{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:09:48Z","timestamp":1753888188990,"version":"3.41.2"},"reference-count":23,"publisher":"FapUNIFESP (SciELO)","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"am","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT","award":["2020.08843.BD"],"award-info":[{"award-number":["2020.08843.BD"]}]},{"name":"FCT","award":["UIDB\/04107\/2020"],"award-info":[{"award-number":["UIDB\/04107\/2020"]}]},{"name":"UIDEF","award":["2020.08843.BD"],"award-info":[{"award-number":["2020.08843.BD"]}]},{"name":"UIDEF","award":["UIDB\/04107\/2020"],"award-info":[{"award-number":["UIDB\/04107\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bolema"],"abstract":"<jats:p>Resumo Este artigo tem como objetivo compreender como, no quadro de uma experi\u00eancia de ensino que enfatiza a promo\u00e7\u00e3o do racioc\u00ednio matem\u00e1tico, se caracterizam as conjeturas, generaliza\u00e7\u00f5es e justifica\u00e7\u00f5es de alunos de 8.\u00b0 ano, ao resolverem tarefas de cunho alg\u00e9brico. Adotando uma abordagem qualitativa e interpretativa, utilizamos as resolu\u00e7\u00f5es escritas e orais de alunos de 8.\u00b0 ano ao resolverem tarefas alg\u00e9bricas, no contexto de uma experi\u00eancia de ensino baseada na promo\u00e7\u00e3o do racioc\u00ednio matem\u00e1tico. Como resultados, destacamos o surgimento de v\u00e1rias conjeturas e generaliza\u00e7\u00f5es emp\u00edricas, com algumas generaliza\u00e7\u00f5es te\u00f3ricas\/estruturais\/simb\u00f3licas. Destacamos, tamb\u00e9m, o uso de justifica\u00e7\u00f5es emp\u00edricas, por exemplos aleat\u00f3rios, selecionados e gen\u00e9ricos, e poucos epis\u00f3dios de justifica\u00e7\u00f5es por convic\u00e7\u00e3o externa, tanto por manipula\u00e7\u00f5es simb\u00f3licas como por apar\u00eancia dos argumentos. Al\u00e9m disso, ressaltamos que a discuss\u00e3o em torno das generaliza\u00e7\u00f5es emp\u00edricas favoreceu a mobiliza\u00e7\u00e3o de outras formas de justifica\u00e7\u00e3o que n\u00e3o estavam baseadas apenas no uso de exemplos.<\/jats:p>","DOI":"10.1590\/1980-4415v39a230164","type":"journal-article","created":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T12:44:17Z","timestamp":1743770657000},"source":"Crossref","is-referenced-by-count":0,"title":["Racioc\u00ednio Matem\u00e1tico de Alunos do 8.\u00ba ano: Conjeturas, generaliza\u00e7\u00f5es e justifica\u00e7\u00f5es"],"prefix":"10.1590","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8516-9715","authenticated-orcid":false,"given":"Kelly","family":"Aguiar","sequence":"first","affiliation":[{"name":"Universidade de Lisboa (IE-ULisboa),  Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6203-7616","authenticated-orcid":false,"given":"Jo\u00e3o Pedro da","family":"Ponte","sequence":"additional","affiliation":[{"name":"Universidade de Lisboa (IE-ULisboa),  Portugal"}]}],"member":"530","published-online":{"date-parts":[[2025]]},"reference":[{"key":"ref1","series-title":"Mathematics, teachers and children.","first-page":"216","volume-title":"Aspects of proof in pupils\u2019 practice of school mathematics.","author":"BALACHEFF N.","year":"1988"},{"year":"1994","series-title":"Investiga\u00e7\u00e3o qualitativa em educa\u00e7\u00e3o: uma introdu\u00e7\u00e3o \u00e0 teoria e aos m\u00e9todos","author":"BOGDAN R.","key":"ref2"},{"year":"2018","series-title":"Base Nacional Comum Curricular: educa\u00e7\u00e3o \u00e9 a base","key":"ref3"},{"key":"ref4","first-page":"125","article-title":"Guiding principles for teaching mathematics via reasoning and proving","author":"BUCHBINDER O.","year":"2022","journal-title":"Proceedings..."},{"year":"2021","series-title":"Aprendizagens Essenciais de Matem\u00e1tica no Ensino B\u00e1sico","author":"CANAVARRO A. P.","key":"ref5"},{"issue":"1","key":"ref6","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s11858-007-0067-7","article-title":"Early algebra and mathematical generalization","volume":"40","author":"CARRAHER D.","year":"2008","journal-title":"ZDM Mathematics Education"},{"key":"ref7","series-title":"Handbook of international research in mathematics education","first-page":"481","volume-title":"Design research: An analysis and critique.","author":"COBB P.","year":"2016","edition":"3"},{"year":"2017","series-title":"Tasks and competencies in the teaching and learning of algebra.","author":"FRIEDLANDER A.","key":"ref8"},{"key":"ref9","series-title":"Second handbook of research on mathematics teaching and learning","first-page":"805","volume-title":"Toward comprehensive perspectives on the learning and teaching of proof.","author":"HAREL G","year":"2007"},{"issue":"3","key":"ref10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10649-017-9761-8","article-title":"A conceptual model of mathematical reasoning for school mathematics","volume":"96","author":"JEANNOTTE D.","year":"2017","journal-title":"Educational Studies in Mathematics"},{"year":"2011","series-title":"Developing essential understanding of mathematics reasoning for teaching mathematics in prekindergarten-grade 8.","author":"LANNIN J.","key":"ref11"},{"key":"ref12","series-title":"Encyclopedia of mathematics education","first-page":"505","volume-title":"Mathematical cognition: In secondary years.","author":"MANOUCHEHRI A.","year":"2020","edition":"2"},{"issue":"62","key":"ref13","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1590\/1980-4415v32n62a02","article-title":"Promover o racioc\u00ednio matem\u00e1tico dos alunos: Uma investiga\u00e7\u00e3o baseada em design","volume":"32","author":"MATA-PEREIRA J.","year":"2018","journal-title":"Bolema"},{"issue":"4","key":"ref14","doi-asserted-by":"crossref","first-page":"552","DOI":"10.17648\/acta.scientiae.v20iss4id3892","article-title":"Mathematical reasoning fostered by (fostering) transformations of rational number representations","volume":"20","author":"MORAIS C","year":"2018","journal-title":"Acta Scientiae"},{"year":"2009","series-title":"Focus in high school mathematics: Reasoning and sense making","key":"ref15"},{"key":"ref16","series-title":"Gest\u00e3o Curricular em Matem\u00e1tica","first-page":"11","volume-title":"O professor e o desenvolvimento curricular.","author":"PONTE J. P.","year":"2005"},{"year":"2022","series-title":"Racioc\u00ednio matem\u00e1tico e forma\u00e7\u00e3o de professores.","author":"PONTE J. P.","key":"ref17"},{"issue":"156","key":"ref18","first-page":"7","article-title":"Como desenvolver o racioc\u00ednio matem\u00e1tico na sala de aula?","author":"PONTE J. P.","year":"2020","journal-title":"Educa\u00e7\u00e3o e Matem\u00e1tica,"},{"issue":"1","key":"ref19","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1207\/S15327833MTL0501_02","article-title":"Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students\u2019 types of generalization","volume":"5","author":"RADFORD L.","year":"2003","journal-title":"Mathematical Thinking and Learning,"},{"issue":"4","key":"ref20","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/j.jmathb.2012.07.001","article-title":"Justification as a teaching and learning practice: Its (potential) multifacted role in middle grades mathematics classrooms","volume":"31","author":"STAPLES M.","year":"2012","journal-title":"The Journal of Mathematical Behavior,"},{"issue":"1","key":"ref21","first-page":"9","article-title":"An analytic framework of reasoning-and-proving","volume":"28","author":"STYLIANIDES G.","year":"2008","journal-title":"For the Learning of Mathematics,"},{"issue":"3","key":"ref22","doi-asserted-by":"crossref","first-page":"314","DOI":"10.5951\/jresematheduc.40.3.0314","article-title":"Facilitating the transition from empirical arguments to proof","volume":"40","author":"STYLIANIDES G","year":"2009","journal-title":"Journal for Research in Mathematics Education,"},{"key":"ref23","series-title":"Compendium for research in mathematics education.","first-page":"237","volume-title":"WEBER. Research on the teaching and learning of proof: Taking stock and moving forward.","author":"STYLIANIDES G","year":"2017"}],"container-title":["Bolema: Boletim de Educa\u00e7\u00e3o Matem\u00e1tica"],"original-title":["Grade 8 Students\u2019 Mathematical Reasoning: Conjectures, generalizations and justifications"],"link":[{"URL":"http:\/\/www.scielo.br\/scielo.php?script=sci_pdf&pid=S0103-636X2025000100516&tlng=pt","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T12:45:56Z","timestamp":1743770756000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.scielo.br\/scielo.php?script=sci_arttext&pid=S0103-636X2025000100516&tlng=pt"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":23,"alternative-id":["S0103-636X2025000100516"],"URL":"https:\/\/doi.org\/10.1590\/1980-4415v39a230164","relation":{},"ISSN":["1980-4415","0103-636X"],"issn-type":[{"type":"electronic","value":"1980-4415"},{"type":"print","value":"0103-636X"}],"subject":[],"published":{"date-parts":[[2025]]},"article-number":"e230164"}}