Students' distributive reasoning with fractions and unknowns.
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| Title: | Students' distributive reasoning with fractions and unknowns. |
|---|---|
| Authors: | Hackenberg, Amy1 ahackenb@indiana.edu, Lee, Mi2 mlee115@asu.edu |
| Source: | Educational Studies in Mathematics. Oct2016, Vol. 93 Issue 2, p245-263. 19p. |
| Subject Terms: | *Reasoning, *Reason, *Thought & thinking, *Higher education, Fractions |
| Abstract: | To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite units (units of units). Students participated in two 45-min semi-structured interviews and completed a written fraction assessment. This paper reports on how 12 students operating with the second and third multiplicative concepts demonstrated distributive reasoning in equal sharing problems and in taking fractions of unknowns. Students operating with the second multiplicative concept who demonstrated distributive reasoning appeared to lack awareness of the results of their reasoning, while students operating with the third multiplicative concept demonstrated this awareness and the construction of more advanced distributive reasoning when they worked with unknowns. Implications for relationships between students' fractional knowledge and algebraic reasoning are explored. [ABSTRACT FROM AUTHOR] |
| Copyright of Educational Studies in Mathematics is the property of Springer Nature 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: 118371184 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Students' distributive reasoning with fractions and unknowns. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hackenberg%2C+Amy%22">Hackenberg, Amy</searchLink><relatesTo>1</relatesTo><i> ahackenb@indiana.edu</i><br /><searchLink fieldCode="AR" term="%22Lee%2C+Mi%22">Lee, Mi</searchLink><relatesTo>2</relatesTo><i> mlee115@asu.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Educational+Studies+in+Mathematics%22">Educational Studies in Mathematics</searchLink>. Oct2016, Vol. 93 Issue 2, p245-263. 19p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Reasoning%22">Reasoning</searchLink><br />*<searchLink fieldCode="DE" term="%22Reason%22">Reason</searchLink><br />*<searchLink fieldCode="DE" term="%22Thought+%26+thinking%22">Thought & thinking</searchLink><br />*<searchLink fieldCode="DE" term="%22Higher+education%22">Higher education</searchLink><br /><searchLink fieldCode="DE" term="%22Fractions%22">Fractions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite units (units of units). Students participated in two 45-min semi-structured interviews and completed a written fraction assessment. This paper reports on how 12 students operating with the second and third multiplicative concepts demonstrated distributive reasoning in equal sharing problems and in taking fractions of unknowns. Students operating with the second multiplicative concept who demonstrated distributive reasoning appeared to lack awareness of the results of their reasoning, while students operating with the third multiplicative concept demonstrated this awareness and the construction of more advanced distributive reasoning when they worked with unknowns. Implications for relationships between students' fractional knowledge and algebraic reasoning are explored. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Educational Studies in Mathematics is the property of Springer Nature 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=118371184 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10649-016-9704-9 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 19 StartPage: 245 Subjects: – SubjectFull: Reasoning Type: general – SubjectFull: Reason Type: general – SubjectFull: Thought & thinking Type: general – SubjectFull: Higher education Type: general – SubjectFull: Fractions Type: general Titles: – TitleFull: Students' distributive reasoning with fractions and unknowns. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hackenberg, Amy – PersonEntity: Name: NameFull: Lee, Mi IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2016 Type: published Y: 2016 Identifiers: – Type: issn-print Value: 00131954 Numbering: – Type: volume Value: 93 – Type: issue Value: 2 Titles: – TitleFull: Educational Studies in Mathematics Type: main |
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