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[{"key": "dc.contributor.advisor", "value": "Lehrb\u00e4ck, Juha", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Kovanen, Taina", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2022-06-17T06:21:51Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2022-06-17T06:21:51Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2022", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/81829", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Sini ja kosini ovat matemaattisen mallintamisen ja analyysin perustavaa laatua\nolevia ty\u00f6kalufunktioita. Syv\u00e4llisempi matematiikan ymm\u00e4rrys edellytt\u00e4\u00e4 trigonometristen funktioiden k\u00e4ytt\u00e4ytymisen ja ominaisuuksien hahmottamista. T\u00e4m\u00e4n tutkielman tarkoitus on tarjota lukijalleen tietoa sini- ja kosinifunktion erilaisista m\u00e4\u00e4rittelytavoista sek\u00e4 niiden haasteista ja mahdollisuuksista pedagogiikan n\u00e4k\u00f6kulmasta tarkasteltuna. Sini ja kosini ovat syntyneet t\u00e4htitieteen parissa, ja niiden vaikutus on ollut suuri my\u00f6s k\u00e4sitykseen maapallon liikkeist\u00e4 suhteessa aurinkoon. Matematiikan kehittyess\u00e4 sini ja kosini saivat paikkansa funktioiden joukossa. Niiden avulla mallinnetaan monien eri tieteenalojen sovelluksia. Sini ja kosini voidaan m\u00e4\u00e4ritell\u00e4 geometrisesti yksikk\u00f6ympyr\u00e4n, suorakulmaisen kolmion sek\u00e4 pinta-alan avulla. Analyyttisemmin sini\u00e4 ja kosinia l\u00e4hestyt\u00e4\u00e4n m\u00e4\u00e4rittelem\u00e4ll\u00e4 ne differentiaaliyht\u00e4l\u00f6iden ja kompleksilukujen avulla.\nPeruskoulussa k\u00e4ytet\u00e4\u00e4n yleens\u00e4 m\u00e4\u00e4rittelyss\u00e4 suorakulmaista kolmiota ja lukiossa lis\u00e4ksi yksikk\u00f6ympyr\u00e4\u00e4. Muut m\u00e4\u00e4rittelytavat opiskelija kohtaa korkeakouluopinnoissa. Tutkimusten mukaan opiskelijat kokevat trigonometrian vaikeana matematiikan osa-alueena. Mielenkiintoista on se, ett\u00e4 niiden opettamiseen ja oppimiseen liittyvi\u00e4 tutkimuksia on tehty v\u00e4h\u00e4n, ja tutkimuksissa otoskoot ovat olleet pieni\u00e4. Yksikk\u00f6ympyr\u00e4ss\u00e4 k\u00e4ytett\u00e4v\u00e4n mittayksik\u00f6n eli radiaanien ymm\u00e4rt\u00e4minen koetaan usein haasteellisena. Luvussa 4 esitell\u00e4\u00e4n er\u00e4\u00e4ss\u00e4 tutkimuksessa k\u00e4ytetty\u00e4 l\u00e4hestymistapaa sinin ja kosinin opettamiseen, mill\u00e4 oli t\u00e4ss\u00e4 pieness\u00e4 opiskelijaryhm\u00e4ss\u00e4 saavutettu oppimisessa hyvi\u00e4 tuloksia.\nKoska sini ja kosini ovat erityisesti jatko-opiskelun ja eri tieteenalojen sovellusten\nkannalta keskeisi\u00e4 funktioita, niiden opettamiseen ja oppimiseen liittyv\u00e4\u00e4 tutkimusta tarvitaan jatkossa. Aineenopettajaksi opiskeleville olisi hyv\u00e4 tarjota opinnoissa sini- ja kosinifunktioon liittyvi\u00e4 analyyttisia m\u00e4\u00e4rittelytapoja ja k\u00e4ytt\u00f6sovelluksia kokonaisuutena, jotta heille muodostuisi yhten\u00e4inen ja laaja-alainen ymm\u00e4rrys, kuinka keskeisi\u00e4 funktioita ne ovat. N\u00e4in he voivat omassa ty\u00f6ss\u00e4\u00e4n antaa oppilaille ev\u00e4it\u00e4 trigonometrian oppimiseen.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Miia Hakanen (mihakane@jyu.fi) on 2022-06-17T06:21:51Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2022-06-17T06:21:51Z (GMT). No. of bitstreams: 0\n Previous issue date: 2022", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "41", "language": "", "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.title", "value": "Sinin ja kosinin loiste", "language": "", "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-202206173438", "language": "", "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": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikan opettajankoulutus", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Teacher education programme in Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "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": "restrictedAccess", "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": "", "element": "subject", "qualifier": "oppiainekoodi", "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": "oppiminen", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "trigonometria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "trigonometriset funktiot", "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.rights.accessrights", "value": "The author has not given permission to make the work publicly available electronically. Therefore the material can be read only at the archival workstation at Jyv\u00e4skyl\u00e4 University Library (https://kirjasto.jyu.fi/collections/archival-workstation).", "language": "en", "element": "rights", "qualifier": "accessrights", "schema": "dc"}, {"key": "dc.rights.accessrights", "value": "Tekij\u00e4 ei ole antanut lupaa avoimeen julkaisuun, joten aineisto on luettavissa vain Jyv\u00e4skyl\u00e4n yliopiston kirjaston arkistoty\u00f6semalta. Ks. https://kirjasto.jyu.fi/kokoelmat/arkistotyoasema..", "language": "fi", "element": "rights", "qualifier": "accessrights", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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