Expressing Distance in Graphs of Functions in the Cartesian Plane: Obstacles and Interventions.
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| Title: | Expressing Distance in Graphs of Functions in the Cartesian Plane: Obstacles and Interventions. |
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| Authors: | Parr, Erika David1 parre@rhodes.edu, Lippe, Samuel1 |
| Source: | Mathematics Enthusiast. Aug2024, Vol. 21 Issue 3, p501-539. 39p. |
| Subject Terms: | *Distance education students, *Learning goals, *Student activities, *Calculus, Cartesian plane |
| Abstract: | Connecting algebraic and graphical representations encompasses a large portion of mathematical activity for students in grades 8-14. In Calculus, the ability to represent distances on graphs using algebraic expressions is foundational for a wide range of results. However, research has shown that students may struggle to make such connections. In this article, we seek to answer the following questions: (1) What are the underlying conceptions critical to expressing distances on graphs of functions algebraically? and (2) What types of tasks may support students in developing this skill? We first offer a conceptual analysis of the connections between algebraic expressions and distances in graphs of functions. Next, we describe a hypothetical learning trajectory of tasks and associated learning goals we developed to support students in expressing distances. We then report the outcome of implementing the tasks with groups of Calculus students. While the results include some success in supporting students to express distances, they also pointed to some persistent obstacles as well as limitations of the tasks. We focus on two such obstacles that emerged: the role of conceptualizing symbols as variables in the algebraic register and the role of conceptualizing distances within the graphical register. We discuss directions for future research and ways to support students in connecting algebraic expressions and graphs. [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: 178743267 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Expressing Distance in Graphs of Functions in the Cartesian Plane: Obstacles and Interventions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Parr%2C+Erika+David%22">Parr, Erika David</searchLink><relatesTo>1</relatesTo><i> parre@rhodes.edu</i><br /><searchLink fieldCode="AR" term="%22Lippe%2C+Samuel%22">Lippe, Samuel</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+Enthusiast%22">Mathematics Enthusiast</searchLink>. Aug2024, Vol. 21 Issue 3, p501-539. 39p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Distance+education+students%22">Distance education students</searchLink><br />*<searchLink fieldCode="DE" term="%22Learning+goals%22">Learning goals</searchLink><br />*<searchLink fieldCode="DE" term="%22Student+activities%22">Student activities</searchLink><br />*<searchLink fieldCode="DE" term="%22Calculus%22">Calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Cartesian+plane%22">Cartesian plane</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Connecting algebraic and graphical representations encompasses a large portion of mathematical activity for students in grades 8-14. In Calculus, the ability to represent distances on graphs using algebraic expressions is foundational for a wide range of results. However, research has shown that students may struggle to make such connections. In this article, we seek to answer the following questions: (1) What are the underlying conceptions critical to expressing distances on graphs of functions algebraically? and (2) What types of tasks may support students in developing this skill? We first offer a conceptual analysis of the connections between algebraic expressions and distances in graphs of functions. Next, we describe a hypothetical learning trajectory of tasks and associated learning goals we developed to support students in expressing distances. We then report the outcome of implementing the tasks with groups of Calculus students. While the results include some success in supporting students to express distances, they also pointed to some persistent obstacles as well as limitations of the tasks. We focus on two such obstacles that emerged: the role of conceptualizing symbols as variables in the algebraic register and the role of conceptualizing distances within the graphical register. We discuss directions for future research and ways to support students in connecting algebraic expressions and graphs. [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=178743267 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.54870/1551-3440.1641 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 39 StartPage: 501 Subjects: – SubjectFull: Distance education students Type: general – SubjectFull: Learning goals Type: general – SubjectFull: Student activities Type: general – SubjectFull: Calculus Type: general – SubjectFull: Cartesian plane Type: general Titles: – TitleFull: Expressing Distance in Graphs of Functions in the Cartesian Plane: Obstacles and Interventions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Parr, Erika David – PersonEntity: Name: NameFull: Lippe, Samuel 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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