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[{"key": "dc.contributor.advisor", "value": "Juutinen, Petri", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Koski, Nanni", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2017-09-10T11:53:19Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2017-09-10T11:53:19Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2017", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1722126", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/55299", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Mit\u00e4 enemm\u00e4n oppilas tai opiskelija oivaltaa itse, sit\u00e4 enemm\u00e4n h\u00e4n oppii ja nauttii ongelmanratkaisusta. T\u00e4m\u00e4 ajatus toimii l\u00e4ht\u00f6kohtana tutkielmassa. \nK\u00e4sitelt\u00e4v\u00e4t teht\u00e4v\u00e4t ovat tasoltaan yl\u00e4kouluun ja / tai lukioon soveltuvia. Tutkielma antaa opettajalle k\u00e4yt\u00e4nn\u00f6nl\u00e4heisi\u00e4 esimerkkej\u00e4 opetustilanteessa hy\u00f6dynnett\u00e4vist\u00e4 todenn\u00e4k\u00f6isyysongelmista. Teht\u00e4vist\u00e4 esitet\u00e4\u00e4n useita ratkaisuvaihtoehtoja, jotta opettajan on helpompi samaistua erilaisiin ajattelutapoihin. Mik\u00e4 t\u00e4rkeint\u00e4, tutkielmaan on kehitetty kysymyksi\u00e4, joilla oppijaa voi ohjata hienovaraisesti eteenp\u00e4in ratkaisussaan. Tavoitteena on, ett\u00e4 ratkoja keksii kysymysten avulla itse ratkaisun kuhunkin ongelmaan. \n\nOngelmanratkaisutaitojen kehitt\u00e4minen kuuluu peruskoulun ja lukion opetussuunnitelman perusteisiin (Opetushallitus, 2016 ja 2015). \nTutkielmassa esitell\u00e4\u00e4n Polyan (1973) ongelmanratkaisumalli, jota hy\u00f6dynnet\u00e4\u00e4n ongelmien ratkaisemisessa. Malli perustuu nelj\u00e4\u00e4n vaiheeseen: ongelman ymm\u00e4rt\u00e4minen, ratkaisusuunnitelman tekeminen, ratkaisusuunnitelman toteuttaminen ja ratkaisun tarkastelu. Viimeiseen kohtaan kuuluu my\u00f6s opitun soveltaminen toisessa ongelmassa. T\u00e4h\u00e4n tarkoitukseen sek\u00e4 opetuksen eriytt\u00e4miseen voi k\u00e4ytt\u00e4\u00e4 tutkielmassa esitettyj\u00e4 lis\u00e4teht\u00e4vi\u00e4.\n\nPohdinnassa esitet\u00e4\u00e4n erilaisia keinoja ottaa ongelmanratkaisu osaksi opetusta. \nKoska ongelmanratkaisu kuuluu useiden oppiaineiden opetussuunnitelmaan, voisi peruskouluun rakentaa ongelmanratkaisun ymp\u00e4rille monialaisen teemap\u00e4iv\u00e4n.\nEsimerkkin\u00e4 esitet\u00e4\u00e4n suomen kielen opetukseen sopiva ongelma.\nPohdinnassa tarkastellaan my\u00f6s matemaattisen ongelmanratkaisun ja peleiss\u00e4 esiintyvien ongelmien yht\u00e4l\u00e4isyyksi\u00e4 ja eroja. Pelien n\u00e4k\u00f6kulmasta oppilaat voivat kehitt\u00e4\u00e4 k\u00e4sityst\u00e4\u00e4n ongelmanratkaisusta.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Nanni Koski (nataanko) on 2017-09-10 11:53:18.674874. Form: Pro gradu -lomake (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake). JyX data: [jyx_publishing-allowed (fi) =True]", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija.group@korppi.jyu.fi) on 2017-09-10T11:53:19Z\nNo. of bitstreams: 2\nURN:NBN:fi:jyu-201709103693.pdf: 949210 bytes, checksum: 67dc15f4b3762ee43d01cffd847cb5d5 (MD5)\nlicense.html: 4810 bytes, checksum: 6b1701ce6bd73d9ff372007f4482ad89 (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2017-09-10T11:53:19Z (GMT). No. of bitstreams: 2\nURN:NBN:fi:jyu-201709103693.pdf: 949210 bytes, checksum: 67dc15f4b3762ee43d01cffd847cb5d5 (MD5)\nlicense.html: 4810 bytes, checksum: 6b1701ce6bd73d9ff372007f4482ad89 (MD5)\n Previous issue date: 2017", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (76 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": "Po\u0301lya, George", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Polyan ongelmanratkaisumalli", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Ongelmanratkaisun opettaminen todenn\u00e4k\u00f6isyysteht\u00e4viss\u00e4", "language": null, "element": "title", "qualifier": null, "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-201709103693", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.date.updated", "value": "2017-09-10T11:53:19Z", "language": null, "element": "date", "qualifier": "updated", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": null, "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": "fi", "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": null, "element": "subject", 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