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Secondary school teachers' conceptions of functions in algebra
Author
Kwek, Meek Lin
Supervisor
Foong, Pui Yee
Abstract
The purpose of this study was to examine secondary school mathematics teachers‟ conceptions of functions. The study was framed in terms of concept image and pedagogical concept image of functions. Through the use of an open-ended questionnaire and card-sorting task, eighteen teachers‟ definitions, paraphrases and identification of a function were analyzed. Their responses formed a basis for profiling teachers‟ concept image of functions. The richness of this concept image was then examined from their knowledge organization of mathematical relationships in different representations.
Although the teachers gave the definition of functions that were similar to the concept definition, their concept images may show otherwise. This observation reinforced the view that concept images are primarily formed by one‟s experiences, and not the concept definition. Hence an adequate concept image was important for subsequent learning to be effective and contribute to the subject matter knowledge that is less compartmentalized. Compartmentalization can potentially lead to misunderstanding of the concept definition and incoherence in reasoning. The findings also showed that the capacity to recall and apply the concept definition itself was not necessarily associated to a rich concept image. A competent understanding of the concept definition and the ability to make connections between different representations of functions were believed to be the contributing factors to its richness.
The nature of the teachers‟ conceptions also has important implications on their pedagogical approaches. The findings from the study supported that there was a positive relationship between the teachers‟ concept image and pedagogical concept image. This implied that with an ability to perceive the definition of functions structurally, the teachers could potentially develop their students‟ understanding of the definition beyond its operational procedures and move them towards a broader view of functions.
Although the teachers gave the definition of functions that were similar to the concept definition, their concept images may show otherwise. This observation reinforced the view that concept images are primarily formed by one‟s experiences, and not the concept definition. Hence an adequate concept image was important for subsequent learning to be effective and contribute to the subject matter knowledge that is less compartmentalized. Compartmentalization can potentially lead to misunderstanding of the concept definition and incoherence in reasoning. The findings also showed that the capacity to recall and apply the concept definition itself was not necessarily associated to a rich concept image. A competent understanding of the concept definition and the ability to make connections between different representations of functions were believed to be the contributing factors to its richness.
The nature of the teachers‟ conceptions also has important implications on their pedagogical approaches. The findings from the study supported that there was a positive relationship between the teachers‟ concept image and pedagogical concept image. This implied that with an ability to perceive the definition of functions structurally, the teachers could potentially develop their students‟ understanding of the definition beyond its operational procedures and move them towards a broader view of functions.
Date Issued
2010
Call Number
QA159 Kwe
Date Submitted
2010