Connecting the Tangent Function to Cardinality: A Method for Introducing Set Theory to High School Students
High school students often ask questions about the nature of infinity. When contemplating what the “largest number” is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Columbia University Libraries
2019-12-01
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| Series: | Journal of Mathematics Education at Teachers College |
| Subjects: | |
| Online Access: | https://journals-test.library.columbia.edu/index.php/jmetc/article/view/4190 |
| _version_ | 1811265678365163520 |
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| author | Steve Deihl Mara P. Markinson |
| author_facet | Steve Deihl Mara P. Markinson |
| author_sort | Steve Deihl |
| collection | DOAJ |
| description | High school students often ask questions about the nature of infinity. When contemplating what the “largest number” is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or “set theory,” are generally unknown to high school students. The authors propose a method for introducing basic ideas in set theory to high school trigonometry students by connecting prior knowledge of the tangent function and the unit circle to Georg Cantor’s ideas about infinity. By doing so, high school teachers have an opportunity to inspire their students with rich mathematics. |
| first_indexed | 2024-04-12T20:28:19Z |
| format | Article |
| id | doaj.art-7aaf67805db640859d71e484b9168400 |
| institution | Directory Open Access Journal |
| issn | 2156-1400 2156-1397 |
| language | English |
| last_indexed | 2024-04-12T20:28:19Z |
| publishDate | 2019-12-01 |
| publisher | Columbia University Libraries |
| record_format | Article |
| series | Journal of Mathematics Education at Teachers College |
| spelling | doaj.art-7aaf67805db640859d71e484b91684002022-12-22T03:17:48ZengColumbia University LibrariesJournal of Mathematics Education at Teachers College2156-14002156-13972019-12-01102Connecting the Tangent Function to Cardinality: A Method for Introducing Set Theory to High School StudentsSteve Deihl0Mara P. Markinson1East-West School of International StudiesQueens College City University of New YorkHigh school students often ask questions about the nature of infinity. When contemplating what the “largest number” is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or “set theory,” are generally unknown to high school students. The authors propose a method for introducing basic ideas in set theory to high school trigonometry students by connecting prior knowledge of the tangent function and the unit circle to Georg Cantor’s ideas about infinity. By doing so, high school teachers have an opportunity to inspire their students with rich mathematics.https://journals-test.library.columbia.edu/index.php/jmetc/article/view/4190algebra IIasymptotecardinalityconnecting representationsGeorg Cantorinfinity |
| spellingShingle | Steve Deihl Mara P. Markinson Connecting the Tangent Function to Cardinality: A Method for Introducing Set Theory to High School Students Journal of Mathematics Education at Teachers College algebra II asymptote cardinality connecting representations Georg Cantor infinity |
| title | Connecting the Tangent Function to Cardinality: A Method for Introducing Set Theory to High School Students |
| title_full | Connecting the Tangent Function to Cardinality: A Method for Introducing Set Theory to High School Students |
| title_fullStr | Connecting the Tangent Function to Cardinality: A Method for Introducing Set Theory to High School Students |
| title_full_unstemmed | Connecting the Tangent Function to Cardinality: A Method for Introducing Set Theory to High School Students |
| title_short | Connecting the Tangent Function to Cardinality: A Method for Introducing Set Theory to High School Students |
| title_sort | connecting the tangent function to cardinality a method for introducing set theory to high school students |
| topic | algebra II asymptote cardinality connecting representations Georg Cantor infinity |
| url | https://journals-test.library.columbia.edu/index.php/jmetc/article/view/4190 |
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