Examples and generalizations in mathematical reasoning – A study with potentially mathematically gifted children
Mathematical arguments are central components of mathematics and play a role in certain types of modelling of potential mathematical giftedness. However, particular characteristics of arguments are interpreted differently in the context of mathematical giftedness. Some models of giftedness see no co...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sriwijaya University
2022-12-01
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| Series: | Journal on Mathematics Education |
| Subjects: | |
| Online Access: | http://jme.ejournal.unsri.ac.id/index.php/jme/article/view/208 |
| _version_ | 1828044966933299200 |
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| author | Simone Jablonski Matthias Ludwig |
| author_facet | Simone Jablonski Matthias Ludwig |
| author_sort | Simone Jablonski |
| collection | DOAJ |
| description | Mathematical arguments are central components of mathematics and play a role in certain types of modelling of potential mathematical giftedness. However, particular characteristics of arguments are interpreted differently in the context of mathematical giftedness. Some models of giftedness see no connection, whereas other models consider the formulation of complete and plausible arguments as a partial aspect of giftedness. Furthermore, longitudinal changes in argumentation characteristics remain open. This leads to the research focus of this article, which is to identify and describe the changes of argumentation products in potentially mathematically gifted children over a longer period. For this purpose, the argumentation products of children from third to sixth grade are collected throughout a longitudinal study and examined with respect to the use of examples and generalizations. The analysis of all products results in six different types of changes in the characteristics of the argumentation products identified over the survey period and case studies are used to illustrate student use of examples and generalizations of these types. This not only reveals the general importance of the use of examples in arguments. For one type, an increase in generalized arguments can be observed over the survey period. The article will conclude with a discussion of the role of argument characteristics in describing potential mathematical giftedness. |
| first_indexed | 2024-04-10T18:03:52Z |
| format | Article |
| id | doaj.art-76e038004ab44577a01148cbefdbf788 |
| institution | Directory Open Access Journal |
| issn | 2087-8885 |
| language | English |
| last_indexed | 2024-04-10T18:03:52Z |
| publishDate | 2022-12-01 |
| publisher | Sriwijaya University |
| record_format | Article |
| series | Journal on Mathematics Education |
| spelling | doaj.art-76e038004ab44577a01148cbefdbf7882023-02-02T14:21:55ZengSriwijaya UniversityJournal on Mathematics Education2087-88852022-12-0113460563010.22342/jme.v13i4.pp605-630208Examples and generalizations in mathematical reasoning – A study with potentially mathematically gifted childrenSimone Jablonski0https://orcid.org/0000-0002-1691-4435Matthias Ludwig1https://orcid.org/0000-0003-1296-8898Department of Mathematics and Computer Science Education, Goethe University Frankfurt, GermanyDepartment of Mathematics and Computer Science Education, Goethe University Frankfurt, GermanyMathematical arguments are central components of mathematics and play a role in certain types of modelling of potential mathematical giftedness. However, particular characteristics of arguments are interpreted differently in the context of mathematical giftedness. Some models of giftedness see no connection, whereas other models consider the formulation of complete and plausible arguments as a partial aspect of giftedness. Furthermore, longitudinal changes in argumentation characteristics remain open. This leads to the research focus of this article, which is to identify and describe the changes of argumentation products in potentially mathematically gifted children over a longer period. For this purpose, the argumentation products of children from third to sixth grade are collected throughout a longitudinal study and examined with respect to the use of examples and generalizations. The analysis of all products results in six different types of changes in the characteristics of the argumentation products identified over the survey period and case studies are used to illustrate student use of examples and generalizations of these types. This not only reveals the general importance of the use of examples in arguments. For one type, an increase in generalized arguments can be observed over the survey period. The article will conclude with a discussion of the role of argument characteristics in describing potential mathematical giftedness.http://jme.ejournal.unsri.ac.id/index.php/jme/article/view/208exampleslongitudinal studymathematical giftednessmathematical reasoningtypology |
| spellingShingle | Simone Jablonski Matthias Ludwig Examples and generalizations in mathematical reasoning – A study with potentially mathematically gifted children Journal on Mathematics Education examples longitudinal study mathematical giftedness mathematical reasoning typology |
| title | Examples and generalizations in mathematical reasoning – A study with potentially mathematically gifted children |
| title_full | Examples and generalizations in mathematical reasoning – A study with potentially mathematically gifted children |
| title_fullStr | Examples and generalizations in mathematical reasoning – A study with potentially mathematically gifted children |
| title_full_unstemmed | Examples and generalizations in mathematical reasoning – A study with potentially mathematically gifted children |
| title_short | Examples and generalizations in mathematical reasoning – A study with potentially mathematically gifted children |
| title_sort | examples and generalizations in mathematical reasoning a study with potentially mathematically gifted children |
| topic | examples longitudinal study mathematical giftedness mathematical reasoning typology |
| url | http://jme.ejournal.unsri.ac.id/index.php/jme/article/view/208 |
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