Didactic transposition and the knowledge to be taught: towards an archeorganisation for concave/convex functions.
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| Title: | Didactic transposition and the knowledge to be taught: towards an archeorganisation for concave/convex functions. |
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| Authors: | Strømskag, Heidi1 (AUTHOR) heidi.stromskag@ntnu.no, Chevallard, Yves2 (AUTHOR) |
| Source: | International Journal of Mathematical Education in Science & Technology. Jul2026, Vol. 57 Issue 7, p1342-1369. 28p. |
| Subject Terms: | *Curriculum, *Curriculum planning, *Education theory, *Secondary education, *Teacher education, *Higher education, Concave functions, Convex functions |
| Abstract: | This study is framed within the anthropological theory of the didactic. The first part is a comparative study of the mathematical organisation of concave/convex functions on the one hand at university, and on the other hand in secondary education. Data for this analysis are from a university textbook on calculus and a secondary school textbook. The analytic results show how the mathematics (to be) taught at secondary level consists of a largely demathematised logos block. The corresponding institutional fragmentation of knowledge reveals a missing praxeological organisation from which the organisations of knowledge we consider in this paper could be derived by transposition. Responding to this insight, in the second part of the paper, we have outlined what we call an archeorganisation for concave/convex functions, a framework that teacher education institutions could refer to when trying to satisfy the specific constraints they are subjected to (notably because of its publics), without for that matter isolating themselves epistemically from other academic institutions. Formulating an archeorganisation represents a meta-curricular study, with the objective of transforming the institutional conditions and constraints that guide mathematics educators and curriculum designers in their deliberations about the concept of concave/convex functions. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Mathematical Education in Science & Technology is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Education Research Complete |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 194898366 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Didactic transposition and the knowledge to be taught: towards an archeorganisation for concave/convex functions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Strømskag%2C+Heidi%22">Strømskag, Heidi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> heidi.stromskag@ntnu.no</i><br /><searchLink fieldCode="AR" term="%22Chevallard%2C+Yves%22">Chevallard, Yves</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Mathematical+Education+in+Science+%26+Technology%22">International Journal of Mathematical Education in Science & Technology</searchLink>. Jul2026, Vol. 57 Issue 7, p1342-1369. 28p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Curriculum%22">Curriculum</searchLink><br />*<searchLink fieldCode="DE" term="%22Curriculum+planning%22">Curriculum planning</searchLink><br />*<searchLink fieldCode="DE" term="%22Education+theory%22">Education theory</searchLink><br />*<searchLink fieldCode="DE" term="%22Secondary+education%22">Secondary education</searchLink><br />*<searchLink fieldCode="DE" term="%22Teacher+education%22">Teacher education</searchLink><br />*<searchLink fieldCode="DE" term="%22Higher+education%22">Higher education</searchLink><br /><searchLink fieldCode="DE" term="%22Concave+functions%22">Concave functions</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+functions%22">Convex functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This study is framed within the anthropological theory of the didactic. The first part is a comparative study of the mathematical organisation of concave/convex functions on the one hand at university, and on the other hand in secondary education. Data for this analysis are from a university textbook on calculus and a secondary school textbook. The analytic results show how the mathematics (to be) taught at secondary level consists of a largely demathematised logos block. The corresponding institutional fragmentation of knowledge reveals a missing praxeological organisation from which the organisations of knowledge we consider in this paper could be derived by transposition. Responding to this insight, in the second part of the paper, we have outlined what we call an archeorganisation for concave/convex functions, a framework that teacher education institutions could refer to when trying to satisfy the specific constraints they are subjected to (notably because of its publics), without for that matter isolating themselves epistemically from other academic institutions. Formulating an archeorganisation represents a meta-curricular study, with the objective of transforming the institutional conditions and constraints that guide mathematics educators and curriculum designers in their deliberations about the concept of concave/convex functions. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Mathematical Education in Science & Technology is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=ehh&AN=194898366 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/0020739X.2024.2305879 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 28 StartPage: 1342 Subjects: – SubjectFull: Curriculum Type: general – SubjectFull: Curriculum planning Type: general – SubjectFull: Education theory Type: general – SubjectFull: Secondary education Type: general – SubjectFull: Teacher education Type: general – SubjectFull: Higher education Type: general – SubjectFull: Concave functions Type: general – SubjectFull: Convex functions Type: general Titles: – TitleFull: Didactic transposition and the knowledge to be taught: towards an archeorganisation for concave/convex functions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Strømskag, Heidi – PersonEntity: Name: NameFull: Chevallard, Yves IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0020739X Numbering: – Type: volume Value: 57 – Type: issue Value: 7 Titles: – TitleFull: International Journal of Mathematical Education in Science & Technology Type: main |
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