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Mathematical thinking in differential equations through a computer algebra system

This study is an effort to promote the mathematical thinking of students in differential equations through a computer algebra system. Mathematical thinking enhances the complexity of the mathematical ideas as an important goal of mathematics education which has not been widely achieved yet in mathem...

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Main Author: Zeynivannezhad, FereshtehFereshteh
Format: Thesis
Language:English
Published: 2014
Subjects:
LB Theory and practice of education
Online Access:http://eprints.utm.my/id/eprint/78012/1/FereshtehZeynivannezhadPFP2014.pdf
http://eprints.utm.my/id/eprint/78012/
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spelling my.utm.780122018-07-23T06:05:22Z http://eprints.utm.my/id/eprint/78012/ Mathematical thinking in differential equations through a computer algebra system Zeynivannezhad, FereshtehFereshteh LB Theory and practice of education This study is an effort to promote the mathematical thinking of students in differential equations through a computer algebra system. Mathematical thinking enhances the complexity of the mathematical ideas as an important goal of mathematics education which has not been widely achieved yet in mathematics instruction. This study was conducted in two parts comprising the teaching experiment in the main study and task based interviews in the follow up study. The experiment was conducted with an undergraduate class of differential equations with thirty-seven chemical engineering students in a public university in Malaysia. Maxima, an open source software, was the computer algebra system chosen to be used as a cognitive tool in the learning activities. The instruments included the worksheets designed by the researcher based on instrumental genesis, Three Worlds of Mathematics, and prompts and questions. Seventeen observation sessions and twelve semi-structured task based in-depth interviews with six students were conducted in the main study. In addition, eighteen interviews were carried out in the follow up study with the same six students. Qualitative analysis was used to classify the type of mathematical thinking powers as well as the mathematical structures. The findings showed that mathematical thinking powers to make sense of mathematical structures were interwoven and students used them in a non-sequential manner. The students applied specializing powers, imagining and expressing, changing, varying, comparing, sorting, and organizing, and checking the calculation in general to make sense of mathematical structures such as facts, techniques, and representations. In addition, the relationships among the main contributing factors that support this innovative approach were determined which include the type of tasks, the role of the teacher, class discourse, and the capabilities of technology. The approach can be incorporated not only in the mathematics curriculum at the tertiary level but could also be extended to schools. 2014-10 Thesis NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/78012/1/FereshtehZeynivannezhadPFP2014.pdf Zeynivannezhad, FereshtehFereshteh (2014) Mathematical thinking in differential equations through a computer algebra system. PhD thesis, Universiti Teknologi Malaysia, Faculty of Education. http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:98011
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
language English
topic LB Theory and practice of education
spellingShingle LB Theory and practice of education
Zeynivannezhad, FereshtehFereshteh
Mathematical thinking in differential equations through a computer algebra system
description This study is an effort to promote the mathematical thinking of students in differential equations through a computer algebra system. Mathematical thinking enhances the complexity of the mathematical ideas as an important goal of mathematics education which has not been widely achieved yet in mathematics instruction. This study was conducted in two parts comprising the teaching experiment in the main study and task based interviews in the follow up study. The experiment was conducted with an undergraduate class of differential equations with thirty-seven chemical engineering students in a public university in Malaysia. Maxima, an open source software, was the computer algebra system chosen to be used as a cognitive tool in the learning activities. The instruments included the worksheets designed by the researcher based on instrumental genesis, Three Worlds of Mathematics, and prompts and questions. Seventeen observation sessions and twelve semi-structured task based in-depth interviews with six students were conducted in the main study. In addition, eighteen interviews were carried out in the follow up study with the same six students. Qualitative analysis was used to classify the type of mathematical thinking powers as well as the mathematical structures. The findings showed that mathematical thinking powers to make sense of mathematical structures were interwoven and students used them in a non-sequential manner. The students applied specializing powers, imagining and expressing, changing, varying, comparing, sorting, and organizing, and checking the calculation in general to make sense of mathematical structures such as facts, techniques, and representations. In addition, the relationships among the main contributing factors that support this innovative approach were determined which include the type of tasks, the role of the teacher, class discourse, and the capabilities of technology. The approach can be incorporated not only in the mathematics curriculum at the tertiary level but could also be extended to schools.
format Thesis
author Zeynivannezhad, FereshtehFereshteh
author_facet Zeynivannezhad, FereshtehFereshteh
author_sort Zeynivannezhad, FereshtehFereshteh
title Mathematical thinking in differential equations through a computer algebra system
title_short Mathematical thinking in differential equations through a computer algebra system
title_full Mathematical thinking in differential equations through a computer algebra system
title_fullStr Mathematical thinking in differential equations through a computer algebra system
title_full_unstemmed Mathematical thinking in differential equations through a computer algebra system
title_sort mathematical thinking in differential equations through a computer algebra system
publishDate 2014
url http://eprints.utm.my/id/eprint/78012/1/FereshtehZeynivannezhadPFP2014.pdf
http://eprints.utm.my/id/eprint/78012/
http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:98011
_version_ 1643657701675237376
score 13.211869

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