想象中的元认知意识和可视化:看不见的圆圈的情况

IF 0.3 Q4 EDUCATION, SCIENTIFIC DISCIPLINES
D. Jagals, Martha Van der Walt
{"title":"想象中的元认知意识和可视化:看不见的圆圈的情况","authors":"D. Jagals, Martha Van der Walt","doi":"10.4102/PYTHAGORAS.V39I1.396","DOIUrl":null,"url":null,"abstract":"Awareness of one’s own strengths and weaknesses during visualisation is often initiated by the imagination – the faculty for intuitively visualising and modelling an object. Towards exploring the role of metacognitive awareness and imagination in facilitating visualisation in solving a mathematics task, four secondary schools in the North West province of South Africa were selected for instrumental case studies. Understanding how mathematical objects are modelled in the mind may explain the transfer of the mathematical ideas between metacognitive awareness and the rigour of the imaginer’s mental images. From each school, a top achiever in mathematics was invited to an individual interview (n = 4) and was video-recorded while solving a mathematics word problem. Participants also had to identify metacognitive statements from a sample of statement cards (n = 15) which provided them the necessary vocabulary to express their thinking during the interview. During their attempts, participants were asked questions about what they were thinking, what they did and why they did what they had done. Analysis with a priori coding suggests the three types of imagination consistent with the metacognitive awareness and visualisation include initiating, conceiving and transformative imaginations. These results indicate the tenets by which metacognitive awareness and visualisation are conceptually related with the imagination as a faculty of self-directedness. Based on these findings, a renewed understanding of the role of metacognition and imagination in mathematics tasks is revealed and discussed in terms of the tenets of metacognitive awareness and imagination. These tenets advance the rational debate about mathematics to promote a more imaginative mathematics.","PeriodicalId":43521,"journal":{"name":"Pythagoras","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2018-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4102/PYTHAGORAS.V39I1.396","citationCount":"5","resultStr":"{\"title\":\"Metacognitive awareness and visualisation in the imagination: The case of the invisible circles\",\"authors\":\"D. Jagals, Martha Van der Walt\",\"doi\":\"10.4102/PYTHAGORAS.V39I1.396\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Awareness of one’s own strengths and weaknesses during visualisation is often initiated by the imagination – the faculty for intuitively visualising and modelling an object. Towards exploring the role of metacognitive awareness and imagination in facilitating visualisation in solving a mathematics task, four secondary schools in the North West province of South Africa were selected for instrumental case studies. Understanding how mathematical objects are modelled in the mind may explain the transfer of the mathematical ideas between metacognitive awareness and the rigour of the imaginer’s mental images. From each school, a top achiever in mathematics was invited to an individual interview (n = 4) and was video-recorded while solving a mathematics word problem. Participants also had to identify metacognitive statements from a sample of statement cards (n = 15) which provided them the necessary vocabulary to express their thinking during the interview. During their attempts, participants were asked questions about what they were thinking, what they did and why they did what they had done. Analysis with a priori coding suggests the three types of imagination consistent with the metacognitive awareness and visualisation include initiating, conceiving and transformative imaginations. These results indicate the tenets by which metacognitive awareness and visualisation are conceptually related with the imagination as a faculty of self-directedness. Based on these findings, a renewed understanding of the role of metacognition and imagination in mathematics tasks is revealed and discussed in terms of the tenets of metacognitive awareness and imagination. These tenets advance the rational debate about mathematics to promote a more imaginative mathematics.\",\"PeriodicalId\":43521,\"journal\":{\"name\":\"Pythagoras\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2018-08-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.4102/PYTHAGORAS.V39I1.396\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pythagoras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4102/PYTHAGORAS.V39I1.396\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"EDUCATION, SCIENTIFIC DISCIPLINES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pythagoras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4102/PYTHAGORAS.V39I1.396","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"EDUCATION, SCIENTIFIC DISCIPLINES","Score":null,"Total":0}
引用次数: 5

摘要

在可视化过程中,对自己的长处和弱点的认识通常是由想象力发起的-直观地将物体可视化和建模的能力。为了探索元认知意识和想象力在促进可视化解决数学任务中的作用,南非西北省的四所中学被选中进行工具性案例研究。理解数学对象是如何在大脑中建模的,可以解释数学思想在元认知意识和想象者心理图像的严谨性之间的转移。每所学校邀请一名数学成绩最好的学生进行单独面试(n = 4),并在解决数学单词问题时进行录像。参与者还必须从陈述卡样本(n = 15)中识别元认知陈述,这为他们提供了必要的词汇来表达他们在面试过程中的想法。在他们的尝试过程中,参与者被问及他们在想什么,他们做了什么以及他们为什么这么做。先验编码分析表明,与元认知意识和视觉化相一致的三种想象类型包括启动想象、构思想象和转化想象。这些结果表明,元认知意识和可视化在概念上与想象作为一种自我指导的能力相关的原则。基于这些发现,本文从元认知意识和元想象的原则出发,揭示和讨论了元认知和想象在数学任务中的作用。这些原则推动了关于数学的理性辩论,促进了更具想象力的数学。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Metacognitive awareness and visualisation in the imagination: The case of the invisible circles
Awareness of one’s own strengths and weaknesses during visualisation is often initiated by the imagination – the faculty for intuitively visualising and modelling an object. Towards exploring the role of metacognitive awareness and imagination in facilitating visualisation in solving a mathematics task, four secondary schools in the North West province of South Africa were selected for instrumental case studies. Understanding how mathematical objects are modelled in the mind may explain the transfer of the mathematical ideas between metacognitive awareness and the rigour of the imaginer’s mental images. From each school, a top achiever in mathematics was invited to an individual interview (n = 4) and was video-recorded while solving a mathematics word problem. Participants also had to identify metacognitive statements from a sample of statement cards (n = 15) which provided them the necessary vocabulary to express their thinking during the interview. During their attempts, participants were asked questions about what they were thinking, what they did and why they did what they had done. Analysis with a priori coding suggests the three types of imagination consistent with the metacognitive awareness and visualisation include initiating, conceiving and transformative imaginations. These results indicate the tenets by which metacognitive awareness and visualisation are conceptually related with the imagination as a faculty of self-directedness. Based on these findings, a renewed understanding of the role of metacognition and imagination in mathematics tasks is revealed and discussed in terms of the tenets of metacognitive awareness and imagination. These tenets advance the rational debate about mathematics to promote a more imaginative mathematics.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Pythagoras
Pythagoras EDUCATION, SCIENTIFIC DISCIPLINES-
CiteScore
1.50
自引率
16.70%
发文量
12
审稿时长
20 weeks
期刊介绍: Pythagoras is a scholarly research journal that provides a forum for the presentation and critical discussion of current research and developments in mathematics education at both national and international level. Pythagoras publishes articles that significantly contribute to our understanding of mathematics teaching, learning and curriculum studies, including reports of research (experiments, case studies, surveys, philosophical and historical studies, etc.), critical analyses of school mathematics curricular and teacher development initiatives, literature reviews, theoretical analyses, exposition of mathematical thinking (mathematical practices) and commentaries on issues relating to the teaching and learning of mathematics at all levels of education.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信