Skip to main content
SpringerLink
Log in

Conservation—Nonconservation: Alternative Explanations

  • Chapter
Children’s Logical and Mathematical Cognition

Part of the book series: Springer Series in Cognitive Development ((2116))

Abstract

As cognitively mature adults we know that a quantity remains constant across a transformation as long as there is no addition or subtraction of the specific quantity in question. That is, we appear to be aware of an identity rule: In the absence of addition or subtraction quantity (amount) is maintained. Furthermore, we appear to know that this rule is more than just one of many available cues for judging quantity. To the extent that the possibility of addition or subtraction can be monitored during a transformation, we know that the identity rule should take precedence over any other potential cue for judging the presence or absence of a change in quantity.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

References Notes

  1. Shultz, T. R. Concepts of natural and logical necessity. Paper presented at the biennial meeting of the Society for Research in Child Development, April 1981.

    Google Scholar 

  2. Silverman, I. W. & Briga, J. Does conservation training provoke the child to discover new rules for judging quantity. Paper presented at the biennial meeting of the Society for Research in Child Development, April 1981.

    Google Scholar 

  3. Acredolo, C. & Acredolo, L. P. Equilibration and conservation. Paper presented at the meeting of the Piaget Society, May 1980.

    Google Scholar 

References

  • Acredolo, C. The acquisition of conservation: A clarification of Piagetian terminology, some recent findings, and an alternative formulation. Human Development, 1981, 24, 120–137.

    Article  Google Scholar 

  • Acredolo, C. & Acredolo, L. P. Identity, compensation, and conservation. Child Development, 1979, 50, 524–535.

    Article  Google Scholar 

  • Acredolo, C. & Acredolo, L. P. The anticipation of conservation phenomenon: Conservation or pseudoconservation. Child Development, 1980, 51, 667–675.

    Article  Google Scholar 

  • Anderson, N. H. & Cuneo, D. O. The height + width rule in children’s judgment of quantity. Journal of Experimental Psychology: General, 1978, 107, 335–378.

    Article  Google Scholar 

  • Bates, E. Language and context. New York: Academic Press, 1976.

    Google Scholar 

  • Braine, M. D. S. & Shanks, B. L. The conservation of a shape property and a proposal about the origin of conservations. Canadian Journal of Psychology, 1965, 19, 197–207. (a)

    Article  PubMed  Google Scholar 

  • Braine, M. D. S. & Shanks, B. L. The development of conservation of size. Journal of Verbal Learning and Verbal Behavior, 1965, 4, 227–242. (b)

    Article  Google Scholar 

  • Brainerd, C. J. Judgments and explanations as criteria for the presence of cognitive structures. Psychological Bulletin, 1973, 79, 172–179.

    Article  Google Scholar 

  • Brainerd, C. J. Feedback, rule knowledge, and conservation learning. Child Development, 1911, 48, 404–411.

    Article  Google Scholar 

  • Brainerd, C. J. & Hooper, F. H. A methodological analysis of developmental studies of identity conservation and equivalence conservation. Psychological Bulletin, 1975, 52, 725–737.

    Article  Google Scholar 

  • Brainerd, C. J. & Hooper, F. H. More on the identity-equivalence sequences: An update and some replies to Miller. Psychological Bulletin, 1978, 85, 70–75.

    Google Scholar 

  • Breslow, L. Réévaluation of the literature on the development of transitive inferences. Psychological Bulletin, 1981, 89, 325–351.

    Article  Google Scholar 

  • Bruner, J. S. On the conservation of liquids. In J. S. Bruner, R. R. Olver, P. M. Greenfield, et al. (Eds.), Studies in cognitive growth. New York: Wiley, 1966.

    Google Scholar 

  • Bryant, P. E. The understanding of invariance by very young children. Canadian Journal of Psychology, 1972, 26, 78–96.

    Article  Google Scholar 

  • Bryant, P. E. Perception and understanding in young children: An experimental approach. New York: Basic Books, 1974.

    Google Scholar 

  • Bryant, P. E. & Trabasso, T. Transitive inferences and memory in young children. Nature, 1971, 232, 456–458.

    Article  PubMed  Google Scholar 

  • Carnap, R. Philosophical foundations of physics. New York: Basic Books, 1966.

    Google Scholar 

  • Clark, H. The primitive nature of children’s relational concepts. In J. R. Hayes (Ed.), Cognition and the development of language. New York: Wiley, 1970.

    Google Scholar 

  • Cowan, R. A reappraisal of the relation between performance of quantitative identity and quantitative equivalence conservation tasks. Journal of Experimental Child Psychology, 1979, 28, 68–80.

    Article  Google Scholar 

  • Cuneo, D. O. A general strategy for quantity judgments: The height + width rule. Child Development, 1980, 51, 299–301.

    Article  PubMed  Google Scholar 

  • Curcio, F., Kattef, E., Levine, D. & Robbins, O. Compensation and susceptibility to conservation training. Developmental Psychology, 1972, 7, 259–265.

    Article  Google Scholar 

  • Dockrell, J., Campbell, R. & Neilson, I. Conservation accidents revisited. International Journal of Behavioral Development, 1980, 3, 423–439.

    Google Scholar 

  • Donaldson, M. & Balfour, G. Less is more. British Journal of Psychology, 1968, 59, 461–471.

    Article  Google Scholar 

  • Donaldson, M. & Wales, R. On the acquisition of some relational terms. In J. R. Hayes (Ed.), Cognition and the development of language. New York: Wiley, 1970.

    Google Scholar 

  • Elkind, D. Conservation across illusory transformations in young children. Acta Psychologia, 1966, 25, 389–400.

    Article  Google Scholar 

  • Elkind, D. Piaget’s conservation problems. Child Development, 1967, 38, 15–27.

    Article  Google Scholar 

  • Flavell, J. H. The developmental psychology of Jean Piaget. New York: Van Nostrand-Reinhold, 1963.

    Book  Google Scholar 

  • Flavell, J. H. Cognitive development. Englewood Cliffs, New Jersey: Prentice-Hall, 1977.

    Google Scholar 

  • Gelman, R. Conservation acquisition: A problem of learning to attend to relevant attributes. Journal of Experimental Child Psychology, 1969, 7, 167–186.

    Article  Google Scholar 

  • Gelman, R. Logical capacity of very young children: Number variance rules. Child Development, 1912, 43, 75–90.

    Article  Google Scholar 

  • Gelman, R. & Gallistel, C. R. The child’s understanding of number. Cambridge, Massachusetts: Harvard University Press, 1978.

    Google Scholar 

  • Gelman, R. & Tucker, M. R. Further investigations of the young child’s conception of number. Child Development, 1915, 46, 167–175.

    Article  Google Scholar 

  • Gelman, R. & Weinberg, D. H. The relationship between liquid conservation and compensation. Child Development, 1912, 43, 371–383.

    Article  Google Scholar 

  • Gibson, E. J. Principles of perceptual learning and development. New York: Appleton-Century-Crofts, 1969.

    Google Scholar 

  • Gibson, J. J. The ecological approach to visual perception. Boston, Massachusetts: Houghton Mifflin, 1979.

    Google Scholar 

  • Goodnow, J. J. Compensation arguments on conservation tasks. Developmental Psychology, 1913, 8, 140.

    Article  Google Scholar 

  • Griffiths, J. A., Shantz, C. A. & Sigel, I. A methodological problem in conservation studies: The use of relational terms. Child Development, 1967, 38, 841–848.

    PubMed  Google Scholar 

  • Hall, V. C. & Kaye, D. B. The necessity of logical necessity in Piaget’s theory. L. S. Siegel,,, C. J. Brainerd (Eds.), Alternatives to Piaget: Critical essays on the theory. New York: Academic Press, 1978.

    Google Scholar 

  • Hamel, B. R. On the conservation of liquids. Human Development, 1971, 14, 39–46.

    Article  Google Scholar 

  • Hamel, B. R. & Riksen, B. O. M. Identity, reversibility, verbal rule instruction and conservation. Developmental Psychology, 1973, J, 66–72.

    Google Scholar 

  • Hamel, B. R., Van der Veer, M. A. A. & Westerhof, R. Identity, language-activation training and conservation. British Journal of Educational Psychology, 1972, 42, 186–191.

    Article  Google Scholar 

  • Hood, H. B. An experimental study of Piaget’s theory of the development of number in children. British Journal of Psychology, 1962, 53, 273–286.

    Article  PubMed  Google Scholar 

  • Hulsebus, R. C. An interaction between vertical dimension and age in children’s judgment of size. Perceptual and Motor Skills, 1969, 28, 841–842.

    Article  PubMed  Google Scholar 

  • Inhelder, B., Bovet, M., Sinclair, H. & Smock, C. D. On cognitive development. American Psychologist, 1966, 21, 160–164.

    Article  Google Scholar 

  • Inhelder, B., Sinclair, H. & Bovet, M. Learning and development of cognition. Cambridge, Massachusetts: Harvard University Press, 1974.

    Google Scholar 

  • Katz, H. & Beilin, H. A test of Bryant’s claims concerning the young child’s understanding of quantitative invariance. Child Development, 1976, 47, 877–880.

    Article  Google Scholar 

  • Klahr, D. & Wallace, J. G. Cognitive development: An information-processing view. Hillsdale, New Jersey: Lawrence Erlbaum Assoc., 1976.

    Google Scholar 

  • Larsen, G. Y. & Flavell, J. H. Verbal factors in compensation performance and the relationship between conservation and compensation. Child Development, 1970, 41, 965–911.

    Article  PubMed  Google Scholar 

  • Leahey, T. H. The development of conservation abilities: An intertask analysis of continuous quantity. Merrill-Palmer Quarterly of Behavior and Development, 1977, 23, 215–225.

    Google Scholar 

  • Lee, L. C. The concomitant development of cognitive and moral modes of thought: A test of selected deductions from Piaget’s theory. Genetic Psychology Monographs, 1911, 83, 93–146.

    Google Scholar 

  • Lumsden, E. A. & Kling, J. K. The relevance of an adequate concept of “bigger” for investigations of size conservation: A methodological critique. Journal of Experimental Child Psychology, 1969, 8, 82–91.

    Article  PubMed  Google Scholar 

  • Lumsden, E. A. & Poteat, B. W. S. The salience of the vertical dimension in the concept of “bigger” in five- and six-year-olds. Journal of Verbal Learning and Verbal Behavior, 1968, 7, 404–408.

    Article  Google Scholar 

  • Lunzer, E. A. Formal reasoning. In E. A. Lunzer, J. F. Morris (Eds.), Development in human learning. New York: American Elsevier, 1968.

    Google Scholar 

  • Maratsos, M. P. Decrease in preschool children’s understanding of the word big. Child Development, 1973, 4, 747–752.

    Article  Google Scholar 

  • Maratsos, M. P. When is a high thing the big one. Developmental Psychology, 1914, 10, 361–315.

    Google Scholar 

  • McGarrigle, J. & Donaldson, M. Conservation accidents. Cognition, 1975, 3, 341–350.

    Article  Google Scholar 

  • Mehler, J. & Bever, T. C. Cognitive capacity of very young children. Science, 1967, 158, 141–142.

    Article  PubMed  Google Scholar 

  • Miller, P. H. & Heldmeyer, K. H. Perceptual information in conservation: Effects of screening. Child Development, 1915, 46, 588–592.

    Article  Google Scholar 

  • Miller, P. H. & Heller, K. Facilitation of attention to number and conservation of number. Journal of Experimental Child Psychology, 1976, 22, 454–467.

    Article  Google Scholar 

  • Miller, S. A. Contradiction, surprise, and cognitive change: The effects of disconfirmation of belief on conservers and nonconservers. Journal of Experimental Child Psychology, 1973, 15, 47–62.

    Article  Google Scholar 

  • Miller, S. A. Extinction of Piagetian concepts: An updating. Merrill-Palmer Quarterly of Behavior and Development, 1976, 22, 257–281. (a)

    Google Scholar 

  • Miller, S. A. Nonverbal assessment of Piagetian concepts. Psychological Bulletin, 1976, 83, 405–430. (b)

    Article  Google Scholar 

  • Miller, S. A. A disconfirmation of the quantitative identity-quantitative equivalence sequence. Journal of Experimental Child Psychology, 1977, 24, 180–189.

    Article  Google Scholar 

  • Miller, S. A. Identity conservation and equivalence conservation: A critique of Brainerd and Hooper’s analysis. Psychological Bulletin, 1978, 85, 58 - 69.

    Article  Google Scholar 

  • Palermo, D. S. More about less: A study of language comprehension. Journal of Verbal Learning and Verbal Behavior, 1973, 72, 211–221.

    Article  Google Scholar 

  • Palermo, D. S. Still more about the comprehension of less. ’ Developmental Psychology, 1974, 10, 827–829.

    Article  Google Scholar 

  • Pennington, B. F., Wallach, L. & Wallach, M. A. Nonconservers’ use and understanding of number and arithmetic. Genetic Psychology Monographs, 1980, 101, 231–243.

    Google Scholar 

  • Perner, J., Steiner, G. & Staehelin, C. Mental representation of length and weight series and transitive inferences in young children. Journal of Experimental Child Psychology, 1981, 31, 177–192.

    Article  PubMed  Google Scholar 

  • Phye, G. & Tenbrick, T. Stimulus position and functional direction: Confounds in the concept of “bigger” in 5- and 6-year-olds. Psychonomic Science, 1972, 29, 357–359.

    Google Scholar 

  • Piaget, J. The child’s conception of number. New York: Humanities Press, 1952.

    Google Scholar 

  • Piaget, J. Cognitions and conservations: Two views. Contemporary Psychology, 1967, 72, 532–533.

    Google Scholar 

  • Piaget, J. Quantification, conservation, and nativism. Science, 1968, 162, 976–979.

    Article  PubMed  Google Scholar 

  • Piaget, J. Biology and knowledge. Chicago: University of Chicago Press, 1971.

    Google Scholar 

  • Piaget, J. Identity and conservation. In B. Inhelder,,, H. H. Chipman (Eds.), Piaget and his school New York: Springer-Verlag, 1976.

    Google Scholar 

  • Piaget, J. & Inhelder, B. Images and thought: The role of images in the preparation and function of operations. In P. Fraisse,,, J. Piaget (Eds.), Experimental psychology: Its scope and method, Vol. 7: Intelligence. New York: Basic Books, 1969.

    Google Scholar 

  • Piaget, J. & Inhelder, B. Mental imagery in the child. New York: Basic Books, 1971.

    Google Scholar 

  • Piaget, J. & Inhelder, B. The child’s construction of quantities: Conservation and atomism. London: Routledge and Kegan Paul, 1974.

    Google Scholar 

  • Pinard, A. & Chase, G. Pseudoconservation of volume and surface area of a solid object. Child Development, 1911, 48, 1559–1566.

    Article  Google Scholar 

  • Poteat, B. W. S. & Hulsebus, R. C. A vertical dimension: A significant cue in the preschool child’s concept of “bigger. ” Psychonomic Science, 1968, 12, 369–370.

    Google Scholar 

  • Rose, S. A. & Blank, M. The potency of context in children’s cognition: An illustration through conservation. Child Development, 1974, 45, 499–502.

    Article  Google Scholar 

  • Rothenberg, B. A. Conservation of number among four- and five-year-old children: Some methodological considerations. Child Development, 1969, 40, 383–406.

    Article  Google Scholar 

  • Russell, J. Nonconservation of area: Do children succeed where adults fail. Developmental Psychology, 1976, 12, 367–368.

    Article  Google Scholar 

  • Shultz, T. R., Dover, A. & Amsel, E. The logical and empirical bases of conservation judgments. Cognition, 1979, 7, 99–123.

    Article  Google Scholar 

  • Sheppard, J. L. Compensation and combinational systems in the acquisition and generalization of conservation. Child Development, 1974, 45, 717–730.

    Article  Google Scholar 

  • Siegel, L. S. The relationship of language and thought in the preoperational child: A reconsideration of nonverbal alternatives to Piagetian tasks. In L. S. Siegel,,, C. J. Brainerd (Eds.), Alternatives to Piaget: Critical essays on the theory. New York: Academic Press, 1978.

    Google Scholar 

  • Siegler, R. S. Developmental sequences within and between concepts. Monographs of the Society for Research in Child Development, 1981. 46 (Whole No. 189).

    Google Scholar 

  • Silverman, I. & Schneider, D. S. A study of the development of conservation by a nonverbal method. Journal of Genetic Psychology, 1968, 112, 287–291.

    PubMed  Google Scholar 

  • Silverman, I. W. Context and number conservation. Child Study Journal, 1979, 9, 205–212.

    Google Scholar 

  • Silverman, I. W. & Briga, J. By what process do young children solve small number conservation problems. Journal of Experimental Child Psychology, 1981, 32, 115–126.

    Article  Google Scholar 

  • Silverman, I. W. & Rose, A. P. Compensation and conservation. Psychological Bul-letin, in press.

    Google Scholar 

  • Silverman, I. W., Rose, A. P. & Phillis, D. E. The “magic” paradigm revisited. Journal of Experimental Child Psychology, 1919, 28, 30–42.

    Article  Google Scholar 

  • Smedslund, J. The acquisition of conservation of substance and weight in children: V. Practice in conflict situations without external reinforcement. Scandanavian Journal of Psychology, 1961, 2, 156–160.

    Article  Google Scholar 

  • Smedslund, J. Microanalysis of concrete reasoning: I, II, III. Scandanavian Journal of Psychology, 1966, 7, 145–167.

    Google Scholar 

  • Starkey, P. Young children’s performance in number conservation tasks: Evidence for a hierarchy of strategies. Journal of Genetic Psychology, 1981, 138, 103–110.

    Google Scholar 

  • Strauss, S. & Liberman, D. The empirical violation of conservation laws and its relation to structural change. Journal of Experimental Child Psychology, 1974, 18, 464–479.

    Article  Google Scholar 

  • Thayer, E. S. & Collyer, C. E. The development of transitive inference: A review of recent approaches. Psychological Bulletin, 1978, 55, 1327–1343.

    Article  Google Scholar 

  • Wallach, L. On the bases of conservation. In D. Elkind,,, J. H. Flavell (Eds.), Studies in cognitive development: Essays in honor of Jean Piaget. New York: Oxford University Press, 1969.

    Google Scholar 

  • Weiner, S. L. On the development of more and less. Journal of Experimental Child Psychology, 1974, 17, 271–287.

    Article  Google Scholar 

  • Wheldall, K. & Poborca, B. Conservation without conversation? An alternative, non-verbal paradigm for assessing conservation of liquid quantity. British Journal of Psychology, 1980, 71, 117–134.

    Article  Google Scholar 

  • Winer, G. A. Induced set and acquisition of number conservation. Child Development, 1968, 39, 195–205.

    Article  PubMed  Google Scholar 

  • Winer, G. A. Conservation of different quantities among preschool children. Child Development, 1914, 45, 839–842.

    Article  Google Scholar 

  • Winer, G. A. Analysis of the relation between conservation of large and small quantities. Psychological Reports, 1915, 36, 379–382.

    Article  Google Scholar 

  • Woodruff, G., Premack, D. & Kennel, K. Conservation of liquid and solid quantity by the chimpanzee. Science, 1978, 202, 991–994.

    Article  PubMed  Google Scholar 

  • Zimilies, H. The development of conservation and differentiation of number. Monographs of the Society for Research in Child Development, 1966, 31 (6, Serial No. 180).

    Google Scholar 

Download references

Authors
  1. Curt Acredolo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Psychology, University of Western Ontario, N6A 5C2, London, Ontario, Canada

    Charles J. Brainerd

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Acredolo, C. (1982). Conservation—Nonconservation: Alternative Explanations. In: Brainerd, C.J. (eds) Children’s Logical and Mathematical Cognition. Springer Series in Cognitive Development. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9466-2_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-9466-2_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9468-6

  • Online ISBN: 978-1-4613-9466-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation