\input zb-basic \input zb-matheduc \iteman{ZMATH 2016e.00771} \itemau{Mata-Pereira, Joana; da Ponte, Jo\~ao Pedro} \itemti{Developing mathematical reasoning: generalization and justification in the study of inequalities. (Desenvolvendo o racioc\'{\i}nio matem\'atico: generaliza\c{c}\~ao e justifica\c{c}\~ao no estudo das inequa\c{c}\~oes.)} \itemso{Bol. GEPEM 37, No. 62, 17-31 (2013).} \itemab Summary: This article analyses students' mathematical reasoning processes while working on algebraic tasks with inequalities. This analysis emphasizes generalization and justification as key mathematical reasoning processes and also stresses representations and sense-making. The results show that students follow inductive and abductive approaches in generalizing. In justifying, students present arguments based on previous knowledge or known concepts and properties. The use of different representations seems not to constrain the development of mathematical reasoning and sense-making arises intrinsically linked to presented generalizations or justifications. \itemrv{~} \itemab Resumo: Este artigo analisa os processos de racioc\'{\i}nio matem\'atico de alunos na resolu\c{c}\~ao de tarefas alg\'ebricas envolvendo inequa\c{c}\~oes. Esta an\'alise destaca a generaliza\c{c}\~ao e a justifica\c{c}\~ao enquanto processos-chave do racioc\'{\i}nio matem\'atico, dando tamb\'em aten\c{c}\~ao \as representa\c{c}\~oes e processos de significa\c{c}\~ao. Os resultados mostram que na generaliza\c{c}\~ao os alunos seguem abordagens indutivas e abdutivas e na justifica\c{c}\~ao baseiam-se em conhecimentos anteriores ou conceitos e propriedades conhecidas. O uso de diferentes representa\c{c}\~oes parece n\~ao limitar o desenvolvimento do racioc\'{\i}nio matem\'atico e os processos de significa\c{c}\~ao surgem intrinsecamente ligados \as generaliza\c{c}\~oes ou justifica\c{c}\~oes apresentadas. \itemrv{~} \itemcc{H30 E50} \itemut{mathematical reasoning; generalization; justification; inequalities; algebra} \itemli{} \end