Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA framework
[English]: The fragmentation of thinking structure is a failed construction existing in students’ memory due to disconnections on what they have learned. It makes students undergo difficulties and errors in solving mathematical modeling problems. There is a need to prevent permanent fragmentations....
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | Indonesian |
| Published: |
Universitas Islam Negeri Mataram
2020-11-01
|
| Series: | Beta: Jurnal Tadris Matematika |
| Subjects: | |
| Online Access: | https://jurnalbeta.ac.id/index.php/betaJTM/article/view/327 |
| _version_ | 1818918980305289216 |
|---|---|
| author | Kadek Adi Wibawa I Putu Ade Andre Payadnya I Made Dharma Atmaja Marius Derick Simons |
| author_facet | Kadek Adi Wibawa I Putu Ade Andre Payadnya I Made Dharma Atmaja Marius Derick Simons |
| author_sort | Kadek Adi Wibawa |
| collection | DOAJ |
| description | [English]: The fragmentation of thinking structure is a failed construction existing in students’ memory due to disconnections on what they have learned. It makes students undergo difficulties and errors in solving mathematical modeling problems. There is a need to prevent permanent fragmentations. The problem-solving involving modeling problems requires translational thinking, changing from source representations to targeted representations. This research aimed to formulate undergraduate students’ effort in restructuring their fragmented translational thinking (defragmentation of translational thinking structure). The defragmentation was mapped through the CRA framework (checking, repairing, ascertaining). The subjects were three of eighty-five 4th and 6th-semester students. Data were analyzed through three stages; categorization, reduction, and conclusion. The analysis resulted in three types of defragmentation of translational thinking structure: from verbal representations to graph representations, from graph representations to symbolic representations (algebraic forms), and from the graph and symbolic representations to mathematical models. The finding shows that it is essential for mathematics educators to allow students to manage their thinking structures while experiencing difficulties and errors in mathematical problem-solving.
Keywords: Thinking structure, Fragmentation, Defragmentation, Translational thinking, CRA framework
[Bahasa]: Fragmentasi struktur berpikir merupakan kegagalan konstruksi yang terjadi di dalam memori akibat dari konsep-konsep yang dipelajari tidak terkoneksi dengan baik. Hal ini membuat mahasiswa sering mengalami kesulitan dan kesalahan dalam memecahkan masalah pemodelan matematika. Untuk itu, perlu dilakukan upaya agar tidak terjadi fragmentasi struktur berpikir yang permanen. Dalam memecahkan masalah pemodelan matematika, mahasiswa perlu melakukan berpikir translasi, yaitu mengubah representasi sumber menjadi representasi yang ditargetkan. Penelitian ini bertujuan untuk merumuskan upaya mahasiswa dalam melakukan penataan fragmentasi struktur berpikir translasi yang terjadi (defragmentasi struktur berpikir translasi) dalam memecahkan masalah pemodelan matematika. Defragmentasi yang dilakukan mahasiswa dipetakan melalui kerangka CRA (checking, repairing, dan ascertaining). Subjek penelitian adalah mahasiswa semester 4 dan 6 yang terdiri dari 3 orang dipilih dari 85 mahasiswa. Analisis data dilakukan melalui tiga tahap, yaitu pengategorian data, reduksi data, dan penarikan kesimpulan. Penelitian ini menemukan tiga jenis defragmentasi struktur berpikir translasi: defragmentasi dari representasi verbal ke grafik, dari representasi grafik ke simbol (bentuk aljabar), dan representasi grafik dan simbol (bentuk aljabar) ke model matematika. Penelitian ini menunjukkan pentingnya pengajar matematika memberikan kesempatan kepada mahasiswa dalam menata struktur berpikirnya ketika mengalami kesulitan dan kesalahan dalam memecahkan masalah matematika.
Kata kunci: Struktur berpikir, Fragmentasi, Defragmentasi, Berpikir translasi, Kerangka CRA |
| first_indexed | 2024-12-20T00:58:35Z |
| format | Article |
| id | doaj.art-798da0baa3f14b809eea4014fee3dcad |
| institution | Directory Open Access Journal |
| issn | 2085-5893 2541-0458 |
| language | Indonesian |
| last_indexed | 2024-12-20T00:58:35Z |
| publishDate | 2020-11-01 |
| publisher | Universitas Islam Negeri Mataram |
| record_format | Article |
| series | Beta: Jurnal Tadris Matematika |
| spelling | doaj.art-798da0baa3f14b809eea4014fee3dcad2022-12-21T19:59:02ZindUniversitas Islam Negeri MataramBeta: Jurnal Tadris Matematika2085-58932541-04582020-11-0113213015110.20414/betajtm.v13i2.327240Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA frameworkKadek Adi Wibawa0I Putu Ade Andre Payadnya1I Made Dharma Atmaja2Marius Derick Simons3Universitas Mahasaraswati DenpasarUniversitas Mahasaraswati DenpasarUniversitas Mahasaraswati DenpasarUniversity of the Western Cape[English]: The fragmentation of thinking structure is a failed construction existing in students’ memory due to disconnections on what they have learned. It makes students undergo difficulties and errors in solving mathematical modeling problems. There is a need to prevent permanent fragmentations. The problem-solving involving modeling problems requires translational thinking, changing from source representations to targeted representations. This research aimed to formulate undergraduate students’ effort in restructuring their fragmented translational thinking (defragmentation of translational thinking structure). The defragmentation was mapped through the CRA framework (checking, repairing, ascertaining). The subjects were three of eighty-five 4th and 6th-semester students. Data were analyzed through three stages; categorization, reduction, and conclusion. The analysis resulted in three types of defragmentation of translational thinking structure: from verbal representations to graph representations, from graph representations to symbolic representations (algebraic forms), and from the graph and symbolic representations to mathematical models. The finding shows that it is essential for mathematics educators to allow students to manage their thinking structures while experiencing difficulties and errors in mathematical problem-solving. Keywords: Thinking structure, Fragmentation, Defragmentation, Translational thinking, CRA framework [Bahasa]: Fragmentasi struktur berpikir merupakan kegagalan konstruksi yang terjadi di dalam memori akibat dari konsep-konsep yang dipelajari tidak terkoneksi dengan baik. Hal ini membuat mahasiswa sering mengalami kesulitan dan kesalahan dalam memecahkan masalah pemodelan matematika. Untuk itu, perlu dilakukan upaya agar tidak terjadi fragmentasi struktur berpikir yang permanen. Dalam memecahkan masalah pemodelan matematika, mahasiswa perlu melakukan berpikir translasi, yaitu mengubah representasi sumber menjadi representasi yang ditargetkan. Penelitian ini bertujuan untuk merumuskan upaya mahasiswa dalam melakukan penataan fragmentasi struktur berpikir translasi yang terjadi (defragmentasi struktur berpikir translasi) dalam memecahkan masalah pemodelan matematika. Defragmentasi yang dilakukan mahasiswa dipetakan melalui kerangka CRA (checking, repairing, dan ascertaining). Subjek penelitian adalah mahasiswa semester 4 dan 6 yang terdiri dari 3 orang dipilih dari 85 mahasiswa. Analisis data dilakukan melalui tiga tahap, yaitu pengategorian data, reduksi data, dan penarikan kesimpulan. Penelitian ini menemukan tiga jenis defragmentasi struktur berpikir translasi: defragmentasi dari representasi verbal ke grafik, dari representasi grafik ke simbol (bentuk aljabar), dan representasi grafik dan simbol (bentuk aljabar) ke model matematika. Penelitian ini menunjukkan pentingnya pengajar matematika memberikan kesempatan kepada mahasiswa dalam menata struktur berpikirnya ketika mengalami kesulitan dan kesalahan dalam memecahkan masalah matematika. Kata kunci: Struktur berpikir, Fragmentasi, Defragmentasi, Berpikir translasi, Kerangka CRAhttps://jurnalbeta.ac.id/index.php/betaJTM/article/view/327thinking structurefragmentationdefragmentationtranslational thinkingcra framework |
| spellingShingle | Kadek Adi Wibawa I Putu Ade Andre Payadnya I Made Dharma Atmaja Marius Derick Simons Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA framework Beta: Jurnal Tadris Matematika thinking structure fragmentation defragmentation translational thinking cra framework |
| title | Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA framework |
| title_full | Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA framework |
| title_fullStr | Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA framework |
| title_full_unstemmed | Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA framework |
| title_short | Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA framework |
| title_sort | defragmenting structures of students translational thinking in solving mathematical modeling problems based on cra framework |
| topic | thinking structure fragmentation defragmentation translational thinking cra framework |
| url | https://jurnalbeta.ac.id/index.php/betaJTM/article/view/327 |
| work_keys_str_mv | AT kadekadiwibawa defragmentingstructuresofstudentstranslationalthinkinginsolvingmathematicalmodelingproblemsbasedoncraframework AT iputuadeandrepayadnya defragmentingstructuresofstudentstranslationalthinkinginsolvingmathematicalmodelingproblemsbasedoncraframework AT imadedharmaatmaja defragmentingstructuresofstudentstranslationalthinkinginsolvingmathematicalmodelingproblemsbasedoncraframework AT mariusdericksimons defragmentingstructuresofstudentstranslationalthinkinginsolvingmathematicalmodelingproblemsbasedoncraframework |