Pitta, Demetra (1998) Beyond the obvious : mental representations and elementary arithmetic. PhD thesis, University of Warwick.

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Abstract

This study seeks to answer the question: "What kinds of mental representation do children
project and how may these be associated with their level of achievement in elementary
arithmetic?". Drawing upon theories offering some explanation for the way in which
arithmetical activity is transformed into numerical concepts and those that hypothesise the
form and quality of mental representations the study suggests that qualitatively different
kinds of mental representation may be associated with qualitatively different kinds of
arithmetical behaviour.
The evidence is drawn from the classification and categorisation of data from two series of
semi-clinical interviews carried out with children aged eight to twelve who were at extremes
of numerical achievement. The first, a pilot study, largely concentrated on mental
representations associated with numerical concepts and skills. Its results suggest that
mental representations projected by children may have a disposition towards different kinds
of mental representation which transcends arithmetical and non-arithmetical boundaries.
Issues raised by this study, in conjunction with a re-appraisal of the psychological
evidence, informed the development of the main study. With a similar sample of children
this considered the relationship between children's projections, reports and descriptions of
mental representations in numerical and non-numerical contexts and in elementary
arithmetic. Words, pictures, icons and symbols stimulated the projection of these
representations. The evidence suggests that there is indeed a disposition towards the
formation of particular kinds of mental representation. low achievers' projected mental
representations which have descriptive emphasis. 'High achievers', whilst able to do the
same, also project those with relational characteristics, the frequency of which increases as
the stimulus becomes more 'language like'. This provides them with the flexibility to
oscillate between descriptive and abstract levels of thought.
The study indicates that qualitative different thinking in number processing is closely
associated to a disposition towards qualitatively different kinds of mental representation. Its
concluding comments suggest that these differences may have some considerable
implication for the received belief that active methods may supply all children with a basis
for numerical understanding.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	L Education > LB Theory and practice of education > LB1501 Primary Education
Library of Congress Subject Headings (LCSH):	Arithmetic -- Study and teaching (Primary), Mental representation in children
Official Date:	June 1998
Dates:	Date Event June 1998 Submitted
Institution:	University of Warwick
Theses Department:	Institute of Education
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Gray, Edward Martin
Extent:	xi, 329 leaves
Language:	eng

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