Computational Triangulation in Mathematics Teacher Education
The paper is written to demonstrate the applicability of the notion of triangulation typically used in social sciences research to computationally enhance the mathematics education of future K-12 teachers. The paper starts with the so-called Brain Teaser used as background for (what is called in the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/11/2/31 |
| _version_ | 1827758018227339264 |
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| author | Sergei Abramovich |
| author_facet | Sergei Abramovich |
| author_sort | Sergei Abramovich |
| collection | DOAJ |
| description | The paper is written to demonstrate the applicability of the notion of triangulation typically used in social sciences research to computationally enhance the mathematics education of future K-12 teachers. The paper starts with the so-called Brain Teaser used as background for (what is called in the paper) computational triangulation in the context of four digital tools. Computational problem solving and problem formulating are presented as two sides of the same coin. By revealing the hidden mathematics of Fibonacci numbers included in the Brain Teaser, the paper discusses the role of computational thinking in the use of the well-ordering principle, the generating function method, digital fabrication, difference equations, and continued fractions in the development of computational algorithms. These algorithms eventually lead to a generalized Golden Ratio in the form of a string of numbers independently generated by digital tools used in the paper. |
| first_indexed | 2024-03-11T08:58:40Z |
| format | Article |
| id | doaj.art-262eb4c8601f4fed8aacedb2fcb78367 |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-11T08:58:40Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-262eb4c8601f4fed8aacedb2fcb783672023-11-16T19:52:55ZengMDPI AGComputation2079-31972023-02-011123110.3390/computation11020031Computational Triangulation in Mathematics Teacher EducationSergei Abramovich0School of Education and Professional Studies, State University of New York, Potsdam, NY 13676, USAThe paper is written to demonstrate the applicability of the notion of triangulation typically used in social sciences research to computationally enhance the mathematics education of future K-12 teachers. The paper starts with the so-called Brain Teaser used as background for (what is called in the paper) computational triangulation in the context of four digital tools. Computational problem solving and problem formulating are presented as two sides of the same coin. By revealing the hidden mathematics of Fibonacci numbers included in the Brain Teaser, the paper discusses the role of computational thinking in the use of the well-ordering principle, the generating function method, digital fabrication, difference equations, and continued fractions in the development of computational algorithms. These algorithms eventually lead to a generalized Golden Ratio in the form of a string of numbers independently generated by digital tools used in the paper.https://www.mdpi.com/2079-3197/11/2/31triangulationteacher educationdigital computationsWolfram AlphaMapleGraphing Calculator |
| spellingShingle | Sergei Abramovich Computational Triangulation in Mathematics Teacher Education Computation triangulation teacher education digital computations Wolfram Alpha Maple Graphing Calculator |
| title | Computational Triangulation in Mathematics Teacher Education |
| title_full | Computational Triangulation in Mathematics Teacher Education |
| title_fullStr | Computational Triangulation in Mathematics Teacher Education |
| title_full_unstemmed | Computational Triangulation in Mathematics Teacher Education |
| title_short | Computational Triangulation in Mathematics Teacher Education |
| title_sort | computational triangulation in mathematics teacher education |
| topic | triangulation teacher education digital computations Wolfram Alpha Maple Graphing Calculator |
| url | https://www.mdpi.com/2079-3197/11/2/31 |
| work_keys_str_mv | AT sergeiabramovich computationaltriangulationinmathematicsteachereducation |