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[{"key": "dc.contributor.advisor", "value": "\u00c4kkinen, Tuomo", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "R\u00e4ih\u00e4, Sauli", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2020-03-09T06:09:37Z", "language": "", "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2020-03-09T06:09:37Z", "language": "", "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2019", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/68096", "language": "", "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 pro gradu -tutkielmassa esitell\u00e4\u00e4n Jyv\u00e4skyl\u00e4n yliopiston matematiikan ja tilastotieteen laitoksella luennoitavalle kurssille Lineaarinen algebra ja geometria 1 luotu STACK-teht\u00e4v\u00e4kokoelma ja ty\u00f6prosessin eri vaiheita. STACK-teht\u00e4v\u00e4t soveltuvat ominaisuuksiensa puolesta juuri matemaattisten teht\u00e4vien tekemiseen ja niiden avulla opiskelijoiden on mahdollista saada yksil\u00f6ity\u00e4 palautetta, tukea oppimisessa ja samalla kehitt\u00e4\u00e4 itsen\u00e4isen ty\u00f6skentelyn taitoja.\r\n\r\nTutkielman ensimm\u00e4inen luku k\u00e4sittelee kurssia Lineaarinen algebra ja geometria 1 yleisell\u00e4 tasolla. Luvussa esitell\u00e4\u00e4n my\u00f6s lineaarialgebran erilaisia esitystapoja ja pohditaan virhek\u00e4sitysten merkityst\u00e4 matematiikan oppimisessa. Toisessa luvussa pureudutaan tarkemmin STACK-teht\u00e4vien luomiseen ja ominaisuuksiin. Seuraavissa luvuissa k\u00e4yd\u00e4\u00e4n l\u00e4pi teht\u00e4v\u00e4kokoelma aihepiireitt\u00e4in: Vektorilaskentaa, Lineaarinen yht\u00e4l\u00f6ryhm\u00e4 ja Gaussin ja Jordanin menetelm\u00e4, Vektoriavaruudet ja niiden viritt\u00e4minen, Matriisit ja viimeisen\u00e4 Lineaarikuvaukset. Lukujen sis\u00e4ll\u00f6t noudattavat likimain samaa j\u00e4rjestyst\u00e4 kuin kurssilla ja teht\u00e4v\u00e4kokoelmaan on valittu teht\u00e4vi\u00e4 jokaisen luvun keskeisimmist\u00e4 asiasis\u00e4ll\u00f6ist\u00e4. Jokaisen luvun aluksi esitell\u00e4\u00e4n matematiikkaa teht\u00e4vien taustalla, erityisesti sit\u00e4 teoriaa, jota teht\u00e4vien tekij\u00e4nkin odotetaan tiet\u00e4v\u00e4n. Seuraavaksi esitell\u00e4\u00e4n itse teht\u00e4vi\u00e4: kaikkia ei k\u00e4yd\u00e4 yksityiskohtaisesti l\u00e4pi vaan p\u00e4\u00e4paino on niiss\u00e4 teht\u00e4viss\u00e4, joiden sis\u00e4lt\u00f6ihin opiskelijoilla liittyy virhek\u00e4sityksi\u00e4. Kahdeksannen ja viimeisen varsinaisen luvun aiheena on teht\u00e4v\u00e4kokoelman testaaminen opiskelijoilla, erityisesti sen yhteydess\u00e4 toteutettu kysely ja saatu opiskelijapalaute. Tutkielman lopuksi on koottu viel\u00e4 lyhyesti ajatuksia ty\u00f6prosessista.\r\n\r\nTeht\u00e4v\u00e4kokoelma luotiin syksyn 2019 aikana ja testattiin kurssin opiskelijoilla. Saatu opiskelijapalaute oli p\u00e4\u00e4s\u00e4\u00e4nt\u00f6isesti positiivista. Teht\u00e4v\u00e4t olivat opiskelijoiden mielest\u00e4 selkeit\u00e4 ja monipuolisia, ne testasivat kurssin keskeisi\u00e4 asiasis\u00e4lt\u00f6j\u00e4 ja niist\u00e4 saatu palaute tuki oppimista. Osa opiskelijoista kuitenkin koki STACK-j\u00e4rjestelm\u00e4n k\u00e4yt\u00f6n haasteelliseksi. Opiskelijapalautteen pohjalta teht\u00e4v\u00e4kokoelmaa on kehitetty ja se on tarkoitus ottaa k\u00e4ytt\u00f6\u00f6n osaksi seuraavan syksyn kurssia.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Miia Hakanen (mihakane@jyu.fi) on 2020-03-09T06:09:37Z\r\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2020-03-09T06:09:37Z (GMT). No. of bitstreams: 0\r\n Previous issue date: 2020", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "77", "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.subject.other", "value": "STACK", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "virhek\u00e4sitys", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Itsetarkistuvat STACK-teht\u00e4v\u00e4t kurssille Lineaarinen algebra ja geometria 1", "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-202003092331", "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": 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