Design of 3D Metric Geometry Study and Research Activities within a BIM Framework
This paper presents research work in which an innovative didactic proposal was designed for the study of 3D metric geometry in the second year of A-level courses (secondary education) in the specialty of the sciences. The designed didactic proposal has the format of a workshop of geometry practices...
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| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/9/1358 |
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| author | José M. Olmos-Noguera Eduardo J. Renard-Julián María Socorro García-Cascales |
| author_facet | José M. Olmos-Noguera Eduardo J. Renard-Julián María Socorro García-Cascales |
| author_sort | José M. Olmos-Noguera |
| collection | DOAJ |
| description | This paper presents research work in which an innovative didactic proposal was designed for the study of 3D metric geometry in the second year of A-level courses (secondary education) in the specialty of the sciences. The designed didactic proposal has the format of a workshop of geometry practices and is framed in the Didactic Situations Theory and in the Anthropological Theory of the Didactic. Although the mentioned theories, which the French school has developed since the seventies, are widely known and studied by secondary school mathematics teachers during their training in pedagogy, especially in Spanish- and French-speaking countries, their innovative approach has not been fully implemented in the field of algebraic geometry. Mathematics textbooks follow the traditional approach in which the teacher simply provides the contents and instructs the student, who captures these concepts and reproduces them as they have been supplied. In the presented didactic proposal, the approach proposed by Brousseau is followed, in which three fundamental elements take part: student, teacher, and the didactic environment. The teacher is the one who facilitates the environment in which the student builds his knowledge. In the proposal the <i>didactic contract</i> is stablished, the <i>didactic situations</i> are designed, and the means and didactic variables for the study of 3D metric geometry are chosen. The methodology followed in this study consisted of identifying educational problems; describing the theoretical framework; developing the didactic proposal; and analysis, reflection, and criticism of this training product. The contextualization of the geometry workshop in the field of the construction of structures and the use of deductive reasoning techniques that are applied in synthetic geometry and also in the building information modeling (BIM) methodology may be a way of showing the use of analytical geometry in the industries of engineering and architecture; they also serve as an opportunity for students to better understand this mathematical work. |
| first_indexed | 2024-03-10T03:57:34Z |
| format | Article |
| id | doaj.art-81cd20725a9d482784cbfa2acac4f708 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:57:34Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-81cd20725a9d482784cbfa2acac4f7082023-11-23T08:43:06ZengMDPI AGMathematics2227-73902022-04-01109135810.3390/math10091358Design of 3D Metric Geometry Study and Research Activities within a BIM FrameworkJosé M. Olmos-Noguera0Eduardo J. Renard-Julián1María Socorro García-Cascales2Department of Mining and Civil Engineering, Universidad Politécnica de Cartagena, 52 Paseo Alfonso XIII, 30203 Cartagena, SpainDepartment of Electronics, Computation Technology and Projects, Universidad Politécnica de Cartagena, 1 Plaza del Hospital, 30202 Cartagena, SpainDepartment of Electronics, Computation Technology and Projects, Universidad Politécnica de Cartagena, 1 Plaza del Hospital, 30202 Cartagena, SpainThis paper presents research work in which an innovative didactic proposal was designed for the study of 3D metric geometry in the second year of A-level courses (secondary education) in the specialty of the sciences. The designed didactic proposal has the format of a workshop of geometry practices and is framed in the Didactic Situations Theory and in the Anthropological Theory of the Didactic. Although the mentioned theories, which the French school has developed since the seventies, are widely known and studied by secondary school mathematics teachers during their training in pedagogy, especially in Spanish- and French-speaking countries, their innovative approach has not been fully implemented in the field of algebraic geometry. Mathematics textbooks follow the traditional approach in which the teacher simply provides the contents and instructs the student, who captures these concepts and reproduces them as they have been supplied. In the presented didactic proposal, the approach proposed by Brousseau is followed, in which three fundamental elements take part: student, teacher, and the didactic environment. The teacher is the one who facilitates the environment in which the student builds his knowledge. In the proposal the <i>didactic contract</i> is stablished, the <i>didactic situations</i> are designed, and the means and didactic variables for the study of 3D metric geometry are chosen. The methodology followed in this study consisted of identifying educational problems; describing the theoretical framework; developing the didactic proposal; and analysis, reflection, and criticism of this training product. The contextualization of the geometry workshop in the field of the construction of structures and the use of deductive reasoning techniques that are applied in synthetic geometry and also in the building information modeling (BIM) methodology may be a way of showing the use of analytical geometry in the industries of engineering and architecture; they also serve as an opportunity for students to better understand this mathematical work.https://www.mdpi.com/2227-7390/10/9/1358teaching mathematics3D metric geometrysynthetic geometry and analytic geometryBIM digital geometric modelsdidactic situationsgeometry practice workshop |
| spellingShingle | José M. Olmos-Noguera Eduardo J. Renard-Julián María Socorro García-Cascales Design of 3D Metric Geometry Study and Research Activities within a BIM Framework Mathematics teaching mathematics 3D metric geometry synthetic geometry and analytic geometry BIM digital geometric models didactic situations geometry practice workshop |
| title | Design of 3D Metric Geometry Study and Research Activities within a BIM Framework |
| title_full | Design of 3D Metric Geometry Study and Research Activities within a BIM Framework |
| title_fullStr | Design of 3D Metric Geometry Study and Research Activities within a BIM Framework |
| title_full_unstemmed | Design of 3D Metric Geometry Study and Research Activities within a BIM Framework |
| title_short | Design of 3D Metric Geometry Study and Research Activities within a BIM Framework |
| title_sort | design of 3d metric geometry study and research activities within a bim framework |
| topic | teaching mathematics 3D metric geometry synthetic geometry and analytic geometry BIM digital geometric models didactic situations geometry practice workshop |
| url | https://www.mdpi.com/2227-7390/10/9/1358 |
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