The relational nature of rational numbers
It is commonly accepted that the knowledge and learning of rational numbers is more complex than that of the whole number field. This complexity includes the broader range of application of rational numbers, the increased level of technical complexity in the mathematical structure and symbol systems...
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| Format: | Article |
| Language: | English |
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AOSIS
2015-06-01
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| Series: | Pythagoras |
| Online Access: | https://pythagoras.org.za/index.php/pythagoras/article/view/273 |
| _version_ | 1818139347136806912 |
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| author | Bruce Brown |
| author_facet | Bruce Brown |
| author_sort | Bruce Brown |
| collection | DOAJ |
| description | It is commonly accepted that the knowledge and learning of rational numbers is more complex than that of the whole number field. This complexity includes the broader range of application of rational numbers, the increased level of technical complexity in the mathematical structure and symbol systems of this field and the more complex nature of many conceptual properties of the rational number field. Research on rational number learning is divided as to whether children’s difficulties in learning rational numbers arise only from the increased complexity or also include elements of conceptual change. This article argues for a fundamental conceptual difference between whole and rational numbers. It develops the position that rational numbers are fundamentally relational in nature and that the move from absolute counts to relative comparisons leads to a further level of abstraction in our understanding of number and quantity. The argument is based on a number of qualitative, in-depth research projects with children and adults. These research projects indicated the importance of such a relational understanding in both the learning and teaching of rational numbers, as well as in adult representations of rational numbers on the number line. Acknowledgement of such a conceptual change could have important consequences for the teaching and learning of rational numbers. |
| first_indexed | 2024-12-11T10:26:38Z |
| format | Article |
| id | doaj.art-d0be924c9234493c98e5073a6423d743 |
| institution | Directory Open Access Journal |
| issn | 1012-2346 2223-7895 |
| language | English |
| last_indexed | 2024-12-11T10:26:38Z |
| publishDate | 2015-06-01 |
| publisher | AOSIS |
| record_format | Article |
| series | Pythagoras |
| spelling | doaj.art-d0be924c9234493c98e5073a6423d7432022-12-22T01:11:08ZengAOSISPythagoras1012-23462223-78952015-06-01361e1e810.4102/pythagoras.v36i1.273168The relational nature of rational numbersBruce Brown0Education Department, Rhodes UniversityIt is commonly accepted that the knowledge and learning of rational numbers is more complex than that of the whole number field. This complexity includes the broader range of application of rational numbers, the increased level of technical complexity in the mathematical structure and symbol systems of this field and the more complex nature of many conceptual properties of the rational number field. Research on rational number learning is divided as to whether children’s difficulties in learning rational numbers arise only from the increased complexity or also include elements of conceptual change. This article argues for a fundamental conceptual difference between whole and rational numbers. It develops the position that rational numbers are fundamentally relational in nature and that the move from absolute counts to relative comparisons leads to a further level of abstraction in our understanding of number and quantity. The argument is based on a number of qualitative, in-depth research projects with children and adults. These research projects indicated the importance of such a relational understanding in both the learning and teaching of rational numbers, as well as in adult representations of rational numbers on the number line. Acknowledgement of such a conceptual change could have important consequences for the teaching and learning of rational numbers.https://pythagoras.org.za/index.php/pythagoras/article/view/273 |
| spellingShingle | Bruce Brown The relational nature of rational numbers Pythagoras |
| title | The relational nature of rational numbers |
| title_full | The relational nature of rational numbers |
| title_fullStr | The relational nature of rational numbers |
| title_full_unstemmed | The relational nature of rational numbers |
| title_short | The relational nature of rational numbers |
| title_sort | relational nature of rational numbers |
| url | https://pythagoras.org.za/index.php/pythagoras/article/view/273 |
| work_keys_str_mv | AT brucebrown therelationalnatureofrationalnumbers AT brucebrown relationalnatureofrationalnumbers |