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The relationship between conceptual and procedural knowledge in calculus
Thesis (PhD)--University of Pretoria, 2020.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2021
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| _version_ | 1867613654169419776 |
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| access_status_str | Open Access |
| author2 | Stols, Gerrit H. |
| author_browse | Stols, Gerrit H. |
| author_facet | Stols, Gerrit H. |
| collection | Thesis |
| dc_rights_str_mv | © 2020 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Thesis (PhD)--University of Pretoria, 2020. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/78457 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:39:34.803Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/78457 The relationship between conceptual and procedural knowledge in calculus Stols, Gerrit H. u04367138@tuks.co.za Combrinck, Celeste Hechter, Janine Esther UCTD Procedural knowledge Conceptual knowledge Calculus Mixed methods Content analysis Education theses SDG-04 Education theses SDG-10 Thesis (PhD)--University of Pretoria, 2020. Literature describes different stances with respect to conceptual and procedural mathematical knowledge. The concept-driven versus skills-orientated perspectives have led to “math wars” between researchers, while some mathematics education specialists advocate that the five strands of mathematical proficiency should be seen as interconnected. Conceptual knowledge is the knowledge of concepts or principles, and procedural knowledge the knowledge of procedures. Both types of knowledge are critical components of mathematical proficiency. This study used a mixed methods design to analyse the relationship between conceptual and procedural knowledge. The qualitative content analysis investigated relations between procedural and conceptual knowledge within the solutions of 33 calculus items. The analysis included the number of procedural and conceptual steps needed to answer the item, item label and item classification into one of four knowledge classes based on the type and quality of knowledge. The items were included in a data collection instrument used for quantitative analysis. Rasch analysis was performed to measure item difficulty and person proficiency, and describe the underlying cognitive construct between items. The Rasch person–item map confirmed that items were not clustered together per class and that item difficulty was not linked to the number of procedural and/or conceptual steps needed to do the mathematics. Confirmatory factor analysis showed over-correlation between classes and that defined classes cannot be separated, confirming integration of procedural and conceptual cognitive processes. The relationship between procedural and conceptual knowledge within and between items is complex. Findings indicated that item solutions drew on both procedural and conceptual components that cannot be separated. Solutions could follow more than one approach and analyses could differ, since what is conceptual for one student could be procedural for another. Therefore, teaching strategies should navigate between concepts and procedures, methods and representations. bs2026 Science, Mathematics and Technology Education PhD Unrestricted SDG-04: Quality education SDG-10: Reduced inequalities 2021-02-12T09:37:25Z 2021-02-12T09:37:25Z 20/10/02 2020 Thesis * S2020 http://hdl.handle.net/2263/78457 en © 2020 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Procedural knowledge Conceptual knowledge Calculus Mixed methods Content analysis Education theses SDG-04 Education theses SDG-10 The relationship between conceptual and procedural knowledge in calculus |
| title | The relationship between conceptual and procedural knowledge in calculus |
| title_full | The relationship between conceptual and procedural knowledge in calculus |
| title_fullStr | The relationship between conceptual and procedural knowledge in calculus |
| title_full_unstemmed | The relationship between conceptual and procedural knowledge in calculus |
| title_short | The relationship between conceptual and procedural knowledge in calculus |
| title_sort | relationship between conceptual and procedural knowledge in calculus |
| topic | UCTD Procedural knowledge Conceptual knowledge Calculus Mixed methods Content analysis Education theses SDG-04 Education theses SDG-10 |
| url | http://hdl.handle.net/2263/78457 |