Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/6973
Title: Persistent Errors in Indices: A Cognitive Perspective
Contributor(s): Anderson, Colin (author); Pegg, John  (supervisor); Vine, Ken (supervisor)
Conferred Date: 1998
Copyright Date: 1996
Open Access: Yes
Handle Link: https://hdl.handle.net/1959.11/6973
Abstract: This thesis explores the understanding of indices shown by students in their senior years of secondary schooling. Quantitative and qualitative data are used to investigate how students perceive, and work with, an index as a raised number in arithmetic and in algebra. Earlier research focused largely on identifying errors students make. However, little has been done to explore the thinking being applied when those errors are made. ... The form of understanding being applied was researched in terms of students' use of routine strategies as against accessing underlying concepts. This was done within the framework of 'relational' and 'instrumental' understanding as proposed by Skemp (1978). Students were found, almost invariably, to apply understanding which was instrumental in nature. The way in which the persistent errors emerge from these routine strategies was explored within the concepts of 'connections' (Shevarev 1946) or 'frames' (Davis 1984). Under these constructs, errors result when students adopt approaches which, while correct for certain other items of similar appearance, ignore important aspects of the question. Particular 'connections' or 'frames' were identified for the operations previously mentioned, namely: multiplication and division of expressions involving numerical bases; raising expressions to a power; simplifying algebraic fractions involving indices; and, taking the square root of expressions involving indices.
Publication Type: Thesis Doctoral
Rights Statement: Copyright 1996 - Colin Anderson
HERDC Category Description: T2 Thesis - Doctorate by Research
Statistics to Oct 2018: Visitors: 114
Views: 109
Downloads: 16
Appears in Collections:The National Centre of Science, Information and Communication Technology, and Mathematics Education for Rural and Regional Australia (SiMERR)
Thesis Doctoral

Files in This Item:
10 files
File Description SizeFormat 
open/SOURCE05.pdfThesis, part 24.75 MBAdobe PDF
Download Adobe
View/Open
open/SOURCE06.pdfThesis, part 34.95 MBAdobe PDF
Download Adobe
View/Open
open/SOURCE03.pdfAbstract436.24 kBAdobe PDF
Download Adobe
View/Open
open/SOURCE07.pdfThesis, part 42.91 MBAdobe PDF
Download Adobe
View/Open
open/SOURCE04.pdfThesis, part 15.07 MBAdobe PDF
Download Adobe
View/Open
1 2 Next
Show full item record

Page view(s)

170
checked on Mar 5, 2019

Download(s)

180
checked on Mar 5, 2019
Google Media

Google ScholarTM

Check


Items in Research UNE are protected by copyright, with all rights reserved, unless otherwise indicated.