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[{"key": "dc.contributor.author", "value": "L\u00e4nsivuori, Sofia", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2024-06-06T13:11:19Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2024-06-06T13:11:19Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2024", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/95623", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 tutkielmassa tutustutaan todenn\u00e4k\u00f6isyyslaskentaan ja sen opetukseen peruskoulussa ja lukiossa. Todenn\u00e4k\u00f6isyyslaskennan k\u00e4sitett\u00e4 aletaan rakentamaan alakoulusta aina yliopistomatematiikkaan asti. Tutkielmassa opitaan laskemaan erilaisia todenn\u00e4k\u00f6isyyksi\u00e4, kuten klassisia, geometrisia ja tilastollisia todenn\u00e4k\u00f6isyyksi\u00e4. Tutkielmassa k\u00e4sitell\u00e4\u00e4n my\u00f6s kombinatoriikkaa sek\u00e4 diskreetti\u00e4 jakaumaa. Koulumatematiikan aiheiden lis\u00e4ksi opitaan muun muassa todenn\u00e4k\u00f6isyysavaruuden, todenn\u00e4k\u00f6isyysmitan ja sigma-algebran k\u00e4sitteet ja k\u00e4yd\u00e4\u00e4n l\u00e4pi erilaisia esimerkkej\u00e4. \n\nM\u00e4\u00e4ritelmien ja lauseiden esittelyn ohessa vertaillaan my\u00f6s sit\u00e4, miten n\u00e4it\u00e4 k\u00e4sitell\u00e4\u00e4n eri kouluasteilla, ja mit\u00e4 eroavaisuuksia m\u00e4\u00e4rittelyiss\u00e4 on. T\u00e4m\u00e4n lis\u00e4ksi k\u00e4yd\u00e4\u00e4n l\u00e4pi erilaisia esimerkkej\u00e4 ja verrataan n\u00e4iden teht\u00e4vien haastavuutta peruskoulun ja lukion v\u00e4lill\u00e4. Vertailun apuna k\u00e4ytet\u00e4\u00e4n Sanoma Pron ja Otavan eri oppikirjojen sis\u00e4lt\u00f6j\u00e4 sek\u00e4 lukio-opetuksen ja perusopetuksen opetussuunnitelmia. Lopuksi tutkitaan lukiomatematiikan ja mittateorian eroavaisuuksia.\n\nTutkielman tarkoitus on antaa etenkin matematiikan aineenopettajille hyv\u00e4t valmiudet opettaa todenn\u00e4k\u00f6isyyslaskentaa peruskoulussa ja lukiossa ja syvent\u00e4\u00e4 omaa osaamistaan mittateorian osa-alueella. Tutkielman luettuaan lukijalla on k\u00e4sitys siit\u00e4, mit\u00e4 aiheita todenn\u00e4k\u00f6isyyslaskennasta opetetaan peruskoulussa ja lukiossa, ja mitk\u00e4 aiheet j\u00e4\u00e4v\u00e4t koulumatematiikan ulkopuolelle.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2024-06-06T13:11:19Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2024-06-06T13:11:19Z (GMT). No. of bitstreams: 0\n Previous issue date: 2024", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "71", "language": "", "element": "format", "qualifier": "extent", "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": "Todenn\u00e4k\u00f6isyyslaskentaa koulumatematiikasta mittateoriaan", "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-202406064385", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "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": "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": "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": "todenn\u00e4k\u00f6isyyslaskenta", "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": "lukio", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "opetussuunnitelmat", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}]
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