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Preservice Teachers’ Understanding of the Relation Between a Fraction or Integer and its Decimal Expansion: The Case of 0.9̄ and 1

In this article, we obtain a genetic decomposition of students’ progress in developing an understanding of the decimal 0.9̄ and its relation to 1. The genetic decomposition appears to be valid for a high percentage of the study participants and suggests the possibility of a new stage in APOS Theory...

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Published in:	Canadian journal of science, mathematics and technology education mathematics and technology education, 2013, Vol.13 (3), p.232-258
Main Authors:	Dubinsky, Ed, Arnon, Ilana, Weller, Kirk
Format:	Article
Language:	English
Subjects:	Arithmetic Cognitive Processes Decimals Education Engineering/Technology Education Interviews Knowledge Level Learning Learning Theories Mathematical Concepts Mathematical Formulas Mathematics Education Mathematics teachers Numbers Preservice Teachers Science Education Sequential Approach Student teaching Teaching Methods
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container_end_page	258
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container_start_page	232
container_title	Canadian journal of science, mathematics and technology education
container_volume	13
creator	Dubinsky, Ed Arnon, Ilana Weller, Kirk
description	In this article, we obtain a genetic decomposition of students’ progress in developing an understanding of the decimal 0.9̄ and its relation to 1. The genetic decomposition appears to be valid for a high percentage of the study participants and suggests the possibility of a new stage in APOS Theory that would be the first substantial change in the theory since its inception (Dubinsky & Lewin, 1986). Our analysis includes a relatively objective and highly efficient methodology that might be useful in other research and in assessment of student learning.
doi_str_mv	10.1080/14926156.2013.816389
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subjects	Arithmetic Cognitive Processes Decimals Education Engineering/Technology Education Interviews Knowledge Level Learning Learning Theories Mathematical Concepts Mathematical Formulas Mathematics Education Mathematics teachers Numbers Preservice Teachers Science Education Sequential Approach Student teaching Teaching Methods
title	Preservice Teachers’ Understanding of the Relation Between a Fraction or Integer and its Decimal Expansion: The Case of 0.9̄ and 1
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