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Process- and object-based thinking in arithmetic
Many influential theorists have proposed that learners construct mathematical objects via the encapsulation (or reification) of processes into objects. These processto- object theories posit that object-based thinking comes later in the developmental path than process-based thinking. In this paper w...
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| Main Authors: | , |
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| Format: | Default Conference proceeding |
| Published: |
2008
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| Subjects: | |
| Online Access: | https://hdl.handle.net/2134/8584 |
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| _version_ | 1818175654897647616 |
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| author | Camilla Gilmore Matthew Inglis |
| author_facet | Camilla Gilmore Matthew Inglis |
| author_sort | Camilla Gilmore (1256451) |
| collection | Figshare |
| description | Many influential theorists have proposed that learners construct mathematical objects via the encapsulation (or reification) of processes into objects. These processto- object theories posit that object-based thinking comes later in the developmental path than process-based thinking. In this paper we directly test this hypothesis in the field of early arithmetic. An experiment is reported which studied 8 and 9 year-old children’s use of the inverse relationship between addition and subtraction. We demonstrate that a subset of children were unable to solve arithmetic problems using process-based thinking, but that, nevertheless, they were able to use the inverse relationship between addition and subtraction to solve problems where appropriate. The implications of these findings for process-to-object theories are discussed. |
| format | Default Conference proceeding |
| id | rr-article-9373748 |
| institution | Loughborough University |
| publishDate | 2008 |
| record_format | Figshare |
| spelling | rr-article-93737482008-01-01T00:00:00Z Process- and object-based thinking in arithmetic Camilla Gilmore (1256451) Matthew Inglis (1384290) untagged Many influential theorists have proposed that learners construct mathematical objects via the encapsulation (or reification) of processes into objects. These processto- object theories posit that object-based thinking comes later in the developmental path than process-based thinking. In this paper we directly test this hypothesis in the field of early arithmetic. An experiment is reported which studied 8 and 9 year-old children’s use of the inverse relationship between addition and subtraction. We demonstrate that a subset of children were unable to solve arithmetic problems using process-based thinking, but that, nevertheless, they were able to use the inverse relationship between addition and subtraction to solve problems where appropriate. The implications of these findings for process-to-object theories are discussed. 2008-01-01T00:00:00Z Text Conference contribution 2134/8584 https://figshare.com/articles/conference_contribution/Process-_and_object-based_thinking_in_arithmetic/9373748 CC BY-NC-ND 4.0 |
| spellingShingle | untagged Camilla Gilmore Matthew Inglis Process- and object-based thinking in arithmetic |
| title | Process- and object-based thinking in arithmetic |
| title_full | Process- and object-based thinking in arithmetic |
| title_fullStr | Process- and object-based thinking in arithmetic |
| title_full_unstemmed | Process- and object-based thinking in arithmetic |
| title_short | Process- and object-based thinking in arithmetic |
| title_sort | process- and object-based thinking in arithmetic |
| topic | untagged |
| url | https://hdl.handle.net/2134/8584 |