Mathematics Education in Spain and Portugal
Spain 
Elena Ausejo 
 
This section offers a brief overview of Spanish mathematics education over the last two centuries, in the context of the educational system as a whole, which in turn depended to a very large extent on the country’s political and economic circumstances. Although political instability delayed the regulation of secondary education in Spain until 1836, the syllabi of 1845 and 1857 set up the basic structure throughout the nineteenth century. The country developed a system for preparing mathematics teachers that was relatively demanding – above all with respect to mathematical knowledge – and absorbed international experience through translations of textbooks. Later, Spain took part in the principal international movements in mathematics education, becoming involved in the ICMI and the reform movements of the 1950s–1970s.
CONSTRUÇÃO E MODIFICAÇÃO DA AUTONOMIA DOS SABERES MATEMÁTICOS ESCOLARES EM PORTUGAL
Durante a segunda metade do seculo XIX e inicio do seculo XX a disciplina de Matematica do ensino secundario foi sendo gradualmente construida em Portugal com as suas normas e praticas especificas acompanhando o processo de desenvolvimento de um ensino secundario publico. Emergem professores certificados e sao produzidos livros didaticos, programas, tecnicas especiais de ensino, procedimentos de avaliacao, etc. Este processo de consolidacao termina com o que e descrito por Chervel como a emergencia de disciplinas escolares que desenvolvem o que designa de autonomia e que Julia caracteriza como conjuntos de normas e praticas especificos da funcao escolar, contrariando a visao que entendiam estas disciplinas como meros prolongamentos de campos cientificos. Nesta texto discutirei como se estabeleceu a disciplina escolar de Matematica no ensino secundario em Portugal e como se foi constituindo o seu saber profissional docente. Este processo e indissociavel dos dispositivos de formacao inicial de professores, pelo que observarei em particular os processos de legitimacao profissional com especial atencao aos modos como a autonomia se foi construindo e modificando ao longo do tempo.
Educational innovation in Musical Language Course: responses and the overcoming of limitations
This article presents an innovative methodological proposal for the development of auditory education in the course of the Language of Music. Based on this proposal, we analyze an educational community’s response to the innovations implemented, and we identify the limitations recognized throughout the learning and teaching process, as well as the strategies developed to overcome them. To this end, we applied a qualitative methodology with the classroom-based research method. The compilation of data was carried out through participant observation, captured in the journals of the professor and researcher, interviews and analysis of documents. The research results demonstrate that patience, responsibility and perseverance in their work on behalf of the professors have been key to overcoming the limitations identified and in promoting that students enjoy and learn their class contents in meaningful ways. Recibido 05/02/2018 Aceptado: 09/03/2018