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[{"key": "dc.contributor.author", "value": "Muje, Minna", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2011-05-30T10:30:23Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2011-05-30T10:30:23Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2011", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1159368", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/27094", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Algebran on useissa tutkimuksissa havaittu olevan oppilaille hankala aihe. Kuitenkin sen opettamisesta tavanomaista aiemmin on saatu my\u00f6nteisi\u00e4 kokemuksia. T\u00e4m\u00e4 tutkimus selvitti viidesluokkalaisten valmiuksia k\u00e4sitell\u00e4 muuttujia matematiikassa. Aiempien tutkimusten mukaan algebran oppimista helpottavia keskeisi\u00e4 seikkoja ovat muun muassa kyky merkit\u00e4 muuttuja, k\u00e4sitys muuttujasta sek\u00e4 kyky ratkaista muuttujia sis\u00e4lt\u00e4vi\u00e4 teht\u00e4vi\u00e4. N\u00e4m\u00e4 seikat olivat perusta t\u00e4m\u00e4n tutkimuksen ongelmille. Lis\u00e4ksi selvitettiin yleisi\u00e4 virhetyyppej\u00e4, joita esiintyy oppilaiden ratkaistessa muuttujia sis\u00e4lt\u00e4vi\u00e4 teht\u00e4vi\u00e4. Kiinnostuksen kohteena oli my\u00f6s ohjauksen vaikutus oppilaiden kykyyn k\u00e4sitell\u00e4 muuttujia. Tutkimukseen osallistui 62 viidesluokkalaista. Tutkittavat tekiv\u00e4t matemaattista osaamista mittaavan alkutestin, muuttujan merkitsemiskyky\u00e4 mittaavan testin sek\u00e4 testin, joka selvitti oppilaiden k\u00e4sityst\u00e4 muuttujaa merkitsev\u00e4st\u00e4 symbolista ja kyky\u00e4 ratkaista tuntemattomia lukuja sis\u00e4lt\u00e4vi\u00e4 teht\u00e4vi\u00e4. Lis\u00e4ksi yhdeks\u00e4\u00e4 oppilasta haastateltiin. Aineistoa k\u00e4siteltiin sek\u00e4 laadullisesti ett\u00e4 m\u00e4\u00e4r\u00e4llisesti. Tutkimus osoitti, ett\u00e4 puolet oppilaista kykenee merkitsem\u00e4\u00e4n muuttujan. Kaikilla oppilailla havaittiin olevan k\u00e4sitys muuttujasta, ja tuntemattomia lukuja sis\u00e4lt\u00e4vien teht\u00e4vien ratkaiseminen sujui tutkituilta hyvin. Oppilailla esiintyi kuitenkin muuttujien k\u00e4sittelyyn liittyvi\u00e4 virheellisi\u00e4 k\u00e4sityksi\u00e4. Tutkimus osoitti lis\u00e4ksi, ett\u00e4 tuettuna oppilaat kykenev\u00e4t korkeatasoisempaan algebralliseen ajatteluun. Tutkimuksen tulokset antavat k\u00e4sityksen oppilaiden valmiudesta algebralliseen ajatteluun ja auttavat kehitt\u00e4m\u00e4\u00e4n algebran opetusta.", "language": null, "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Minna Muje (mimamuje) on 2011-05-30 10:30:21.803678. Form: Pro gradu -lomake (1 tekij\u00e4) (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake-1-tekijae). JyX data:", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija@noreply.fi) on 2011-05-30T10:30:23Z\nNo. of bitstreams: 2\nURN:NBN:fi:jyu-2011053010936.pdf: 1747777 bytes, checksum: 33a7dbd219d5725b09b819044198511e (MD5)\nlicense.html: 5003 bytes, checksum: ff5cdc5279a16a1a62e613b551136147 (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2011-05-30T10:30:23Z (GMT). No. of bitstreams: 2\nURN:NBN:fi:jyu-2011053010936.pdf: 1747777 bytes, checksum: 33a7dbd219d5725b09b819044198511e (MD5)\nlicense.html: 5003 bytes, checksum: ff5cdc5279a16a1a62e613b551136147 (MD5)\n Previous issue date: 2011", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "75 sivua", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "matematiikan opettaminen", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "algebra", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "esialgebra", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "muuttuja", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "\"Ne on vaihtelevia lukuja\" : muuttujat viidesluokkalaisten matematiikassa", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.title.alternative", "value": "Muuttujat viidesluokkalaisten matematiikassa", "language": null, "element": "title", "qualifier": "alternative", "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-2011053010936", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.dcmitype", 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