Sutherland, Rosamund.; (1988) A longitudinal study of the development of pupils algebraic thinking in a Logo environment. Doctoral thesis , Institute of Education, University of London.

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Abstract

This thesis is based on research to investigate the hypothesis that programming in Logo will provide pupils with a conceptual basis of algebraic ideas which will enhance their work with "paper and pencil" algebra. The aims of the research were to: • trace the development of the use and understanding of algebra related concepts within a Logo programming context by reference to the work of four case study pairs of pupils during their first three years of secondary schooling (11-14 years) • develop and test out materials designed to help pupils link the conception of variable derived within a Logo to a non-Logo context • relate the pupils' understanding of variable in Logo programming to their understanding in "paper and pencil" algebra The research consisted predominantly of a three year longitudinal case study of pupils programming in Logo during their "normal" secondary school mathematics lessons. The data collected for this longitudinal study included video recordings of the pupils' Logo work together with their spoken language (which was subsequently transcribed for analysis). Initially it was found that the case study pupils did not naturally choose to use variable in Logo as a problem solving tool but it was possible to develop teacher devised tasks which provoked its use. Previous research suggests that pupils often use informal methods which cannot easily be generalised and formalised in algebra. However in the Logo context pupils were able to negotiate a generalisation by interacting with the computer and discussing with their partner to the point where they could then write a Logo procedure to formalise this generalisation. Categories of variable use were derived from the data in order to provide a framework for analysing the pupils' use and understanding of variable. At the end of the three year case study a structured interview was administered to the pupils to probe their understanding of variable in both the Logo and the algebra context. Evidence from the research suggests that the Logo experience does enhance pupils' understanding of variable in an algebra context, but the links which pupils make between variable in Logo and variable in algebra depend more upon the nature and extent of their Logo experience than on any other factor.

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