Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.518676
Title: Misconceptions leading to errors in elementary algebra (generalised arithmetic)
Author: Booth, Lesley Rochelle
Awarding Body: University of London
Current Institution: King's College London (University of London)
Date of Award: 1983
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Abstract:
This thesis describes an investigation into the reasons underlying particular errors in elementary algebra or 'generalised arithmetic ' which an earlier project at Chelsea College - the Concepts in Secondary Mathematics and Science project - had shown were widely prevalent among 13 to 15 year old children. The investigation comprised three phases: (1) an exploration of the conceptual bases of the errors under study, by means of a total of 72 individual interviews with children identified as making the errors; (2) the monitoring, via a series of small-group teaching experiments using three groups of 5-6 children aged 13 to 14 years, of children's interaction with a 'cognitive-instructional' programme based on the interview findings, and which aimed to help children restructure their thinking so as to avoid making the errors; and (3) the development and trial of this instructional programme for use with with whole classes, using four groups of 12 to 15 year olds taught by the researcher, and seven classes in the same age range taught by the usual class teachers. The schools used were mainly in the Greater London Area. The results of the research indicated three main areas of difficulty contributing to the errors in question, namely (i) the way in which children view letters in algebra (as 'objects' or as specific rather than generalised number), (ii) children's difficulties in formalizing and symbolising arithmetic procedures, and in particular the use by children in arithmetic of informal 'child-methods' which do not readily extend to the algebraic case, and (iii) difficulties with This thesis describes an investigation into the reasons underlying particular errors in elementary algebra or 'generalised arithmetic ' which an earlier project at Chelsea College - the Concepts in Secondary Mathematics and Science project - had shown were widely prevalent among 13 to 15 year old children. The investigation comprised three phases: (1) an exploration of the conceptual bases of the errors under study, by means of a total of 72 individual interviews with children identified as making the errors; (2) the monitoring, via a series of small-group teaching experiments using three groups of 5-6 children aged 13 to 14 years, of children's interaction with a 'cognitive-instructional' programme based on the interview findings, and which aimed to help children restructure their thinking so as to avoid making the errors; and (3) the development and trial of this instructional programme for use with with whole classes, using four groups of 12 to 15 year olds taught by the researcher, and seven classes in the same age range taught by the usual class teachers. The schools used were mainly in the Greater London Area. The results of the research indicated three main areas of difficulty contributing to the errors in question, namely (i) the way in which children view letters in algebra (as 'objects' or as specific rather than generalised number), (ii) children's difficulties in formalizing and symbolising arithmetic procedures, and in particular the use by children in arithmetic of informal 'child-methods' which do not readily extend to the algebraic case, and (iii) difficulties with
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.518676  DOI: Not available
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