Knowledge of mathematics teachers in initial training regarding mathematical proofs: Logic-mathematical aspects in the evaluation of arguments
The objective of this study is to characterize the knowledge of mathematics teachers in initial training (MTITs) at the Universidad Nacional (Costa Rica) on the logic-syntactic and mathematical aspects involved in proving, when evaluating mathematical arguments. The research is positioned in the int...
| Main Authors: | , , |
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| Format: | Article |
| Language: | Spanish |
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Universidad Nacional, Costa Rica
2022-01-01
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| Series: | Uniciencia |
| Subjects: | |
| Online Access: | https://www.revistas.una.ac.cr/index.php/uniciencia/article/view/15060 |
| _version_ | 1818470262491840512 |
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| author | Christian Alfaro-Carvajal Pablo Flores-Martínez Gabriela Valverde-Soto |
| author_facet | Christian Alfaro-Carvajal Pablo Flores-Martínez Gabriela Valverde-Soto |
| author_sort | Christian Alfaro-Carvajal |
| collection | DOAJ |
| description | The objective of this study is to characterize the knowledge of mathematics teachers in initial training (MTITs) at the Universidad Nacional (Costa Rica) on the logic-syntactic and mathematical aspects involved in proving, when evaluating mathematical arguments. The research is positioned in the interpretive paradigm and has a qualitative approach. It consists of two empirical phases: in the first, a questionnaire regarding logic-syntactic aspects was applied to 25 subjects, during the months of September and October 2018 and; in the second phase, a second questionnaire covering mathematical aspects was applied to 19 subjects, during the months of May and June 2019. For the analysis of the information, knowledge indicators were proposed. Knowledge indicators are understood as phrases to determine evidence of knowledge in the responses of the subjects. It was appreciated that the vast majority of future mathematics teachers show knowledge to discriminate when a mathematical argument corresponds or not to a proof by virtue of the logic and syntactic aspects, and of mathematical elements associated with propositions with the structure of universal implication. In general, subjects displayed greater evidence of knowledge on the logic-syntactic aspects than on the mathematical aspects. Specifically, they evidenced that consideration of a particular case or the proof of the reciprocal proposition does not prove the result; likewise, subjects evidenced knowledge about the direct and indirect proof of the universal implication. In the case of the mathematical aspects considered as hypotheses, axioms, definitions and theorems, it was appreciated that subjects could have different levels of difficulties to understand a proof. |
| first_indexed | 2024-04-13T21:35:10Z |
| format | Article |
| id | doaj.art-410d18e35a0449a8b5cdfebdd7b3b586 |
| institution | Directory Open Access Journal |
| issn | 2215-3470 |
| language | Spanish |
| last_indexed | 2024-04-13T21:35:10Z |
| publishDate | 2022-01-01 |
| publisher | Universidad Nacional, Costa Rica |
| record_format | Article |
| series | Uniciencia |
| spelling | doaj.art-410d18e35a0449a8b5cdfebdd7b3b5862022-12-22T02:29:01ZspaUniversidad Nacional, Costa RicaUniciencia2215-34702022-01-0136112510.15359/ru.36-1.915060Knowledge of mathematics teachers in initial training regarding mathematical proofs: Logic-mathematical aspects in the evaluation of argumentsChristian Alfaro-Carvajal0Pablo Flores-Martínez1Gabriela Valverde-Soto2Universidad NacionalUniversidad de GranadaUniversidad de Costa RicaThe objective of this study is to characterize the knowledge of mathematics teachers in initial training (MTITs) at the Universidad Nacional (Costa Rica) on the logic-syntactic and mathematical aspects involved in proving, when evaluating mathematical arguments. The research is positioned in the interpretive paradigm and has a qualitative approach. It consists of two empirical phases: in the first, a questionnaire regarding logic-syntactic aspects was applied to 25 subjects, during the months of September and October 2018 and; in the second phase, a second questionnaire covering mathematical aspects was applied to 19 subjects, during the months of May and June 2019. For the analysis of the information, knowledge indicators were proposed. Knowledge indicators are understood as phrases to determine evidence of knowledge in the responses of the subjects. It was appreciated that the vast majority of future mathematics teachers show knowledge to discriminate when a mathematical argument corresponds or not to a proof by virtue of the logic and syntactic aspects, and of mathematical elements associated with propositions with the structure of universal implication. In general, subjects displayed greater evidence of knowledge on the logic-syntactic aspects than on the mathematical aspects. Specifically, they evidenced that consideration of a particular case or the proof of the reciprocal proposition does not prove the result; likewise, subjects evidenced knowledge about the direct and indirect proof of the universal implication. In the case of the mathematical aspects considered as hypotheses, axioms, definitions and theorems, it was appreciated that subjects could have different levels of difficulties to understand a proof.https://www.revistas.una.ac.cr/index.php/uniciencia/article/view/15060mathematics teacher’s knowledgemathematical proofmathematics teachers in initial training |
| spellingShingle | Christian Alfaro-Carvajal Pablo Flores-Martínez Gabriela Valverde-Soto Knowledge of mathematics teachers in initial training regarding mathematical proofs: Logic-mathematical aspects in the evaluation of arguments Uniciencia mathematics teacher’s knowledge mathematical proof mathematics teachers in initial training |
| title | Knowledge of mathematics teachers in initial training regarding mathematical proofs: Logic-mathematical aspects in the evaluation of arguments |
| title_full | Knowledge of mathematics teachers in initial training regarding mathematical proofs: Logic-mathematical aspects in the evaluation of arguments |
| title_fullStr | Knowledge of mathematics teachers in initial training regarding mathematical proofs: Logic-mathematical aspects in the evaluation of arguments |
| title_full_unstemmed | Knowledge of mathematics teachers in initial training regarding mathematical proofs: Logic-mathematical aspects in the evaluation of arguments |
| title_short | Knowledge of mathematics teachers in initial training regarding mathematical proofs: Logic-mathematical aspects in the evaluation of arguments |
| title_sort | knowledge of mathematics teachers in initial training regarding mathematical proofs logic mathematical aspects in the evaluation of arguments |
| topic | mathematics teacher’s knowledge mathematical proof mathematics teachers in initial training |
| url | https://www.revistas.una.ac.cr/index.php/uniciencia/article/view/15060 |
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