Este libro se ha escrito pensando en la necesidad de aportar materiales que sirvan para trabajar las competencias profesionales relacionadas con los procesos de investigación e innovación en el aula, las cuales son una parte fundamental de las competencias profesionales que queremos desarrollar. Las buenas prácticas que se incluyen en este libro pretenden ejemplificar a nivel del aula muchas de las ideas desarrolladas en los apartados destinados a los procesos de investigación e innovación citados anteriormente. Útil tanto para el profesorado en formación inicial (Máster de Secundaria) como para los docentes en ejercicio que deseen potenciar su desarrollo profesional.

Our current society faces enormous environmental challenges. Now is the time to stand up for a sustainable future. This request for action also concerns our STEM education community to take the transformational potential of teaching and learning. Teachers are decisive factors in ensuring the achievement of creative and sustainable learning outcomes in mathematics and science education, in fostering young peoples’ competences and empowering them to become responsible and active citizens. We need to share good practices, research results and innovative classroom materials that allow for implementing approaches that support the implementation and scaling up of education for sustainability. Educating the Educators (ETE) is an international conference series on professional development in STEM (science, technology, engineering and mathematics) education that brings together teacher educators, policy makers, teachers and various other stakeholders related to STEM education. The fourth edition of the ETE conference series was hosted by Utrecht University, ICSE and the Naturalis Biodiversity Center in the Netherlands, in collaboration with the MOST project. ETE IV focused on implementing and scaling up innovative teaching approaches in STEM education with an emphasis on open schooling for sustainability education. The aim was to discuss different ways of working, the roles of teaching materials, and structures needed for innovations in STEM education. ETE IV featured both traditional and innovative formats to benefit of a diverse circle of participants from research, practice and policy. Vivid exchange and collaborative work were ensured through spaces for co-creation. This volume reflects the main topics of discussion and the participants’ conference experiences.

No one disputes how important it is, in today's world, to prepare students to un derstand mathematics as well as to use and communicate mathematics in their future lives. That task is very difficult, however. Refocusing curricula on funda mental concepts, producing new teaching materials, and designing teaching units based on 'mathematicians' common sense' (or on logic) have not resulted in a better understanding of mathematics by more students. The failure of such efforts has raised questions suggesting that what was missing at the outset of these proposals, designs, and productions was a more profound knowledge of the phenomena of learning and teaching mathematics in socially established and culturally, politically, and economically justified institutions - namely, schools. Such knowledge cannot be built by mere juxtaposition of theories in disci plines such as psychology, sociology, and mathematics. Psychological theories focus on the individual learner. Theories of sociology of education look at the general laws of curriculum development, the specifics of pedagogic discourse as opposed to scientific discourse in general, the different possible pedagogic rela tions between the teacher and the taught, and other general problems in the inter face between education and society. Mathematics, aside from its theoretical contents, can be looked at from historical and epistemological points of view, clarifying the genetic development of its concepts, methods, and theories. This view can shed some light on the meaning of mathematical concepts and on the difficulties students have in teaching approaches that disregard the genetic development of these concepts.

Ratio and Proportion—Research and Teaching in Mathematics Teachers’ Education offers its readers an intellectual adventure where they can acquire invaluable tools to turn teaching ratio and proportion to professionals and school children into an enjoyable experience. Based on in-depth research, it presents a deep, comprehensive view of the topic, focusing on both the mathematical and psychological-didactical aspects of teaching it. The unique teaching model incorporates both theoretical and practical knowledge, allowing instructors to custom-design teacher courses according to their speci?c needs. The book reports on hands-on experience in the college classes plus teachers’ experience in the actual classroom setting. An important feature is the extensive variety of interesting, meaningful authentic activities. While these activities are on a level that will engage pre- and in-service mathematics teachers in training, most can also be utilized in upper elementary and middle school classes. Accompanying the majority of these activities are detailed remarks, explanations, and solutions, along with creative ideas on how to conduct and expand the learning adventure. While primarily written for educators of mathematics teachers, this book can be an invaluable source of information for mathematics teachers of elementary and middle school classes, pre-service teachers, and mathematics education researchers.

How can we deal with the diversity of theories in mathematics education? This was the main question that led the authors of this book to found the Networking Theories Group. Starting from the shared assumption that the existence of different theories is a resource for mathematics education research, the authors have explored the possibilities of interactions between theories, such as contrasting, coordinating, and locally integrating them. The book explains and illustrates what it means to network theories; it presents networking as a challenging but fruitful research practice and shows how the Group dealt with this challenge considering five theoretical approaches, namely the approach of Action, Production, and Communication (APC), the Theory of Didactical Situations (TDS), the Anthropological Theory of the Didactic (ATD), the approach of Abstraction in Context (AiC), and the Theory of Interest-Dense Situations (IDS). A synthetic presentation of each theory and their connections shows how the activity of networking generates questions at the theoretical, methodological and practical levels and how the work on these questions leads to both theoretical and practical progress. The core of the book consists of four new networking case studies which illustrate what exactly can be gained by this approach and what kind of difficulties might arise.