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Learners' Functional Understandings of Proof (LFUP) in Mathematics: A Qualitative Approach.

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Title: Learners' Functional Understandings of Proof (LFUP) in Mathematics: A Qualitative Approach.
Authors: Shongwe, Benjamin1 shongweb@ukzn.ac.za
Source: International Journal of Innovation in Science & Mathematics Education. 2020, Vol. 28 Issue 3, p24-36. 13p.
Subject Terms: *Learning, *High schools, *Educators, *Formative tests, Mathematics
Abstract: The purpose of this study was to present a revision and validation of the Learners' Functional Understandings of Proof (LFUP) scale in mathematics using data collected from Grade 11 learners (n = 87) in a high school in South Africa. The LFUP scale was linked to the five-factor model (verification, explanation, communication, discovery, and systematisation) whose items were derived from existing literature on proof functions. Unlike the previous version of the scale, the new scale being validated here blends Likert-scale and constructed-response items to evaluate learners' conceptions of the essence of the functions of an aspect central to mathematical knowledge development: proof. It is my contention that the LFUP instrument can be used as either a summative or a formative assessment tool, given the argument that learners often require motivation as to why they are required to write proofs. In short, this study provided an instrument to introduce learners to the concept of mathematical proof. Multiple regression analysis revealed that all five LFUP tenets correlated significantly with the total sum of all the functions of proof taken together. In the qualitative analysis, a substantial number of learners (52%) were found to hold hybrid beliefs about the functions of proof in mathematics. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Innovation in Science & Mathematics Education is the property of Institute for Innovation in Science & Mathematics Education 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: Learners' Functional Understandings of Proof (LFUP) in Mathematics: A Qualitative Approach.
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Innovation+in+Science+%26+Mathematics+Education%22">International Journal of Innovation in Science & Mathematics Education</searchLink>. 2020, Vol. 28 Issue 3, p24-36. 13p.
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  Data: *<searchLink fieldCode="DE" term="%22Learning%22">Learning</searchLink><br />*<searchLink fieldCode="DE" term="%22High+schools%22">High schools</searchLink><br />*<searchLink fieldCode="DE" term="%22Educators%22">Educators</searchLink><br />*<searchLink fieldCode="DE" term="%22Formative+tests%22">Formative tests</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink>
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  Data: The purpose of this study was to present a revision and validation of the Learners' Functional Understandings of Proof (LFUP) scale in mathematics using data collected from Grade 11 learners (n = 87) in a high school in South Africa. The LFUP scale was linked to the five-factor model (verification, explanation, communication, discovery, and systematisation) whose items were derived from existing literature on proof functions. Unlike the previous version of the scale, the new scale being validated here blends Likert-scale and constructed-response items to evaluate learners' conceptions of the essence of the functions of an aspect central to mathematical knowledge development: proof. It is my contention that the LFUP instrument can be used as either a summative or a formative assessment tool, given the argument that learners often require motivation as to why they are required to write proofs. In short, this study provided an instrument to introduce learners to the concept of mathematical proof. Multiple regression analysis revealed that all five LFUP tenets correlated significantly with the total sum of all the functions of proof taken together. In the qualitative analysis, a substantial number of learners (52%) were found to hold hybrid beliefs about the functions of proof in mathematics. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of International Journal of Innovation in Science & Mathematics Education is the property of Institute for Innovation in Science & Mathematics Education 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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        Value: 10.30722/ijisme.28.03.003
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