Track Prospective Mathematics Teachers' Understanding of Special Quadrilaterals: An Exploration of Level 3 of Geometric Thinking
Acknowledging the value of understanding defining and classifying special quadrilaterals for prospective mathematics teachers (PMTs), the present study attempts to track this understanding so that the progress of thinking from Van Hiele's level 2 to level 3 could be theorised. Thus, a bounded c...
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| Format: | Article |
| Language: | English |
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Futurity Research Publishing
2023-09-01
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| Series: | Futurity Education |
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| Online Access: | https://futurity-education.com/index.php/fed/article/view/157 |
| _version_ | 1797649139169755136 |
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| author | Samah Gamal Ahmed Elbehary Shimaa Mohamed Fahem Nur Robiah Nofikusumawati Peni |
| author_facet | Samah Gamal Ahmed Elbehary Shimaa Mohamed Fahem Nur Robiah Nofikusumawati Peni |
| author_sort | Samah Gamal Ahmed Elbehary |
| collection | DOAJ |
| description | Acknowledging the value of understanding defining and classifying special quadrilaterals for prospective mathematics teachers (PMTs), the present study attempts to track this understanding so that the progress of thinking from Van Hiele's level 2 to level 3 could be theorised. Thus, a bounded case study sample of PMTs, who had graduated and joined the mathematics teacher preparation diploma at the Faculty of Education, Tanta University in Egypt, were selected and requested to (a) define trapezoid, parallelogram, rhombus, rectangle, and square, and (b) represent the relationship among these quadrilaterals. The data were collected and analysed in two cycles. During the first cycle, participants' responses were scrutinised upon Prototype 1; it was developed based on the literature review to describe levels of special quadrilaterals understanding as faulty, partitional-uneconomical, partitional-economical, hierarchical-uneconomical, and hierarchical economical. Similarly, the researchers replicated the same analytical process in the second cycle in order to validate the levels suggested in Prototype 1. Also, some clinical interviews were conducted to confirm the participants’ representations of relationships among the defined quadrilaterals. The results enabled advancing the hypothetical Prototype 1 to Prototype 2. Prototype 2 reconceptualised the levels of understanding into faulty, slightly economical, fairly economical, and economical, wherein each level was determined based on (a) the economics of the concept definition and (b) the awareness of relationships among other related definitions to the concept defined (recognising subsets and supersets). These results are prospective for further investigations to sufficiently unpack all sub-levels of geometric thinking embedded in Van Hiele’s fixed levels. It also provides basics on proper pedagogical approaches and corresponding interventions to train PMTs effectively teach geometric thinking. |
| first_indexed | 2024-03-11T15:41:56Z |
| format | Article |
| id | doaj.art-2981a32017334814bd8c159421c7ea7d |
| institution | Directory Open Access Journal |
| issn | 2956-3402 |
| language | English |
| last_indexed | 2024-03-11T15:41:56Z |
| publishDate | 2023-09-01 |
| publisher | Futurity Research Publishing |
| record_format | Article |
| series | Futurity Education |
| spelling | doaj.art-2981a32017334814bd8c159421c7ea7d2023-10-26T11:45:04ZengFuturity Research PublishingFuturity Education2956-34022023-09-0133204510.57125/FED.2023.09.25.02Track Prospective Mathematics Teachers' Understanding of Special Quadrilaterals: An Exploration of Level 3 of Geometric ThinkingSamah Gamal Ahmed Elbehary0https://orcid.org/0000-0002-7481-5451Shimaa Mohamed Fahem1https://orcid.org/0009-0001-3928-1749Nur Robiah Nofikusumawati Peni2https://orcid.org/0000-0001-7841-6135Tanta University, EgyptTanta University, EgyptUniversitas Ahmad Dahlan, IndonesiaAcknowledging the value of understanding defining and classifying special quadrilaterals for prospective mathematics teachers (PMTs), the present study attempts to track this understanding so that the progress of thinking from Van Hiele's level 2 to level 3 could be theorised. Thus, a bounded case study sample of PMTs, who had graduated and joined the mathematics teacher preparation diploma at the Faculty of Education, Tanta University in Egypt, were selected and requested to (a) define trapezoid, parallelogram, rhombus, rectangle, and square, and (b) represent the relationship among these quadrilaterals. The data were collected and analysed in two cycles. During the first cycle, participants' responses were scrutinised upon Prototype 1; it was developed based on the literature review to describe levels of special quadrilaterals understanding as faulty, partitional-uneconomical, partitional-economical, hierarchical-uneconomical, and hierarchical economical. Similarly, the researchers replicated the same analytical process in the second cycle in order to validate the levels suggested in Prototype 1. Also, some clinical interviews were conducted to confirm the participants’ representations of relationships among the defined quadrilaterals. The results enabled advancing the hypothetical Prototype 1 to Prototype 2. Prototype 2 reconceptualised the levels of understanding into faulty, slightly economical, fairly economical, and economical, wherein each level was determined based on (a) the economics of the concept definition and (b) the awareness of relationships among other related definitions to the concept defined (recognising subsets and supersets). These results are prospective for further investigations to sufficiently unpack all sub-levels of geometric thinking embedded in Van Hiele’s fixed levels. It also provides basics on proper pedagogical approaches and corresponding interventions to train PMTs effectively teach geometric thinking.https://futurity-education.com/index.php/fed/article/view/157definitions understandingegyptian educationgeometry educationquadrilateralsvan hiele theory |
| spellingShingle | Samah Gamal Ahmed Elbehary Shimaa Mohamed Fahem Nur Robiah Nofikusumawati Peni Track Prospective Mathematics Teachers' Understanding of Special Quadrilaterals: An Exploration of Level 3 of Geometric Thinking Futurity Education definitions understanding egyptian education geometry education quadrilaterals van hiele theory |
| title | Track Prospective Mathematics Teachers' Understanding of Special Quadrilaterals: An Exploration of Level 3 of Geometric Thinking |
| title_full | Track Prospective Mathematics Teachers' Understanding of Special Quadrilaterals: An Exploration of Level 3 of Geometric Thinking |
| title_fullStr | Track Prospective Mathematics Teachers' Understanding of Special Quadrilaterals: An Exploration of Level 3 of Geometric Thinking |
| title_full_unstemmed | Track Prospective Mathematics Teachers' Understanding of Special Quadrilaterals: An Exploration of Level 3 of Geometric Thinking |
| title_short | Track Prospective Mathematics Teachers' Understanding of Special Quadrilaterals: An Exploration of Level 3 of Geometric Thinking |
| title_sort | track prospective mathematics teachers understanding of special quadrilaterals an exploration of level 3 of geometric thinking |
| topic | definitions understanding egyptian education geometry education quadrilaterals van hiele theory |
| url | https://futurity-education.com/index.php/fed/article/view/157 |
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