Toward A Coherent Treatment of Negative Numbers
The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Notin...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Columbia University Libraries
2013-04-01
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| Series: | Journal of Mathematics Education at Teachers College |
| Online Access: | https://journals.library.columbia.edu/index.php/jmetc/article/view/775 |
| _version_ | 1819050452463910912 |
|---|---|
| author | Kurt Kreith Al Mendle |
| author_facet | Kurt Kreith Al Mendle |
| author_sort | Kurt Kreith |
| collection | DOAJ |
| description | The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the horizontal bar that is often referred to as “minus sign,” the authors introduce a novel notation intended to address this ambiguity. In this system, the symbol “−” is reserved exclusively for subtraction. The four arithmetic operations and the concept of a number's opposite are then illustrated in light of such a notational shift. A valuable aspect of this excursion is that it encourages teachers to reflect on the relationship between some important mathematics and the pedagogical approaches they now use. |
| first_indexed | 2024-12-21T11:48:16Z |
| format | Article |
| id | doaj.art-f21be1fb34d542758fdcf7bbd834d2a1 |
| institution | Directory Open Access Journal |
| issn | 2156-1400 2156-1397 |
| language | English |
| last_indexed | 2024-12-21T11:48:16Z |
| publishDate | 2013-04-01 |
| publisher | Columbia University Libraries |
| record_format | Article |
| series | Journal of Mathematics Education at Teachers College |
| spelling | doaj.art-f21be1fb34d542758fdcf7bbd834d2a12022-12-21T19:05:07ZengColumbia University LibrariesJournal of Mathematics Education at Teachers College2156-14002156-13972013-04-014110.7916/jmetc.v4i1.775Toward A Coherent Treatment of Negative NumbersKurt Kreith0Al Mendle1University of California, DavisUniversity of California, DavisThe transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the horizontal bar that is often referred to as “minus sign,” the authors introduce a novel notation intended to address this ambiguity. In this system, the symbol “−” is reserved exclusively for subtraction. The four arithmetic operations and the concept of a number's opposite are then illustrated in light of such a notational shift. A valuable aspect of this excursion is that it encourages teachers to reflect on the relationship between some important mathematics and the pedagogical approaches they now use.https://journals.library.columbia.edu/index.php/jmetc/article/view/775 |
| spellingShingle | Kurt Kreith Al Mendle Toward A Coherent Treatment of Negative Numbers Journal of Mathematics Education at Teachers College |
| title | Toward A Coherent Treatment of Negative Numbers |
| title_full | Toward A Coherent Treatment of Negative Numbers |
| title_fullStr | Toward A Coherent Treatment of Negative Numbers |
| title_full_unstemmed | Toward A Coherent Treatment of Negative Numbers |
| title_short | Toward A Coherent Treatment of Negative Numbers |
| title_sort | toward a coherent treatment of negative numbers |
| url | https://journals.library.columbia.edu/index.php/jmetc/article/view/775 |
| work_keys_str_mv | AT kurtkreith towardacoherenttreatmentofnegativenumbers AT almendle towardacoherenttreatmentofnegativenumbers |