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[{"key": "dc.contributor.advisor", "value": "Juutinen, Petri", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Sauram\u00e4ki, Arja", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2017-12-13T11:07:57Z", "language": "", "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2017-12-13T11:07:57Z", "language": "", "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:1808357", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/56300", "language": "", "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Opinn\u00e4ytety\u00f6ss\u00e4 selvitell\u00e4\u00e4n lukion pitk\u00e4n matematiikan opiskelijoiden k\u00e4sityksi\u00e4 visuaalisesta tangenttisuorasta (lyh. tangentista). Ty\u00f6 sis\u00e4lt\u00e4\u00e4 tietokoosteen tutkielman aihepiirin visuaalisesta tangentista. Lukio-opiskelijoiden k\u00e4sityksi\u00e4 tangentista esitell\u00e4\u00e4n Tallin 1980-luvun tietokoneavusteisesta opetuskokeilusta ja Bizan 2000-luvun tutkimuksesta. Empiirisess\u00e4 tutkimuksessa tutkittiin lukion pitk\u00e4n matematiikan oppikirjasarjan visuaalista tangenttia.\r\n\r\nIhmiset ymm\u00e4rt\u00e4v\u00e4t aistein havainnoitavat kohteet p\u00e4\u00e4osin intuition avulla, kun taasen matemaattiset k\u00e4sitteet voidaan ymm\u00e4rt\u00e4\u00e4 aksioomien, m\u00e4\u00e4ritelmien ja lauseiden pohjalta. Kuitenkin Bizan laaja tutkimus osoittaa, ett\u00e4 lukio-opiskelijoiden k\u00e4sityksiin tangentista vaikuttavat merkitt\u00e4v\u00e4sti heid\u00e4n geometriassa kohtaamansa visuaaliset tangentit. Opiskelijat voivat aluksi ymm\u00e4rt\u00e4\u00e4 visuaalisen tangentin esimerkiksi suorana, joka sivuaa koko k\u00e4yr\u00e4\u00e4 yhdess\u00e4 pisteess\u00e4 leikkaamatta k\u00e4yr\u00e4\u00e4. Opiskelijoiden yksil\u00f6lliset k\u00e4sitykset voivat s\u00e4ily\u00e4 tai ne voivat kehitty\u00e4 my\u00f6hemmin alkuvaiheen suuntaisina my\u00f6s paikallista geometrista tai analyyttist\u00e4 n\u00e4k\u00f6kulmaa edellytt\u00e4viss\u00e4 uusissa tilanteissa. N\u00e4in Bizan mukaan opiskelijoiden geometriassa muotoutuneet ajattelumallit riitt\u00e4v\u00e4t kuvaamaan heid\u00e4n k\u00e4sityksi\u00e4\u00e4n tangentista koko lukioajan ja lukion j\u00e4lkeenkin. K\u00e4sitysten tulisi koko tangentin oppimisprosessin ajan konstruoitua todenmukaisina, sill\u00e4 vahvoiksi kehittyneit\u00e4 mielensis\u00e4isi\u00e4 ajattelumalleja ei ole en\u00e4\u00e4 helppo muokata. Toisaalta tarkoituksenmukaisesti valittujen visuaalisten tangenttien avulla opiskelijoiden k\u00e4sityksi\u00e4 voidaan oppimisen alkuvaiheesta alkaen my\u00f6s korjata ja kehitt\u00e4\u00e4. Lis\u00e4ksi visuaalisuus tukee opiskelijoiden luovaa matemaattista ajattelua sek\u00e4 mielikuvitusta, joka toimii yhteydess\u00e4 intuitioon ja luovuuteen.\r\n\r\nLaadullisessa tapaustutkimuksessa kuvaillaan yhden lukion pitk\u00e4n matematiikan oppikirjasarjan visuaalista tangenttia. Kirjasarjan analysoiduissa Geometria- ja Analyyttinen geometria -kirjoissa tarkastellaan visuaalisena ainoastaan ympyr\u00e4n tangenttia. Kirjoissa ei verbaalisesti nosteta esille kuvioissa havaittavia tangentin yleisi\u00e4 ominaisuuksia. Tangentin k\u00e4site yleistyy merkitt\u00e4v\u00e4sti vasta Derivaatta -kirjassa, kun derivaattaa havainnollistetaan hahmotellulla tangentilla. Visuaalinen tangentti j\u00e4\u00e4 kumminkin hiukan ep\u00e4selv\u00e4ksi. Pienimuotoisen tutkimuksen pohjalta n\u00e4ytt\u00e4isi silt\u00e4, ett\u00e4 oppikirjan analysoidussa osuudessa voisi hy\u00f6dynt\u00e4\u00e4 enemm\u00e4n visuaalisen tangentin ja intuition merkityksi\u00e4.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Arja Sauram\u00e4ki (artusaur) on 2017-12-13 11:07:57.013603. 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 2017-12-13T11:07:57Z\r\nNo. of bitstreams: 2\r\nURN:NBN:fi:jyu-201712134664.pdf: 3254532 bytes, checksum: b4b39d9203e20687e239f54f0e69d6c7 (MD5)\r\nlicense.html: 4815 bytes, checksum: 6152a0a0cf1ba257e777f48cd2c8bac5 (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2017-12-13T11:07:57Z (GMT). No. of bitstreams: 2\r\nURN:NBN:fi:jyu-201712134664.pdf: 3254532 bytes, checksum: b4b39d9203e20687e239f54f0e69d6c7 (MD5)\r\nlicense.html: 4815 bytes, checksum: 6152a0a0cf1ba257e777f48cd2c8bac5 (MD5)\r\n Previous issue date: 2017", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (91 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": "analyyttinen tangentti", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": 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