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 t...
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| Format: | Article |
| Language: | English |
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AOSIS
2018-08-01
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| Series: | Pythagoras |
| Subjects: | |
| Online Access: | https://pythagoras.org.za/index.php/pythagoras/article/view/396 |
| _version_ | 1811338132183842816 |
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| author | Divan Jagals Martha van der Walt |
| author_facet | Divan Jagals Martha van der Walt |
| author_sort | Divan Jagals |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T18:06:27Z |
| format | Article |
| id | doaj.art-61484f20c40a4fb1879e4159195b1f81 |
| institution | Directory Open Access Journal |
| issn | 1012-2346 2223-7895 |
| language | English |
| last_indexed | 2024-04-13T18:06:27Z |
| publishDate | 2018-08-01 |
| publisher | AOSIS |
| record_format | Article |
| series | Pythagoras |
| spelling | doaj.art-61484f20c40a4fb1879e4159195b1f812022-12-22T02:36:04ZengAOSISPythagoras1012-23462223-78952018-08-01391e1e1010.4102/pythagoras.v39i1.396205Metacognitive awareness and visualisation in the imagination: The case of the invisible circlesDivan Jagals0Martha van der Walt1School for Professional Studies in Education, Faculty of Education Sciences, North-West UniversitySchool for Science and Technology Education, Faculty of Education Sciences, North-West UniversityAwareness 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.https://pythagoras.org.za/index.php/pythagoras/article/view/396circle geometryvisualisationmetacognitionawarenessimagination |
| spellingShingle | Divan Jagals Martha van der Walt Metacognitive awareness and visualisation in the imagination: The case of the invisible circles Pythagoras circle geometry visualisation metacognition awareness imagination |
| title | Metacognitive awareness and visualisation in the imagination: The case of the invisible circles |
| title_full | Metacognitive awareness and visualisation in the imagination: The case of the invisible circles |
| title_fullStr | Metacognitive awareness and visualisation in the imagination: The case of the invisible circles |
| title_full_unstemmed | Metacognitive awareness and visualisation in the imagination: The case of the invisible circles |
| title_short | Metacognitive awareness and visualisation in the imagination: The case of the invisible circles |
| title_sort | metacognitive awareness and visualisation in the imagination the case of the invisible circles |
| topic | circle geometry visualisation metacognition awareness imagination |
| url | https://pythagoras.org.za/index.php/pythagoras/article/view/396 |
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