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Why It Is Important for In-Service Elementary Mathematics Teachers to Understand the Equality 0.999...=1

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Title: Why It Is Important for In-Service Elementary Mathematics Teachers to Understand the Equality 0.999...=1
Language: English
Authors: Yopp, David A., Burroughs, Elizabeth A., Lindaman, Brian J.
Source: Journal of Mathematical Behavior. Dec 2011 30(4):304-318.
Availability: Elsevier. 6277 Sea Harbor Drive, Orlando, FL 32887-4800. Tel: 877-839-7126; Tel: 407-345-4020; Fax: 407-363-1354; e-mail: usjcs@elsevier.com; Web site: http://www.elsevier.com
Peer Reviewed: Y
Physical Description: PDF
Page Count: 15
Publication Date: 2011
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Descriptors: Evidence, Mathematics Curriculum, Interviews, Grade 5, Mathematics Teachers, Elementary School Teachers, Mathematics Instruction, Researchers, Preservice Teacher Education, Mathematical Concepts
DOI: 10.1016/j.jmathb.2011.07.007
ISSN: 0732-3123
Abstract: Researchers conducted semi-structured interviews with in-service fifth grade teachers. The purpose of these interviews was to examine teachers' reactions to arguments that 0.999... = 1. Previously reported results indicate that some pre-service elementary school teachers possess misunderstandings about mathematical issues related to decimals with single repeating digits. This research investigates whether some in-service teachers possess misunderstandings about mathematical issues related to 0.999.... This paper reports on one instance of a teacher whose responses indicate that the teacher's sense of number and sense of measurement are intertwined, resulting in fragile understanding of repeating decimals. These data present evidence that teachers continue to develop repeated decimal understandings and misunderstandings throughout their careers, and that the curriculum, everyday experience, and perceptions of student learning combine to form or reinforce these understandings. Because decimals with a single repeating digit (e.g. 0.333... and 0.666...) are an integral part of the elementary mathematics curriculum, we argue that it is important that in-service elementary mathematics teachers have a clear understanding of concepts related to the concept of infinity as they emerge through the study of the equality 0.999... = 1. (Contains 2 illustrations.)
Abstractor: As Provided
Entry Date: 2011
Accession Number: EJ943281
Database: ERIC
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  Data: Researchers conducted semi-structured interviews with in-service fifth grade teachers. The purpose of these interviews was to examine teachers' reactions to arguments that 0.999... = 1. Previously reported results indicate that some pre-service elementary school teachers possess misunderstandings about mathematical issues related to decimals with single repeating digits. This research investigates whether some in-service teachers possess misunderstandings about mathematical issues related to 0.999.... This paper reports on one instance of a teacher whose responses indicate that the teacher's sense of number and sense of measurement are intertwined, resulting in fragile understanding of repeating decimals. These data present evidence that teachers continue to develop repeated decimal understandings and misunderstandings throughout their careers, and that the curriculum, everyday experience, and perceptions of student learning combine to form or reinforce these understandings. Because decimals with a single repeating digit (e.g. 0.333... and 0.666...) are an integral part of the elementary mathematics curriculum, we argue that it is important that in-service elementary mathematics teachers have a clear understanding of concepts related to the concept of infinity as they emerge through the study of the equality 0.999... = 1. (Contains 2 illustrations.)
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