Teachers and subtraction problems: expert-novice differences revisited

Briars D. J. , and Larkin J. H. . (1984), ‘An integrated model of skill in solving elementary word problems’, Cognition and Instruction 1, pp. 245–90.

Carpenter T. P. , and Moser J. M. . (1982), ‘The development of addition and subtraction problem-solving skills’, in Carpenter T. P. , Moser J. M. , and Romberg J. , Addition and Subtraction: a cognitive perspective, Hillsdale, N.J.: Erlbaum.

Carpenter T. P. , Hiebert J. , and Moser J. M. . (1981), ‘The effect of problem structure on first graders’ initial solution processes for simple addition and subtraction problems’, Journal for Research in Mathematics Education 12, pp. 27–39.

Chi M. T. H. , Feltovich P. J. , and Glaser R. . (1981), ‘Categorization and representation of physics problems by experts and novices’, Cognitive Science 5, pp. 121–52.

Cobb P. , Yackel E. , and Wood T. . (1992), ‘A constructivist alternative to the representational view of the mind’, Journal for Research in Mathematics Education 23, pp. 2–23.

Dean A. L. , and Malik M. M. . (1986), ‘Representing and solving arithmetic word problems: a study of developmental interaction’, Cognition and Instruction 3, pp. 211–27.

Fischbein E. , Deri M. , Nello M. , and Marino M. . (1985), ‘The role of implicit models in solving problems in multiplication and division’, Journal for Research in Mathematics Education 16, pp. 3–17.

Foxman D. D. , Ruddock G. , and McCallum I. . (1990), Assessment Matters, No. 3, APU Mathematics Monitoring, 1984-88 (Phase 2), London: SEAC.

Graeber A. , Tirosh D. , and Glover R. . (1989), ‘Pre-service teachers’ misconceptions in solving verbal problems in multiplication and division’, Journal for Research in Mathematics Education 20, pp. 95–102.

Lewis A. L. . (1989), ‘Training students to represent arithmetic word problems’, Journal of Educational Psychology 81, pp. 521–31.

Morales R. V. , Shute V. J. , and Pellegrino J. W. . (1985), ‘Developmental differences in understanding and solving simple mathematics word problems’, Cognition and Instruction 2, pp. 41–57.

Nesher P. , Greeno J. G. , and Heller J. I. . (1982), ‘The development of semantic categories for addition and subtraction’, Educational Studies in Mathematics 13, pp. 373–94.

Riley M. S. , and Greeno J. G. . (1988), ‘Developmental analysis of understanding language about quantities and of solving problems’, Cognition and Instruction 5(1), pp. 49–101.

Riley M. S. , and Greeno J. G. , and Heller J. I. . (1983), ‘Development of children's problem-solving ability in arithmetic’, in Ginsburg H. P. (ed.), The Development of Mathematical Thinking, New York: Academic Press.

Scottish Primary Mathematics Group (1990), Primary Mathematics: a development through activity, Oxford: Heinemann.

Simon M. A. . (1993), ‘Prospective elementary teachers’ knowledge of division’, Journal for Research in Mathematics Education 24, pp. 233–54.

Thompson A. G. . (1992), ‘Teachers’ beliefs and conceptions: a synthesis of the research’, in Grouws D. A. (ed.), Handbook of Research on Mathematics Teaching and Learning, New York: Macmillan.

Van Essen G. , and Hamaker C. . (1990), ‘Using self-generated drawings to solve arithmetic word problems’, Journal of Educational Research 83, pp. 301–12.

Vergnaud G. . (1982), ‘A classification of cognitive tasks and operations of thought involved in addition and subtraction problems’, in Carpenter T. P. , Moser J. M. , and Romberg J. (eds.), Addition and Subtraction: a cognitive perspective, Hillsdale, N. J.: Erlbaum.

Willis G. B. , and Fuson K. C. . (1988), ‘Teaching children to use schematic drawings to solve addition and subtraction word problems’, Journal of Educational Psychology 80, pp. 192–201.