-Laird, P. N., Legrenzi, P., and Legrenzi, M. S.: 1972, “Reasoning and a sense of reality”, British Journal of Psychology 63, 395–400.

    Article  Google Scholar 

  112. Karplus, E., and Karplus, R.: 1970, “Intellectual development beyond elementary school I: Deductive reasoning”, School Science and Mathematics 70, 398–406.

    Article  Google Scholar 

  113. Lawson, A.: 1978, “The development and validation of a classroom test of formal reasoning”, Journal of Research in Science Teaching 15, 11–24.

    Article  Google Scholar 

  114. Lawson, A., Karplus, R., and Adi, H.: 1978, “The acquisition of propositional logic and formal operational schemata during the secondary school years”, Journal of Research in Science Teaching 15, 465–478.

    Article  Google Scholar 

  115. O’Brien, T.: 1975, “Deformation and the four-card problem”, Educational Studies in Mathematics 6, 23–29.

    Article  Google Scholar 

  116. Paris, S. G.: 1973, “Comprehension of language connectives and propositional logic relationships”, Journal of Experimental Psychology 16, 278–291.

    Google Scholar 

  117. Resnick, L.: 1976, The Nature of Intelligence, Lawrence Erlbaum Assoc, Hillsdale, New Jersey.

    Google Scholar 

  118. Roberge, J.J.: 1970, “A study of children’s abilities to reason with basic principles of deductive reasoning”, American Education Research Journal 7, 583–596.

    Google Scholar 

  119. Roberge, J.J.: 1972, “Recent research on the development of children’s comprehension of deductive reasoning schemes”, School Science and Mathematics 72, 197–200.

    Article  Google Scholar 

  120. Roberge, J.J., and Paulus, D.: 1971, “Developmental patterns for children’s class and conditional reasoning abilities”, Developmental Psychology 4, 191–200.

    Article  Google Scholar 

  121. Wason, P. C., and Johnson-Laird, P. M.: 1972, Psychology of Reasoning: Structure and Content. Havard University Press, Cambridge, Mass.

    Google Scholar 

  122. Wildman, T., and Fletcher, H.: 1977, “Developmental increases and decreases in solutions of conditional syllogism problems”, Developmental Psychology 13, 63–636.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Kluwer Academic/Plenum Publishers, New York

About this chapter

Cite this chapter

Khoury, H.A. et al. (2002). Central Role of Students’ Reasoning. In: Fuller, R.G. (eds) A Love of Discovery. Innovations in Science Education and Technology. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0876-1_6

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-0876-1_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-306-46687-8

  • Online ISBN: 978-94-007-0876-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics