{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:14:53Z","timestamp":1753888493088,"version":"3.41.2"},"reference-count":29,"publisher":"FapUNIFESP (SciELO)","license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"am","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Educ. Pesqui."],"abstract":"<jats:p>Resumo As produ\u00e7\u00f5es escritas de estudantes podem ser objeto de an\u00e1lise com vista \u00e0 investiga\u00e7\u00e3o e ao ensino. Neste trabalho, um dos poucos sobre erros e n\u00fameros complexos, analisam-se as produ\u00e7\u00f5es, elaboradas por estudantes do ensino superior, para uma tarefa de demonstra\u00e7\u00e3o de um caso particular da identidade do paralelogramo. Num trabalho que pode dar pistas para a pr\u00e1tica letiva de professores do ensino secund\u00e1rio e do ensino superior, procura-se classificar os esquemas de demonstra\u00e7\u00e3o nessas produ\u00e7\u00f5es, identificar os erros neles cometidos e relacionar estas duas vertentes de an\u00e1lise. A natureza da investiga\u00e7\u00e3o \u00e9 qualitativa, recorrendo \u00e0 an\u00e1lise de conte\u00fado empregando, por um lado, crit\u00e9rios pr\u00e9vios de categoriza\u00e7\u00f5es de esquemas de demonstra\u00e7\u00e3o e, por outro, crit\u00e9rios novos de categoriza\u00e7\u00f5es de erros. Constatou-se que os estudantes utilizaram, principalmente, esquemas de demonstra\u00e7\u00e3o de convic\u00e7\u00e3o externa, inclu\u00eddos numa subcategoria nova designada por n\u00e3o v\u00e1lidos no universo, e esquemas de demonstra\u00e7\u00e3o dedutivos, inclu\u00eddos num n\u00edvel novo que se caracteriza por discernimento incipiente da compreens\u00e3o da tarefa, do contexto matem\u00e1tico, de hip\u00f3teses e tese, e dos conhecimentos pr\u00e9vios a mobilizar. Os erros dominantes nas produ\u00e7\u00f5es est\u00e3o relacionados \u00e0 compreens\u00e3o dos conceitos de linearidade de uma fun\u00e7\u00e3o e de m\u00f3dulo de um n\u00famero complexo, apresentando-se poss\u00edveis explica\u00e7\u00f5es para os mesmos. Apesar de n\u00e3o se identificar uma rela\u00e7\u00e3o propriamente significativa entre os esquemas de demonstra\u00e7\u00e3o produzidos pelos estudantes e os erros cometidos, obteve-se material para constru\u00e7\u00e3o e discuss\u00e3o de quest\u00f5es conceituais no \u00e2mbito do t\u00f3pico n\u00fameros complexos.<\/jats:p>","DOI":"10.1590\/s1678-4634202248235587","type":"journal-article","created":{"date-parts":[[2022,2,16]],"date-time":"2022-02-16T12:12:04Z","timestamp":1645013524000},"source":"Crossref","is-referenced-by-count":2,"title":["Erros em esquemas de demonstra\u00e7\u00e3o com n\u00fameros complexos"],"prefix":"10.1590","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0266-7055","authenticated-orcid":false,"given":"Patr\u00edcia Damas","family":"Beites","sequence":"first","affiliation":[{"name":"Universidade da Beira Interior,  Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8589-1310","authenticated-orcid":false,"given":"Maria 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