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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Bibliographic Details
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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Summary: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.
ISSN:1492-6156
1942-4051
DOI:10.1080/14926156.2013.816389