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[{"key": "dc.contributor.author", "value": "Vapa, Miia", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2013-07-26T07:30:01Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2013-07-26T07:30:01Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2013", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1274830", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/41909", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4m\u00e4n tutkielman tarkoituksena on esitell\u00e4 matemaattinen ongelmanratkaisuprosessi, kuuluisimpia ongelmanratkaisumalleja, sek\u00e4 aktivoida lukija kokeilemaan kykyj\u00e4\u00e4n ongelmanratkaisun parissa. Pedagogista n\u00e4k\u00f6kulmaa tutkielmaan tuovat luvut ongelmal\u00e4ht\u00f6isest\u00e4 matematiikan opetuksesta sek\u00e4 peruskoulun ja lukion matematiikan opetuksen tarpeisiin luotu teht\u00e4v\u00e4paketti. Tutkielman tavoitteena on siis, informaatiopaketin lis\u00e4ksi, tehd\u00e4 lukijasta entist\u00e4 osaavampi ja monipuolisempi ongelmanratkaisija niin, ett\u00e4 h\u00e4nen suhtautumisensa k\u00e4sitett\u00e4 \u2019ongelma\u2019 kohtaan muuttuu entist\u00e4 positiivisempaan suuntaan.\u2028Tutkielmassa, niinkuin kaikissa aihetta k\u00e4sitteleviss\u00e4 l\u00e4hdekirjoissa, ongelmanratkaisuprosessi on pilkottu moniin pieniin osasiin, ja tarkasteltu n\u00e4it\u00e4 osasia erill\u00e4\u00e4n itse kokonaisuudesta. Kuitenkin ongelmanratkaisu on ennenkaikkea kokonaisvaltaista, t\u00e4yden tilanteen hahmottavaa toimintaa, jossa l\u00e4ht\u00f6tiedot, p\u00e4\u00e4m\u00e4\u00e4r\u00e4, ratkaisumetodit, intuitio, luovuus, keskittymiskyky, j\u00e4rki ja tunteet sekoittuvat toinen toisiinsa vaikuttaviksi tekij\u00f6iksi, inhimilliseksi ja mielenkiintoiseksi kokemukseksi, joka ongelmanratkaisu pohjimmiltaan on. T\u00e4m\u00e4 kokonaisvaltaisuus n\u00e4kyy my\u00f6s tutkielman lukuisissa viittauksissa (ks. teht\u00e4v\u00e4...) (ks. luku...), jotka yhdist\u00e4v\u00e4t eri osa-alueita saumattomaksi kokonaisuudeksi.\u2028Tutkielman informatiivinen osa alkaa perehtymisell\u00e4 heuristiikkaan, eli \u2019keksimisen tieteeseen\u2019, jota voidaan pit\u00e4\u00e4 vanhimpana ongelmanratkaisun teoreettisena pohdintana. Heuristiikan varhaisimmista teksteist\u00e4 tarkemmin k\u00e4yd\u00e4\u00e4n l\u00e4pi Pappuksen (noin 400 jKr) p\u00e4\u00e4ttelymetodi \u201danalyysi ja synteesi\u201d, joka on yh\u00e4 edelleen muuttumaton ja elinvoimainen matemaattinen ongelmanratkaisutapa.Tutkielmassa esitell\u00e4\u00e4n my\u00f6s ongelmanratkaisuprosessia edist\u00e4vi\u00e4 ongelman muuntelun keinoja, joista monilla on juuret antiikin ajan geometriassa.\u2028Ongelman muuntelun j\u00e4lkeen pohditaan ongelmanratkaisua yleisell\u00e4 tasolla ja perehdyt\u00e4\u00e4n eri ongelmanratkaisumalleihin, kuuluisimpana n\u00e4ist\u00e4 George Polyan (1887- 1985) luoma ongelmanratkaisumalli vuodelta 1948. Metodeja ongelmanratkaisuun - luvussa esitell\u00e4\u00e4n konkreettisia erilaisiin ja -tasoisiin matemaattisiin ongelmiin hy\u00f6dynnett\u00e4vi\u00e4 ongelmanratkaisumalleja, joista useimmat pohjautuvat luvussa 2 esittelemiimme ongelman muuntelun keinoihin. Malleista siirryt\u00e4\u00e4n katsaukseen ongelmanratkaisun opettamisesta kouluissa, sek\u00e4 tulevaisuuden matematiikan opetuksen suuntaan -ongelmal\u00e4ht\u00f6iseen matematiikan opetukseen. Lopuksi pohditaan luovaa ongelmanratkaisua ei niink\u00e4\u00e4n loogisin ja tieteellisin keinoin, vaan enemm\u00e4nkin filosofisin pohdinnoin.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Miia Vapa (mianvapa) on 2013-07-26 07:30:00.462545. 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 2013-07-26T07:30:00Z\nNo. of bitstreams: 2\nURN:NBN:fi:jyu-201307262096.pdf: 661441 bytes, checksum: 4b7e08dd039c2dcf09c2b15a2cd04063 (MD5)\nlicense.html: 107 bytes, checksum: a7d86e598caa500b1b433bbb9dc8ef1c (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2013-07-26T07:30:01Z (GMT). No. of bitstreams: 2\nURN:NBN:fi:jyu-201307262096.pdf: 661441 bytes, checksum: 4b7e08dd039c2dcf09c2b15a2cd04063 (MD5)\nlicense.html: 107 bytes, checksum: a7d86e598caa500b1b433bbb9dc8ef1c (MD5)\n Previous issue date: 2013", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto.", "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": "ongelmanratkaisu", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Ongelmanratkaisu", "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-201307262096", "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": "2013-07-26T07:30:01Z", "language": null, "element": "date", "qualifier": "updated", "schema": "dc"}, {"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": null, "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", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "ongelmanratkaisu", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "opetus", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "heuristiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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