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.
Construction and modification of the autonomy of school mathematical knowledge in Portugal
During the second half of the nineteenth century and early twentieth century the discipline of secondary mathematics was gradually built in Portugal and certified teachers, textbooks, programs, special teaching techniques emerge. This consolidation process ends with the emergency of school subjects that develop some kind of autonomy as Chervel puts it. This article discusses how the school discipline of mathematics in secondary education in Portugal was set. This process is inseparable from teacher training and so we will observe professional legitimation processes paying special attention to ways in which autonomy has been building and modifying over time. Construcción y modificación de la autonomía del conocimiento matemático escolar en Portugal Durante la segunda mitad del siglo XIX y principios del siglo XX la disciplina de las matemáticas en secundaria fue construida gradualmente en Portugal y emergen libros de texto, programas, técnicas de enseñanza especiales y la certificación de maestros. Este proceso de consolidación termina con el surgimiento de disciplinas escolares desarrolladas con algún tipo de autonomía como la planteada por Chervel. Este artículo describe cómo se creó la disciplina escolar de las matemáticas en la educación secundaria en Portugal. Este proceso va unido a la formación docente y, por tanto, se observan procesos de legitimación profesional, prestando especial atención a las formas en que la autonomía se ha estado construyendo y modificando en el tiempo.Handle: http://hdl.handle.net/10481/39494WOS-ESCI
A Matemática Moderna em Portugal: o que dizem os cadernos escolares dos alunos?
This paper analyses some exercise notebooks of students who attended the called “pilot-classes”, meaning classes in which the fi rst pedagogical experiences proposed by the teaching of mathematics modernization movement in Portugal were developed. Such notebooks were used together with the didactical material designed by Sebastiao e Silva, to the 6th and 7th years of the liceu’s 3rd cycle. 
This work aims, by the use of these materials, to search for historical interpretations of practices that happened in the pilot-classes. It is considered that the analysis of such sources — school notebooks — bring important elements to understanding the Modern Mathematics Movement in Portugal, referred by cultural studies. What do notebooks show related to the incorporation of new teaching contents? What are the performed exercises in this new proposal? What is its emphasis? Which are the most studied contents? These, among others, are some of the guiding questions of the analysis.