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RELATIONSHIPS BETWEEN FRACTIONAL KNOWLEDGE AND ALGEBRAIC REASONING: THE CASE OF WILLA.

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Title: RELATIONSHIPS BETWEEN FRACTIONAL KNOWLEDGE AND ALGEBRAIC REASONING: THE CASE OF WILLA.
Authors: Lee, Mi1 mlee115@asu.edu, Hackenberg, Amy2 ahackenb@indiana.edu
Source: International Journal of Science & Mathematics Education. Aug2014, Vol. 12 Issue 4, p975-1000. 26p.
Subject Terms: *Ability, *Reasoning, *High school students, *Middle school students, Iterative methods (Mathematics), Linear equations
Abstract: To investigate 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 students were interviewed twice, once to explore their quantitative reasoning with fractions and once to explore their solutions of problems that required explicit use of unknowns to write equations. As a part of the larger study, the first author conducted a case study of a seventh grade student, Willa. Willa's fractional knowledge-specifically her reversible iterative fraction scheme and use of fractions as multipliers-influenced how she wrote equations to represent multiplicative relationships between two unknown quantities. The finding indicates that implicit use of powerful fractional knowledge can lead to more explicit use of structures and relationships in algebraic situations. Curricular and instructional implications are explored. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Science & Mathematics Education 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
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  Data: RELATIONSHIPS BETWEEN FRACTIONAL KNOWLEDGE AND ALGEBRAIC REASONING: THE CASE OF WILLA.
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  Data: <searchLink fieldCode="AR" term="%22Lee%2C+Mi%22">Lee, Mi</searchLink><relatesTo>1</relatesTo><i> mlee115@asu.edu</i><br /><searchLink fieldCode="AR" term="%22Hackenberg%2C+Amy%22">Hackenberg, Amy</searchLink><relatesTo>2</relatesTo><i> ahackenb@indiana.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Science+%26+Mathematics+Education%22">International Journal of Science & Mathematics Education</searchLink>. Aug2014, Vol. 12 Issue 4, p975-1000. 26p.
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  Data: *<searchLink fieldCode="DE" term="%22Ability%22">Ability</searchLink><br />*<searchLink fieldCode="DE" term="%22Reasoning%22">Reasoning</searchLink><br />*<searchLink fieldCode="DE" term="%22High+school+students%22">High school students</searchLink><br />*<searchLink fieldCode="DE" term="%22Middle+school+students%22">Middle school students</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+equations%22">Linear equations</searchLink>
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  Data: To investigate 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 students were interviewed twice, once to explore their quantitative reasoning with fractions and once to explore their solutions of problems that required explicit use of unknowns to write equations. As a part of the larger study, the first author conducted a case study of a seventh grade student, Willa. Willa's fractional knowledge-specifically her reversible iterative fraction scheme and use of fractions as multipliers-influenced how she wrote equations to represent multiplicative relationships between two unknown quantities. The finding indicates that implicit use of powerful fractional knowledge can lead to more explicit use of structures and relationships in algebraic situations. Curricular and instructional implications are explored. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of International Journal of Science & Mathematics Education 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.)
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