The Summer School on the History of Mathematics Education 2024 aims to deepen the exchange of ideas, experiences, proposals, and results from several studies that have been taking place since 2011 among researchers from Latin America, Portugal, and Spain. The success of the Ibero-American Congresses on the History of Mathematics Education (CIHEM), which has made it possible to learn about the current state of research in these countries, led the International Commission that has been organising them to hold a Summer School in 2024 in Lisbon.

The Summer School aims to create a space that allows for in-depth debate on themes, paradigms, and methodologies. An intense face-to-face experience is proposed at the doctoral and post-doctoral levels where, more than the dissemination of research results, the aim is to present and debate frontier issues that stimulate investigative production.

• The paradigms
• The themes
• The methodologies 
• The relationship with disciplines and neighboring areas 

This separation between thematic axes constitutes only a form of systematisation of the subject and is artificial, as the four axes are naturally interconnected.

The first axis, paradigms, focuses on understanding the major current historiographical currents — cultural history, microhistory, oral history, … — highlighting the strengths and weaknesses of each one and questions how the specific nature of mathematical knowledge fits any of them. It also includes epistemological reflections, both on the historian's work and on school mathematical knowledge, appreciating the social and cultural dimensions of both.

The second axis, themes, refers to what constitutes the center of the investigative work. What topics have been studied and with what success? Topics such as professional knowledge, or textbooks, or the study of school mathematics topics, have received considerable attention in past congresses. Is it possible to formulate syntheses and advance guiding questions for future work? What are the least studied topics? Why have topics such as the circulation of knowledge or the study of practices (or others) been almost absent?

The third axis, methodologies, adds considerations about specific methods of investigating the past. How to study and criticise sources, such as books, notebooks, newspaper articles, student work, teachers' lesson plans, official documentation, teaching materials, etc.? And what are the procedures for establishing and managing archives and documentation centres?

If the first three axes focus on issues predominantly internal to the field, the fourth, the relationship with disciplines and neighboring areas, turns outwards and explores the interaction between academic areas that may establish privileged points of contact with the History of Mathematics Education, namely, the history of education, the history of mathematics, and mathematics education.