Connecting Representations and Ways of Thinking about Slope from Algebra to Calculus.
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| Title: | Connecting Representations and Ways of Thinking about Slope from Algebra to Calculus. |
|---|---|
| Authors: | Moore-Russo, Deborah1 dmr@ou.edu, Nagle, Courtney2,3,4 |
| Source: | Mathematics Enthusiast. Aug2024, Vol. 21 Issue 3, p569-601. 33p. |
| Subject Terms: | *College teachers, *Curriculum, Multivariable calculus, Corpora |
| Abstract: | While slope is a topic in the algebra curriculum, having a robust understanding of slope is needed for students to truly understand several single and multivariable calculus topics with any depth. We begin with a review of the topic of slope and present what is known from its existing corpus of literature. We then outline the tenets of APOS theory. Building from there, we suggest what a robust, flexible understanding of slope involves, as well as how slope is used, with the APOS-slope framework acting as a theoretical lens. This is followed by the cases of two hypothetical students built from amalgamations of research and experience to emphasize why moving easily between different ways of thinking about and the various uses of slope is vital to successfully transition into calculus. We offer suggestions as to how university instructors might consider slope understanding when teaching calculus, then conclude with suggestions for future research on slope. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics Enthusiast is the property of Prof. Bharath Sriraman 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 |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 178743266 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Connecting Representations and Ways of Thinking about Slope from Algebra to Calculus. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Moore-Russo%2C+Deborah%22">Moore-Russo, Deborah</searchLink><relatesTo>1</relatesTo><i> dmr@ou.edu</i><br /><searchLink fieldCode="AR" term="%22Nagle%2C+Courtney%22">Nagle, Courtney</searchLink><relatesTo>2,3,4</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+Enthusiast%22">Mathematics Enthusiast</searchLink>. Aug2024, Vol. 21 Issue 3, p569-601. 33p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22College+teachers%22">College teachers</searchLink><br />*<searchLink fieldCode="DE" term="%22Curriculum%22">Curriculum</searchLink><br /><searchLink fieldCode="DE" term="%22Multivariable+calculus%22">Multivariable calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Corpora%22">Corpora</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: While slope is a topic in the algebra curriculum, having a robust understanding of slope is needed for students to truly understand several single and multivariable calculus topics with any depth. We begin with a review of the topic of slope and present what is known from its existing corpus of literature. We then outline the tenets of APOS theory. Building from there, we suggest what a robust, flexible understanding of slope involves, as well as how slope is used, with the APOS-slope framework acting as a theoretical lens. This is followed by the cases of two hypothetical students built from amalgamations of research and experience to emphasize why moving easily between different ways of thinking about and the various uses of slope is vital to successfully transition into calculus. We offer suggestions as to how university instructors might consider slope understanding when teaching calculus, then conclude with suggestions for future research on slope. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics Enthusiast is the property of Prof. Bharath Sriraman 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=178743266 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.54870/1551-3440.1643 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 33 StartPage: 569 Subjects: – SubjectFull: College teachers Type: general – SubjectFull: Curriculum Type: general – SubjectFull: Multivariable calculus Type: general – SubjectFull: Corpora Type: general Titles: – TitleFull: Connecting Representations and Ways of Thinking about Slope from Algebra to Calculus. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Moore-Russo, Deborah – PersonEntity: Name: NameFull: Nagle, Courtney IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 15513440 Numbering: – Type: volume Value: 21 – Type: issue Value: 3 Titles: – TitleFull: Mathematics Enthusiast Type: main |
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