{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T22:47:33Z","timestamp":1740178053006,"version":"3.37.3"},"reference-count":0,"publisher":"Editora e Distribuidora Educacional","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JIEEM"],"abstract":"<jats:p>ResumoO modelo matem\u00e1tico que, segundo os livros de Hist\u00f3ria da Matem\u00e1tica, \u00e9 atribu\u00eddo, equivocadamente ao matem\u00e1tico Leonardo Pisano, preserva hodiernamente um vigor irrefre\u00e1vel de um progresso maior de evolu\u00e7\u00e3o e de generalidade. N\u00e3o obstante, um car\u00e1ter de obl\u00edvio total pode ser observado no que concerne a uma maior divulga\u00e7\u00e3o e, tamb\u00e9m, melhor forma\u00e7\u00e3o do professor de Matem\u00e1tica, concernentemente a determinados assuntos matem\u00e1ticos espec\u00edficos. Diante de tal entrave, o artigo atual apresenta a descri\u00e7\u00e3o das an\u00e1lises preliminares e an\u00e1lise a priori de uma Engenharia Did\u00e1tica, com o tema quaternions (generalizados) de Fibonacci. A relev\u00e2ncia deste assunto se evidencia, na medida em que, o mesmo pode ser encontrado apenas em artigos cient\u00edficos de Matem\u00e1tica que reproduzem propriedades formais cifradas. Assim, com arrimo da Teoria das Situa\u00e7\u00f5es Did\u00e1ticas \u2013 TSD, o trabalho apresenta, de modo pormenorizado, um planejamento para as fases dial\u00e9ticas de a\u00e7\u00e3o, formula\u00e7\u00e3o, valida\u00e7\u00e3o e institucionaliza\u00e7\u00e3o. Por fim, a atual proposta explora elementos que balizam sua eventual aplica\u00e7\u00e3o e experimenta\u00e7\u00e3o em sala de aula, tendo como p\u00fablico alvo, professores de Matem\u00e1tica em forma\u00e7\u00e3o inicial.\r\nPalavras-Chave: Hist\u00f3ria da Matem\u00e1tica; Sequ\u00eancia de Fibonacci; Investiga\u00e7\u00e3o hist\u00f3rica.\r\nAbstractThe mathematical model, according to the History of Mathematics books, is attributed wrongly to the mathematician Leonardo Pisano, in our times preserves an unstoppable force for further progress of evolution and generality. Nonetheless, a complete forgetfulness character can be seen in relation to greater disclosure and also improved training of the mathematics teacher, concernentemente to specific mathematical topics. Faced with this obstacle, the current article presents a description of the preliminary analysis and a priori analysis of a Didactic Engineering, with the theme quaternions (generalized) Fibonacci. The importance of this matter is evidenced, in so far as the same can be found only in scientific articles Mathematics reproducing encrypted formal properties. So with retaining the Theory of Didactic Situations - TSD, the work presents, in detail, a plan for the dialectics stages of action, formulation, validation and institutionalization. Finally, the current proposal explores elements that guide its possible application and experimentation in the classroom, with the target audience, mathematics teachers in initial training.\r\nKeywords: Didactical Engineering; Fibonacci\u00b4s sequence; Quaternion of Fibonacci; Historical investigation.<\/jats:p>","DOI":"10.17921\/2176-5634.2020v13n3p308-320","type":"journal-article","created":{"date-parts":[[2021,5,4]],"date-time":"2021-05-04T17:18:14Z","timestamp":1620148694000},"page":"308-320","source":"Crossref","is-referenced-by-count":0,"title":["Engenharia Did\u00e1tica: an\u00e1lises preliminares e a priori para a no\u00e7\u00e3o dos Quaternions de Fibonacci."],"prefix":"10.17921","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3710-1561","authenticated-orcid":false,"given":"Francisco Regis","family":"Vieira Alves","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1966-7097","authenticated-orcid":false,"given":"Renata Passos Machado","family":"Vieira","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6917-5093","authenticated-orcid":false,"given":"Paula Maria","family":"Machado Cruz Catarino","sequence":"additional","affiliation":[]}],"member":"7245","published-online":{"date-parts":[[2021,1,12]]},"container-title":["Jornal Internacional de Estudos em Educa\u00e7\u00e3o Matem\u00e1tica"],"original-title":[],"link":[{"URL":"https:\/\/jieem.pgsscogna.com.br\/jieem\/article\/view\/8284\/5829","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T11:56:35Z","timestamp":1696506995000},"score":1,"resource":{"primary":{"URL":"https:\/\/seer.pgsskroton.com\/index.php\/jieem\/article\/view\/8284"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,12]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,12,22]]}},"URL":"https:\/\/doi.org\/10.17921\/2176-5634.2020v13n3p308-320","relation":{},"ISSN":["2176-5634"],"issn-type":[{"type":"electronic","value":"2176-5634"}],"subject":[],"published":{"date-parts":[[2021,1,12]]}}}