A Study on Pre-service Teachers' Discourse about Infinitesimals, Infinite Numbers, and Limits
This study investigated seven pre-service teachers’ (who studied analysis) conceptions about infinitesimals, infinite numbers, and explanation methods of limits. Some pre-service teachers thought that infinitesimals and infinite numbers existed. The pre-service teachers who believed that infinitesim...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Korea Society of Educational Studies in Mathematics
2021-11-01
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| Series: | Journal of Educational Research in Mathematics |
| Subjects: | |
| Online Access: | http://journaleditor.inforang.com/journal/view.html?doi=10.29275/jerm.2021.31.4.471 |
| _version_ | 1818231604814807040 |
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| author | Seungju Baek Jihyun Lee |
| author_facet | Seungju Baek Jihyun Lee |
| author_sort | Seungju Baek |
| collection | DOAJ |
| description | This study investigated seven pre-service teachers’ (who studied analysis) conceptions about infinitesimals, infinite numbers, and explanation methods of limits. Some pre-service teachers thought that infinitesimals and infinite numbers existed. The pre-service teachers who believed that infinitesimals existed explained limits by relying on infinitely small quantities, as did those who believed that infinitesimals did not exist. Some pre-service teachers did not understand the sentences in which quantifiers were used, and they failed to identify statements that contained quantifiers using the Archimedean property of analysis. During interviews, some pre-service teachers demonstrated an intuitive level and did not accept the meta-rules of judging mathematical statements based on axioms and theorems. Their discourse differed from that of analysis in the existence of mathematical objects, endorsed narratives, and meta-rules. This study analyzes the phenomenon of pre-service teachers applying infinitesimals despite having studied standard analysis, focusing on the incommensurability between discourses. This finding can inform teacher education about the curriculum and instruction of analysis. |
| first_indexed | 2024-12-12T10:53:02Z |
| format | Article |
| id | doaj.art-7aae3e58c52248eebebbd451d84dc6a7 |
| institution | Directory Open Access Journal |
| issn | 2288-7733 |
| language | English |
| last_indexed | 2024-12-12T10:53:02Z |
| publishDate | 2021-11-01 |
| publisher | Korea Society of Educational Studies in Mathematics |
| record_format | Article |
| series | Journal of Educational Research in Mathematics |
| spelling | doaj.art-7aae3e58c52248eebebbd451d84dc6a72022-12-22T00:26:44ZengKorea Society of Educational Studies in MathematicsJournal of Educational Research in Mathematics2288-77332021-11-0131447149310.29275/jerm.2021.31.4.471jerm.2021.31.4.471A Study on Pre-service Teachers' Discourse about Infinitesimals, Infinite Numbers, and LimitsSeungju Baek0Jihyun Lee1Teacher, Sejong Science High School, South KoreaProfessor, Incheon National University, South KoreaThis study investigated seven pre-service teachers’ (who studied analysis) conceptions about infinitesimals, infinite numbers, and explanation methods of limits. Some pre-service teachers thought that infinitesimals and infinite numbers existed. The pre-service teachers who believed that infinitesimals existed explained limits by relying on infinitely small quantities, as did those who believed that infinitesimals did not exist. Some pre-service teachers did not understand the sentences in which quantifiers were used, and they failed to identify statements that contained quantifiers using the Archimedean property of analysis. During interviews, some pre-service teachers demonstrated an intuitive level and did not accept the meta-rules of judging mathematical statements based on axioms and theorems. Their discourse differed from that of analysis in the existence of mathematical objects, endorsed narratives, and meta-rules. This study analyzes the phenomenon of pre-service teachers applying infinitesimals despite having studied standard analysis, focusing on the incommensurability between discourses. This finding can inform teacher education about the curriculum and instruction of analysis.http://journaleditor.inforang.com/journal/view.html?doi=10.29275/jerm.2021.31.4.471infinitesimallimitnonstandard analysisquantifierdiscourseincommensurability |
| spellingShingle | Seungju Baek Jihyun Lee A Study on Pre-service Teachers' Discourse about Infinitesimals, Infinite Numbers, and Limits Journal of Educational Research in Mathematics infinitesimal limit nonstandard analysis quantifier discourse incommensurability |
| title | A Study on Pre-service Teachers' Discourse about Infinitesimals, Infinite Numbers, and Limits |
| title_full | A Study on Pre-service Teachers' Discourse about Infinitesimals, Infinite Numbers, and Limits |
| title_fullStr | A Study on Pre-service Teachers' Discourse about Infinitesimals, Infinite Numbers, and Limits |
| title_full_unstemmed | A Study on Pre-service Teachers' Discourse about Infinitesimals, Infinite Numbers, and Limits |
| title_short | A Study on Pre-service Teachers' Discourse about Infinitesimals, Infinite Numbers, and Limits |
| title_sort | study on pre service teachers discourse about infinitesimals infinite numbers and limits |
| topic | infinitesimal limit nonstandard analysis quantifier discourse incommensurability |
| url | http://journaleditor.inforang.com/journal/view.html?doi=10.29275/jerm.2021.31.4.471 |
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