Ursini-Legovich, Sonia.; (1994) Pupil's approaches to different characterizations of variable in logo. Doctoral thesis , Institute of Education, University of London.

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Abstract

This thesis is based on research investigating 12-13 years old pupils' potential to approach through Logo different characterizations of variable prior to formal algebra teaching. The characterizations of variable considered are variable as general number, variables in a functional relationship and variable as specific unknown. Pupils' potential is defined by their capability to solve a range of specific Logo-based tasks involving one characterization of variable. During the solution process peer collaboration was encouraged and support was available from the researcher. The experimental work consisted of case studies of 6 pairs of pupils over a period of one year working in three specially designed Logo microworlds each one focussing on one characterization of variable. The observation of these pupils' work was carried out during their normal computer time with the researcher acting as the teacher of the whole group (34 pupils). Special attention was paid to the strategies pupils used to solve the posed tasks, researcher's interventions, peer collaboration and the influence of the Logo setting. Data included researcher's notes taken during the observation of pupils' work, pupils' written records, individual interviews and the responses to a paper and pencil questionnaire given at the beginning and at the end of the study. Previous studies of pupils' learning of algebra show that they have difficulties with each one of the three characterizations of variable whether they are algebra beginners or more advanced students. Evidence from this study shows that pupils can develop a potential to work with these characterizations of variable prior to formal algebra teaching. Crucial elements provoking this development were: the design of the activities appealing to pupils' prior numeric knowledge; the Logo environment; social interaction between pupils and with the researcher; the use of communicative and egocentric speech. The results of this research show that notions that are crucial to the use of variable can be developed prior to formal algebra teaching. Pupils' arithmetic can provide a basis for the development of these notions.

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