Allport, D. A.: 1980, ‘Patterns and actions: cognitive mechanisms are content-specific’, in G.Claxton (ed.):Cognitive Psychology: New Directions
, Routledge and Kegan Paul, London, pp. 26–64.Google Scholar
Anderson, J. R. and Bower, G. H.: 1973,Human Associative Memory, Wiley, Halstead Press.
Ausubel, D. P.: 1968,Educational Psychology: A Cognitive View, Holt, Rinehart and Winston, pp. 113–114.
Ausubel, D. P.: 1971, ‘Some psychological and educational limitations of learning by discovery’, in D. B. Aichele and R. E. Reyes (eds.):Reading in Secondary School Mathematics, Prindle, Weber and Schmidt, pp. 193–209.
Baddeley, A. D.: 1976,The Psychology of Memory, Basic Books.
Bartlett, F. C.: 1932,Remembering: A Study in Experimental and Social Psychology, Cambridge University Press.
Bell, A. W.: 1976,The Learning of General Mathematical Strategies, Ph.D. Thesis, Centre for Mathematical Education, University of Nottingham, p. 9.18.
Boyer, C. B.: 1968,A History of Mathematics, Wiley, p. 53.
Branca, N. A.: 1980, ‘Communication of mathematical structure and its relationship to achievement’,Journal for Research in Mathematics Education
, 37–49.Google Scholar
Bruner, J. S.: 1961, ‘The act of discovery’,Harvard Educational Review
, 21–32.Google Scholar
Bruner, J. S.: 1962,The Process of Education, Harvard University Press.
Bruner, J. S.: 1973,Beyond the Information Given: Studies in the Psychology of Knowing, Norton.
Burton, L.: 1984, ‘Mathematical thinking: the struggle for meaning’,Journal for Research in Mathematics Education
, 1, 35–49.Google Scholar
Butler, H. C. and Wren, F.: 1941,The Teaching of Secondary Mathematics, 1 st ed., McGraw-Hill.
Byers, V.: 1980, ‘What does it mean to understand mathematics?’,International Journal of Mathematics Education Science and Technology
, 1, 1–10.Google Scholar
Byers, V. and Erlwanger, S. H.: 1984, ‘Content and form in mathematics’,Educational Studies in Mathematics
, 259–275.Google Scholar
Byers, V. and Herscovics, N.: 1977, ‘Understanding school mathematics’,Mathematics Teaching
Carry, L. B., Lewis, C. and Bernard, J. F.: 1980,Psychology of Equation Solving: An Information Processing Study, Final Technical Report, Dept. of Curriculum & Instruction, University of Texas At Austin.
Claxton, G.: 1980, ‘Remembering and understanding’, in G. Claxton (ed.):Cognitive Psychology: New Directions, Routledge and Kegan Paul, pp. 197–235.
Claxton, G.: 1980, ‘Cognitive psychology: a suitable case for what sort of treatment?’, in G. Claxton (ed.):Cognitive Psychology: New Directions, Routledge and Kegan Paul, pp. 1–25.
Collins, A. M. and Quillian, M. R.: 1972, ‘How to make a language user’, in E. Tulvig and W. Donaldson (eds.):Organization of Memory, Academic Press, pp. 309–351.
Davis, E. J.: 1978, ‘A model for understanding understanding in mathematics’,Arithmetic Teacher, September.
Davis, R. R.: 1983, ‘Complex mathematical cognition’, in H. P.Ginsburg (ed.):The Development of Mathematical Thinking
, Academic Press, New York, pp. 254–290.Google Scholar
Erlwanger, S. H.: 1973, ‘Benny's conception of rules and answers in IPI mathematics’,Journal of Childrens' Mathematical Behaviour
, 2.Google Scholar
Flavell, J. H.: 1977,Cognitive Development, Prentice-Hall.
Freemont, H.: 1971, ‘New mathematics and old dilemmas’, in D. B. Aichele and R. E. Reyes (eds.):Readings in Secondary School Mathematics, Prindle, Weber and Schmidt, p. 4.
Gagné, R. M.: 1968, ‘Learning hierarchies’,Educational Psychologist
, 1–9.Google Scholar
Gagné, R. M.: 1970,Conditions of Learning, 2nd Ed., Holt Rinehart and Winston.
Gagné, R. M.: 1983, ‘Some issues in the psychology of mathematics instruction’,Journal for Research in Mathematics Education
, 7–18.Google Scholar
Gagné, R. M. and White, R. T.: 1978, ‘Memory structures and learning outcomes’,Review of Educational Research
, 2, 187–222.Google Scholar
Geeslin, W. E. and Shavelson, R. J.: 1975, ‘Comparison of content structure and cognitive structure in high school students' learning of probability’,Journal for Research in Mathematics Education
, 109–120.Google Scholar
Ginsburg, H.: 1977,Children's Arithmetic: The Learning Process, D. van Nostrand, pp. 128–129.
Greeno, J. G.: 1973, ‘The structure of memory and the process of solving problems’, in R. L. Solso, (ed.):Contemporary Issues in Cognitive Psychology: The Loyola Symposium, Winston, pp. 103–134.
Greer, B.: 1981, ‘Cognitive psychology and mathematical thinking’,For the Learning of Mathematics
, 3, 22–24.Google Scholar
Hebb, D. O.: 1972,Textbook of Psychology, 3rd ed., Saunders, p. 99.
Hilgard, E. R.: 1957,Introduction to Psychology, 2nd ed., Harcourt Brace, pp. 285–302.
Jenks, S. M., Peck, D. M. and Chatterley, L. J.: 1980, ‘Why blame the kids? We teach mistakes!’,Arithmetic Teacher
, 2, 38–41.Google Scholar
Krutetskii, V. A.: 1976,The Psychology of Mathematical Abilities in School Children, in J. Kilpatrick and I. Wirszup (eds.): University of Chicago Press.
Langford, F. G.: 1972,Some Computational Strategies of Seventh Grade Pupils
, University of Virginia, Charlottesville.Google Scholar
Lehman, H.: 1977, ‘On understanding mathematics’,Educational Theory
, 2.Google Scholar
Mandler, G.: 1972, ‘Organization and recognition’, in E. Tulvig and W. Donaldson (eds.):Organization of Memory, Academic Press, pp. 146–167.
Mayer, R. E.: 1977,Thinking and Problem Solving: An Introduction to Human Cognition and Learning, Scott, Foresman & Co.
Mayer, R. E. and Greeno, J. G.: 1972, ‘Structural differences between learning outcomes produced by different instructional methods’,Journal of Educational Psychology
, 165–173.Google Scholar
Michener, E. R.: 1978, ‘Understanding understanding mathematics’,Cognitive Science
, 361–383.Google Scholar
Miller, G. A.: 1956, ‘The magical number seven, plus or minus two: some limits on our capacity for processing information’,Psychological Review
, 81–96.Google Scholar
Morgan, C. T. and Deese, J.: 1957,How to Study, McGraw-Hill.
Morris, J.: 1981, ‘Math anxiety: teaching to avoid it’,Mathematics Teacher
, 6, 414.Google Scholar
Neisser, U.: 1978, ‘What are the important questions?’, in M. M. Guneberg, P. E. Morris, and R. N. Sykes (eds.):Practical Aspects of Memory, Academic Press, pp. 3–24.
Osgood, C. E.: 1953,Method and Theory in Experimental Psychology, Oxford, p. 570.
Paivio, A.: 1971,Imagery and Verbal Processes, Holt, Reinhart & Winston.
Postman, L.: 1972, ‘A pragmatic view of organization theory’, in E. Tulvig and W. Donaldson (eds.):Organization of Memory, Academic Press, pp. 3–48.
Piaget, J. and Inhelder, B.: 1973,Memory and Intelligence, Basic Books.
Radatz, H.: 1979, ‘Error analysis in mathematics education’,Journal for Research in Mathematics Education
, 163–171.Google Scholar
Resnick, L. B.: 1983, ‘A developmental theory of number understanding’, in H. P.Ginsburg (ed.):The Development of Mathematical Thinking
, Academic Press, New York, pp. 109–151.Google Scholar
Riley, M. S., Green, J. G. and Heller, J. I.: 1983, ‘Development of children's problem-solving ability in arithmetic’, in H. P.Ginsburg (ed.):The Development of Mathematical Thinking
, Academic Press, New York, pp. 153–196.Google Scholar
Sadowski, B. R. and McIlveen, D. H.: 1982, ‘Diagnosis and remediation of sentence-solving error patterns’,Arithmetic Teacher
, 5, 42–45.Google Scholar
Scopes, P. G.: 1973,Mathematics in Secondary Schools—A Teaching Approach, Cambridge University Press, p. 86.
Shavelson, R. J.: 1972, ‘Some aspects of the correspondence between content structure and cognitive structure in physics instruction’,Journal of Educational Psychology
, 225–234.Google Scholar
Shavelson, R. J.: 1974, ‘Methods for examining representations of a subject-matter structure in a student's memory’,Journal of Research in Science Teaching
, 231–249.Google Scholar
Shulman, L. S.: 1970, ‘Psychology of mathematics education’, inMathematics Education, Yearbook 69, National Society for the Study of Education, Part I, University of Chicago Press.
Skemp, R. R.: 1976, ‘Relational understanding and instrumental understanding’,Mathematics Teaching 77.
Skemp, R. R.: 1979, ‘Goals of learning and qualities of understanding’,Mathematics Teaching 88.
Skemp, R. R.: 1979,Intelligence, Learning and Action, Wiley, pp. 259–260.
Suydam, M. N. and Dessart, D. J.: 1980, ‘Skill learning’, in R. J.Shumway (ed.):Research in Mathematics Education
, National Council of Teachers of Mathematics, Reston, pp. 207–243.Google Scholar
Tulvig, E.: 1972, ‘Episodic and semantic memory’, in E. Tulvig and W. Donaldson (eds.):Organization of Memory, Academic Press, pp. 381–403.
Vinner, S.: 1981, Personal communication.
Wertheimer, M.: 1959,Productive Thinking, enl. ed., Harper, p. 11.
Wittrock, M. C.: 1974, ‘A generative model of mathematics learning’,Journal of Research in Mathematics Education
, 181–196.Google Scholar
Woodworth, R. S. and Schlossberg, H.: 1954,Experimental Psychology, 2nd ed., Holt, p. 730.