The Emergence of Mathematical Understanding: Connecting to the Closest Superordinate and Convertible Concepts

This study aimed to examine the specific means and internal processes through which mathematical understanding is achieved by focusing on the process of understanding three new mathematical concepts. For this purpose interviews were conducted with 54 junior high school students. The results revealed...

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Autores principales:	Zezhong Yang, Xintong Yang, Kai Wang, Yanqing Zhang, Guanggang Pei, Bin Xu
Formato:	article
Lenguaje:	EN
Publicado:	Frontiers Media S.A. 2021
Materias:	mathematical understanding mathematical concepts cognitive structure internal network connection Psychology BF1-990
Acceso en línea:	https://doaj.org/article/faea1607f9094b8d8aba643f248df316
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spelling	oai:doaj.org-article:faea1607f9094b8d8aba643f248df3162021-11-22T04:29:39ZThe Emergence of Mathematical Understanding: Connecting to the Closest Superordinate and Convertible Concepts1664-107810.3389/fpsyg.2021.525493https://doaj.org/article/faea1607f9094b8d8aba643f248df3162021-11-01T00:00:00Zhttps://www.frontiersin.org/articles/10.3389/fpsyg.2021.525493/fullhttps://doaj.org/toc/1664-1078This study aimed to examine the specific means and internal processes through which mathematical understanding is achieved by focusing on the process of understanding three new mathematical concepts. For this purpose interviews were conducted with 54 junior high school students. The results revealed that mathematical understanding can be achieved when new concepts are connected to at least two existing concepts within a student’s cognitive structure of. One of these two concepts should be the superordinate concept of the new concept or, more accurately, the superordinate concept that is closest to the new concept. The other concept should be convertible, so that a specific example can be derived by changing or transforming its examples. Moreover, the process of understanding a new concept was found to involve two processes, namely, “going” and “coming.” “Going” refers to the process by which a connection is established between a new concept and its closest superordinate concept. In contrast, “coming” is a process by which a connection is established between an existing convertible concept and a new concept. Therefore the connection leading to understanding should include two types of connections: belonging and transforming. These new findings enrich the literature on mathematical understanding and encourage further exploration. The findings suggest that, in order to help students fully understand new mathematical concepts, teachers should first explain the definition of a given concept to students and subsequently teach them how to create a specific example based on examples of an existing concept.Zezhong YangXintong YangKai WangYanqing ZhangGuanggang PeiBin XuFrontiers Media S.A.articlemathematical understandingmathematical conceptscognitive structureinternal networkconnectionPsychologyBF1-990ENFrontiers in Psychology, Vol 12 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	mathematical understanding mathematical concepts cognitive structure internal network connection Psychology BF1-990
spellingShingle	mathematical understanding mathematical concepts cognitive structure internal network connection Psychology BF1-990 Zezhong Yang Xintong Yang Kai Wang Yanqing Zhang Guanggang Pei Bin Xu The Emergence of Mathematical Understanding: Connecting to the Closest Superordinate and Convertible Concepts
description	This study aimed to examine the specific means and internal processes through which mathematical understanding is achieved by focusing on the process of understanding three new mathematical concepts. For this purpose interviews were conducted with 54 junior high school students. The results revealed that mathematical understanding can be achieved when new concepts are connected to at least two existing concepts within a student’s cognitive structure of. One of these two concepts should be the superordinate concept of the new concept or, more accurately, the superordinate concept that is closest to the new concept. The other concept should be convertible, so that a specific example can be derived by changing or transforming its examples. Moreover, the process of understanding a new concept was found to involve two processes, namely, “going” and “coming.” “Going” refers to the process by which a connection is established between a new concept and its closest superordinate concept. In contrast, “coming” is a process by which a connection is established between an existing convertible concept and a new concept. Therefore the connection leading to understanding should include two types of connections: belonging and transforming. These new findings enrich the literature on mathematical understanding and encourage further exploration. The findings suggest that, in order to help students fully understand new mathematical concepts, teachers should first explain the definition of a given concept to students and subsequently teach them how to create a specific example based on examples of an existing concept.
format	article
author	Zezhong Yang Xintong Yang Kai Wang Yanqing Zhang Guanggang Pei Bin Xu
author_facet	Zezhong Yang Xintong Yang Kai Wang Yanqing Zhang Guanggang Pei Bin Xu
author_sort	Zezhong Yang
title	The Emergence of Mathematical Understanding: Connecting to the Closest Superordinate and Convertible Concepts
title_short	The Emergence of Mathematical Understanding: Connecting to the Closest Superordinate and Convertible Concepts
title_full	The Emergence of Mathematical Understanding: Connecting to the Closest Superordinate and Convertible Concepts
title_fullStr	The Emergence of Mathematical Understanding: Connecting to the Closest Superordinate and Convertible Concepts
title_full_unstemmed	The Emergence of Mathematical Understanding: Connecting to the Closest Superordinate and Convertible Concepts
title_sort	emergence of mathematical understanding: connecting to the closest superordinate and convertible concepts
publisher	Frontiers Media S.A.
publishDate	2021
url	https://doaj.org/article/faea1607f9094b8d8aba643f248df316
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The Emergence of Mathematical Understanding: Connecting to the Closest Superordinate and Convertible Concepts

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