Conceptual mis(understandings) of fractions: From area models to multiple embodiments
Area-model representations seem to have been dominant in the teaching and learning of fractions, especially in primary school mathematics curricula. In this study, we investigated 40 fifth grade children’s understandings of the unit fractions, 1 2 , 1 3 and 1 4 , represented through a variety of dif...
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| Veröffentlicht in: | Mathematics education research journal 2015-06, Vol.27 (2), p.233-261 |
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| creator | Zhang, Xiaofen Clements, M. A. (Ken) Ellerton, Nerida F. |
| description | Area-model representations seem to have been dominant in the teaching and learning of fractions, especially in primary school mathematics curricula. In this study, we investigated 40 fifth grade children’s understandings of the unit fractions,
1
2
,
1
3
and
1
4
, represented through a variety of different models. Analyses of pre-teaching test and interview data revealed that although the participants were adept at partitioning regional models, they did not cope well with questions for which unit fractions were embodied in non-area-model scenarios. Analyses of post-teaching test and interview data indicated that after their participation in an instructional intervention designed according to Dienes’ (
1960
) dynamic principle, the students’ performances on tests improved significantly, and their conceptual understandings of unit fractions developed to the point where they could provide reasonable explanations of how they arrived at solutions. Analysis of retention data, gathered more than 3 months after the teaching intervention, showed that the students’ newly found understandings had, in most cases, been retained. |
| doi_str_mv | 10.1007/s13394-014-0133-8 |
| format | Article |
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1
2
,
1
3
and
1
4
, represented through a variety of different models. Analyses of pre-teaching test and interview data revealed that although the participants were adept at partitioning regional models, they did not cope well with questions for which unit fractions were embodied in non-area-model scenarios. Analyses of post-teaching test and interview data indicated that after their participation in an instructional intervention designed according to Dienes’ (
1960
) dynamic principle, the students’ performances on tests improved significantly, and their conceptual understandings of unit fractions developed to the point where they could provide reasonable explanations of how they arrived at solutions. Analysis of retention data, gathered more than 3 months after the teaching intervention, showed that the students’ newly found understandings had, in most cases, been retained.</description><identifier>ISSN: 1033-2170</identifier><identifier>EISSN: 2211-050X</identifier><identifier>DOI: 10.1007/s13394-014-0133-8</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Achievement Gains ; Concept Formation ; Dynamic tests ; Education ; Elementary School Mathematics ; Elementary school students ; Fractions ; Grade 5 ; Instructional Effectiveness ; Intervention ; Interviews ; Learning ; Mathematical Concepts ; Mathematical models ; Mathematics Achievement ; Mathematics Education ; Mathematics Instruction ; Mathematics Skills ; Multiplication ; Original Article ; Pretests Posttests ; Problem Solving ; Representations ; Students ; Teaching ; Teaching Methods ; Texts</subject><ispartof>Mathematics education research journal, 2015-06, Vol.27 (2), p.233-261</ispartof><rights>Mathematics Education Research Group of Australasia, Inc. 2014</rights><rights>Mathematics Education Research Group of Australasia, Inc. 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c371t-b1bc8d2f5d64428b4edfa039ad51dca0c84d351121de92672011965872d491583</citedby><cites>FETCH-LOGICAL-c371t-b1bc8d2f5d64428b4edfa039ad51dca0c84d351121de92672011965872d491583</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s13394-014-0133-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13394-014-0133-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids><backlink>$$Uhttp://eric.ed.gov/ERICWebPortal/detail?accno=EJ1059859$$DView record in ERIC$$Hfree_for_read</backlink></links><search><creatorcontrib>Zhang, Xiaofen</creatorcontrib><creatorcontrib>Clements, M. A. (Ken)</creatorcontrib><creatorcontrib>Ellerton, Nerida F.</creatorcontrib><title>Conceptual mis(understandings) of fractions: From area models to multiple embodiments</title><title>Mathematics education research journal</title><addtitle>Math Ed Res J</addtitle><description>Area-model representations seem to have been dominant in the teaching and learning of fractions, especially in primary school mathematics curricula. In this study, we investigated 40 fifth grade children’s understandings of the unit fractions,
1
2
,
1
3
and
1
4
, represented through a variety of different models. Analyses of pre-teaching test and interview data revealed that although the participants were adept at partitioning regional models, they did not cope well with questions for which unit fractions were embodied in non-area-model scenarios. Analyses of post-teaching test and interview data indicated that after their participation in an instructional intervention designed according to Dienes’ (
1960
) dynamic principle, the students’ performances on tests improved significantly, and their conceptual understandings of unit fractions developed to the point where they could provide reasonable explanations of how they arrived at solutions. Analysis of retention data, gathered more than 3 months after the teaching intervention, showed that the students’ newly found understandings had, in most cases, been retained.</description><subject>Achievement Gains</subject><subject>Concept Formation</subject><subject>Dynamic tests</subject><subject>Education</subject><subject>Elementary School Mathematics</subject><subject>Elementary school students</subject><subject>Fractions</subject><subject>Grade 5</subject><subject>Instructional Effectiveness</subject><subject>Intervention</subject><subject>Interviews</subject><subject>Learning</subject><subject>Mathematical Concepts</subject><subject>Mathematical models</subject><subject>Mathematics Achievement</subject><subject>Mathematics Education</subject><subject>Mathematics Instruction</subject><subject>Mathematics Skills</subject><subject>Multiplication</subject><subject>Original Article</subject><subject>Pretests Posttests</subject><subject>Problem Solving</subject><subject>Representations</subject><subject>Students</subject><subject>Teaching</subject><subject>Teaching Methods</subject><subject>Texts</subject><issn>1033-2170</issn><issn>2211-050X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp1kEtLxTAQhYMoeH38ABdCwI0uqjNJ07Tu5OITwY2Cu5CbpFJpk2vSLvz35lIREVyEgZxvzswcQo4QzhFAXiTkvCkLwM3jvKi3yIIxxAIEvG6TBUL-ZChhl-yl9A4gOK9gQV6WwRu3Hifd06FLp5O3LqZRe9v5t3RGQ0vbqM3YBZ8u6U0MA9XRaToE6_pEx0CHqR-7de-oG1bBdoPzYzogO63ukzv8rvvk5eb6eXlXPD7d3i-vHgvDJY7FClemtqwVtipLVq9KZ1sNvNFWoDUaTF1aLhAZWtewSjJAbCpRS2bLBkXN98np7LuO4WNyaVT5BuP6XnsXpqRQSuAyn11l9OQP-h6m6PN2CispeXZGmSmcKRNDStG1ah27QcdPhaA2Qas5aJWDVpug1WaJ47nHxc788NcPCKKpRZN1Nuspa_7NxV-T_zX9Au8ciPA</recordid><startdate>20150601</startdate><enddate>20150601</enddate><creator>Zhang, Xiaofen</creator><creator>Clements, M. 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A. (Ken) ; Ellerton, Nerida F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c371t-b1bc8d2f5d64428b4edfa039ad51dca0c84d351121de92672011965872d491583</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Achievement Gains</topic><topic>Concept Formation</topic><topic>Dynamic tests</topic><topic>Education</topic><topic>Elementary School Mathematics</topic><topic>Elementary school students</topic><topic>Fractions</topic><topic>Grade 5</topic><topic>Instructional Effectiveness</topic><topic>Intervention</topic><topic>Interviews</topic><topic>Learning</topic><topic>Mathematical Concepts</topic><topic>Mathematical models</topic><topic>Mathematics Achievement</topic><topic>Mathematics Education</topic><topic>Mathematics Instruction</topic><topic>Mathematics Skills</topic><topic>Multiplication</topic><topic>Original Article</topic><topic>Pretests Posttests</topic><topic>Problem Solving</topic><topic>Representations</topic><topic>Students</topic><topic>Teaching</topic><topic>Teaching Methods</topic><topic>Texts</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, Xiaofen</creatorcontrib><creatorcontrib>Clements, M. 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A. (Ken)</au><au>Ellerton, Nerida F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><ericid>EJ1059859</ericid><atitle>Conceptual mis(understandings) of fractions: From area models to multiple embodiments</atitle><jtitle>Mathematics education research journal</jtitle><stitle>Math Ed Res J</stitle><date>2015-06-01</date><risdate>2015</risdate><volume>27</volume><issue>2</issue><spage>233</spage><epage>261</epage><pages>233-261</pages><issn>1033-2170</issn><eissn>2211-050X</eissn><abstract>Area-model representations seem to have been dominant in the teaching and learning of fractions, especially in primary school mathematics curricula. In this study, we investigated 40 fifth grade children’s understandings of the unit fractions,
1
2
,
1
3
and
1
4
, represented through a variety of different models. Analyses of pre-teaching test and interview data revealed that although the participants were adept at partitioning regional models, they did not cope well with questions for which unit fractions were embodied in non-area-model scenarios. Analyses of post-teaching test and interview data indicated that after their participation in an instructional intervention designed according to Dienes’ (
1960
) dynamic principle, the students’ performances on tests improved significantly, and their conceptual understandings of unit fractions developed to the point where they could provide reasonable explanations of how they arrived at solutions. Analysis of retention data, gathered more than 3 months after the teaching intervention, showed that the students’ newly found understandings had, in most cases, been retained.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s13394-014-0133-8</doi><tpages>29</tpages></addata></record> |
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| subjects | Achievement Gains Concept Formation Dynamic tests Education Elementary School Mathematics Elementary school students Fractions Grade 5 Instructional Effectiveness Intervention Interviews Learning Mathematical Concepts Mathematical models Mathematics Achievement Mathematics Education Mathematics Instruction Mathematics Skills Multiplication Original Article Pretests Posttests Problem Solving Representations Students Teaching Teaching Methods Texts |
| title | Conceptual mis(understandings) of fractions: From area models to multiple embodiments |
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