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Article: Students' algebra sense via their understanding of the distributive law

TitleStudents' algebra sense via their understanding of the distributive law
Authors
KeywordsDistributive law
Innovative tasks
Secondary students
Issue Date2010
PublisherRoutledge. The Journal's web site is located at http://www.informaworld.com/smpp/title~content=t775653691~db=all
Citation
Pedagogies, 2010, v. 5 n. 3, p. 251-263 How to Cite?
AbstractThe distributive law or distributive property is a fundamental algebraic property in the arithmetic of numbers and algebraic expressions. This paper reports on an investigation of students' understanding of the distributive law through task-based interviews from the perspectives of constructivists. It explores students' lack of appreciation of the algebraic structure underpinning the distributive law, particularly amongst students who were already proficient in arithmetic and the distributive law. A total of 203 students from one secondary school of average standard in Hong Kong participated in this study, which adopted a cross-sectional approach. Thirty-three students were then interviewed. The study showed that although some students made progress in the understanding and application of the distributive law, others could not make sense of the meaning of variables and algebraic rules. Therefore, their algebra remained a routine instrumental application of rules, and their understanding of the algebraic structure was incomplete. This paper concludes with a discussion on how the tasks used in the interviews provided teachers with an innovative alternative to deepening students' understanding of letters as variables and the distributive law. © 2010 Taylor & Francis.
Persistent Identifierhttp://hdl.handle.net/10722/125518
ISSN
2015 SCImago Journal Rankings: 0.251
References

 

DC FieldValueLanguage
dc.contributor.authorMok, IACen_HK
dc.date.accessioned2010-10-31T11:35:57Z-
dc.date.available2010-10-31T11:35:57Z-
dc.date.issued2010en_HK
dc.identifier.citationPedagogies, 2010, v. 5 n. 3, p. 251-263en_HK
dc.identifier.issn1554-480Xen_HK
dc.identifier.urihttp://hdl.handle.net/10722/125518-
dc.description.abstractThe distributive law or distributive property is a fundamental algebraic property in the arithmetic of numbers and algebraic expressions. This paper reports on an investigation of students' understanding of the distributive law through task-based interviews from the perspectives of constructivists. It explores students' lack of appreciation of the algebraic structure underpinning the distributive law, particularly amongst students who were already proficient in arithmetic and the distributive law. A total of 203 students from one secondary school of average standard in Hong Kong participated in this study, which adopted a cross-sectional approach. Thirty-three students were then interviewed. The study showed that although some students made progress in the understanding and application of the distributive law, others could not make sense of the meaning of variables and algebraic rules. Therefore, their algebra remained a routine instrumental application of rules, and their understanding of the algebraic structure was incomplete. This paper concludes with a discussion on how the tasks used in the interviews provided teachers with an innovative alternative to deepening students' understanding of letters as variables and the distributive law. © 2010 Taylor & Francis.en_HK
dc.languageengen_HK
dc.publisherRoutledge. The Journal's web site is located at http://www.informaworld.com/smpp/title~content=t775653691~db=allen_HK
dc.relation.ispartofPedagogiesen_HK
dc.subjectDistributive lawen_HK
dc.subjectInnovative tasksen_HK
dc.subjectSecondary studentsen_HK
dc.titleStudents' algebra sense via their understanding of the distributive lawen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1554-480X&volume=5&issue=3&spage=251&epage=263&date=2010&atitle=Students%27+Algebra+Sense+Via+Their+Understanding+Of+The+Distributive+Law-
dc.identifier.emailMok, IAC: iacmok@hku.hken_HK
dc.identifier.authorityMok, IAC=rp00939en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1080/1554480X.2010.486156en_HK
dc.identifier.scopuseid_2-s2.0-79960532055en_HK
dc.identifier.hkuros179896en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-79960532055&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume5en_HK
dc.identifier.issue3en_HK
dc.identifier.spage251en_HK
dc.identifier.epage263en_HK
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridMok, IAC=23103801000en_HK

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