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The Transition from Real Numbers to Complex Numbers

Humans make sense of mathematics by relating it to personal conceptions and experiences. This might not be a smooth process as it may involve conceptions that work in an old context but do not work in a new context. The framework proposed by Chin and Tall (2012), Chin (2013) and Chin (2014) highligh...

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Main Authors: Elvent Taliban, Kin Eng Chin, Fui Fong Jiew
Format: Article
Language:English
English
Published: ASM Science Journal 2020
Subjects:
L Education (General)
Online Access:https://eprints.ums.edu.my/id/eprint/27000/1/The%20Transition%20from%20Real%20Numbers%20to%20Complex%20Numbers.pdf
https://eprints.ums.edu.my/id/eprint/27000/2/The%20Transition%20from%20Real%20Numbers%20to%20Complex%20Numbers1.pdf
https://eprints.ums.edu.my/id/eprint/27000/
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spelling my.ums.eprints.270002021-05-27T01:47:11Z https://eprints.ums.edu.my/id/eprint/27000/ The Transition from Real Numbers to Complex Numbers Elvent Taliban Kin Eng Chin Fui Fong Jiew L Education (General) Humans make sense of mathematics by relating it to personal conceptions and experiences. This might not be a smooth process as it may involve conceptions that work in an old context but do not work in a new context. The framework proposed by Chin and Tall (2012), Chin (2013) and Chin (2014) highlights how prior experiences shape humans’ conceptions can be either supportive or problematic in making sense of extended contexts of mathematics. A supportive conception is a conception that supports learning and generalisation in a new context while a problematic conception is a conception that impedes learning and generalisation in a new context. By employing this framework, this study aims to explore how a group of respondents that consists of 30 mathematics undergraduate students from a public university in Malaysia make sense of complex numbers. The system of complex numbers is an extension of real numbers thus students will learn real numbers prior to learning complex numbers. How the respondents cope with the transition from real numbers context to complex numbers context is the focus of this study. Data were collected through a questionnaire and follow up interviews. Respondents participated in the follow up interviews voluntarily and data from three respondents were reported in this study. The result shows that these respondents have several supportive conceptions, such as the concept of addition and multiplication of real variable. The data also support the existence of problematic conceptions in making sense of complex numbers, namely the concept of positive-negative numbers and inequalities. These conceptions are originated from the context of real numbers. ASM Science Journal 2020 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/27000/1/The%20Transition%20from%20Real%20Numbers%20to%20Complex%20Numbers.pdf text en https://eprints.ums.edu.my/id/eprint/27000/2/The%20Transition%20from%20Real%20Numbers%20to%20Complex%20Numbers1.pdf Elvent Taliban and Kin Eng Chin and Fui Fong Jiew (2020) The Transition from Real Numbers to Complex Numbers. ASM Science Journal, 13. pp. 1-7. ISSN 1823-6782 file:///C:/Users/user/Downloads/21%20transition_real_complex.pdf
institution Universiti Malaysia Sabah
building UMS Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Sabah
content_source UMS Institutional Repository
url_provider http://eprints.ums.edu.my/
language English
English
topic L Education (General)
spellingShingle L Education (General)
Elvent Taliban
Kin Eng Chin
Fui Fong Jiew
The Transition from Real Numbers to Complex Numbers
description Humans make sense of mathematics by relating it to personal conceptions and experiences. This might not be a smooth process as it may involve conceptions that work in an old context but do not work in a new context. The framework proposed by Chin and Tall (2012), Chin (2013) and Chin (2014) highlights how prior experiences shape humans’ conceptions can be either supportive or problematic in making sense of extended contexts of mathematics. A supportive conception is a conception that supports learning and generalisation in a new context while a problematic conception is a conception that impedes learning and generalisation in a new context. By employing this framework, this study aims to explore how a group of respondents that consists of 30 mathematics undergraduate students from a public university in Malaysia make sense of complex numbers. The system of complex numbers is an extension of real numbers thus students will learn real numbers prior to learning complex numbers. How the respondents cope with the transition from real numbers context to complex numbers context is the focus of this study. Data were collected through a questionnaire and follow up interviews. Respondents participated in the follow up interviews voluntarily and data from three respondents were reported in this study. The result shows that these respondents have several supportive conceptions, such as the concept of addition and multiplication of real variable. The data also support the existence of problematic conceptions in making sense of complex numbers, namely the concept of positive-negative numbers and inequalities. These conceptions are originated from the context of real numbers.
format Article
author Elvent Taliban
Kin Eng Chin
Fui Fong Jiew
author_facet Elvent Taliban
Kin Eng Chin
Fui Fong Jiew
author_sort Elvent Taliban
title The Transition from Real Numbers to Complex Numbers
title_short The Transition from Real Numbers to Complex Numbers
title_full The Transition from Real Numbers to Complex Numbers
title_fullStr The Transition from Real Numbers to Complex Numbers
title_full_unstemmed The Transition from Real Numbers to Complex Numbers
title_sort transition from real numbers to complex numbers
publisher ASM Science Journal
publishDate 2020
url https://eprints.ums.edu.my/id/eprint/27000/1/The%20Transition%20from%20Real%20Numbers%20to%20Complex%20Numbers.pdf
https://eprints.ums.edu.my/id/eprint/27000/2/The%20Transition%20from%20Real%20Numbers%20to%20Complex%20Numbers1.pdf
https://eprints.ums.edu.my/id/eprint/27000/
_version_ 1760230567834550272
score 13.211869

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