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Developing an understanding of algebraic symbols

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Quinlan, Cyril Ronald Edmund (1992) Developing an understanding of algebraic symbols. PhD thesis, University of Tasmania.

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Abstract

The major objective of this research project was to investigate the
difficulties that beginning algebra students experience in developing an
understanding of the meaning and use of algebraic symbols.
Learning problems identified by relevant research projects during
the previous two decades provided a starting point, and items used in
these projects for written tests or interviews were valuable in the
formation of a new test instrument. By incorporating aspects
investigated by several other researchers, a broad-based approach was
employed to extend their work of applying psychological
understandings of cognition to the learning processes involved in early
algebra. Investigations examined interrelationships between measures
previously studied in separate projects.
Data were collected for analysis from a sample of 208 Year 7
secondary school students as they began their study of algebra in the
form of generalized arithmetic. Methods of data collection were
repeated written tests, interviews and lesson observations. To locate
the responses of the beginning Year 7 students in the learning
continuum about algebraic symbols as numerical variables, research
data were also collected from another 309 Years 7 to 12 students.
Scales were established for measuring and reporting on the
patterns of thinking revealed by the students' responses. The pool of
research information about the learning of algebra was expanded by the
frequency data for individual items and for scaled groups of items.
Comparisons and contrasts with findings of earlier researchers were
reported where possible.
Hierarchies of difficulty, as proposed by previous researchers for
distinguishing levels of understanding of algebraic symbols, were
tested for their applicability to the student sample and to see if they
reflected any identifiable learning sequences. The most difficult
challenge for students beginning their study of the algebra of
generalized arithmetic was found to be the attainment of an
understanding of algebraic symbols as representing numerical variables.
Some Year 7 students made little progress towards this goal during the
seven months of the study. The tendency to regard symbols as
standing for objects or people was one focus of attention.
Evidence supported the view that the level of achievement on the
algebraic tasks presented is related to the degree of progress towards
understanding algebraic symbols as numerical variables. Empirical data
were shown to agree with psychological reasons for arranging some of
the tasks into hierarchical orders of difficulty and/or into sequential
orders of learning. There was some elucidation of the key steps in
learning which distinguish students likely to progress in algebra.

Item Type: Thesis (PhD)
Keywords: Mathematical notation, Algebra
Copyright Holders: The Author
Copyright Information:

Copyright the Author - The University is continuing to endeavour to trace the copyright
owner(s) and in the meantime this item has been reproduced here in good faith. We
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Additional Information:

Includes bibliographical references (leaves [352]-362). Thesis (Ph.D.)--University of Tasmania, 1993

Date Deposited: 03 Feb 2015 03:13
Last Modified: 11 Mar 2016 05:55
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