Title page for ETD etd-05162011-165018


Document Type Master's Dissertation
Author Verwey, Johanna Cornelia (Hanlie)
Email hanlie.verwey@gmail.com
URN etd-05162011-165018
Document Title Investigating the interaction of mathematics teachers with learners' mathematical errors
Degree MEd
Department Science, Mathematics and Technology Education
Supervisor
Advisor Name Title
Dr H Stols Co-Supervisor
Dr H Barnes Supervisor
Keywords
  • learners’ mathematical errors
  • mathematics teachers
  • learning mathematics
  • interaction
  • instructional scaffolding
  • formative assessment
  • socio-constructivism
  • secondary school
  • teaching mathematics
Date 2011-04-12
Availability unrestricted
Abstract

This study investigated the interaction of mathematics teachers with learners’ mathematical errors. The teachers’ verbal interaction with learners’ errors during learning periods and their written interaction in assessment tasks were explored. The study was contextualized in grade 9 secondary school classrooms in the Gauteng province of South Africa. The investigation was epistemologically underpinned by constructivism/socio-constructivism. The investigation was qualitatively approached through four case studies. Structured and semi-structured interviews, classroom observations and learners’ written assessment tasks were employed as sources of data. The participating teachers were described in terms of their beliefs about mathematics, their beliefs about learners’ mathematical errors, their observed prevalent teaching approach and their professed and enacted interaction with learners’ mathematical errors. Within-case and cross-case comparisons ensued. The findings proposed that when teachers believed that the value of learners’ errors was vested in the corrections thereof, rather than employing these opportunities for discussion, valuable opportunities for learners to develop and improve their meta-cognitive abilities might potentially be lost. The findings further indicated that a focus on the mere correction of learners’ errors probably denied learners opportunities to develop a mathematical discourse. The results of the investigation illuminated that an emphasis on achievement during assessment, together with a disapproving disposition towards errors among teachers and learners, were hindrances. They acted as barriers to engendering a socio-constructivist learning environment in which interactions with learners’ errors could enhance learning and establish a negotiating mathematical community. A concurrence between the teachers’ prevalent teaching approach and their mathematical beliefs was confirmed. However, in two of the four cases, a dissonance was revealed between their prevalent teaching approach and their interaction with learners’ errors. Interaction with learners’ mathematical errors was hence identified as a separate and discrete component of a teacher’s practice. The findings suggest the explicit inclusion of error-handling in reform-oriented teacher-training and professional development courses to utilize learners’ mathematical errors more constructively.

© 2010, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.

Please cite as follows:

Verwey, JC 2010, Investigating the interaction of mathematics teachers with learners' mathematical errors, MEd dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-05162011-165018/ >

E11/245/gm

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