Mathematics and mathematics education research have an ongoing interest in improving our understanding of mathematical problem posing and solving. This book focuses on problem posing in a context of mathematical giftedness. The contributions particularly address where such problems come from, what properties they should have, and which differences between school mathematics and more complex kinds of mathematics exist. These perspectives are examined internationally, allowing for cross-national insights.

Survival Guide Wissenschaft – der unverzichtbare Begleiter für angehende Wissenschaftler:innen! Wertvolle Ratschläge, bewährte Strategien und Insiderwissen aus vielen Jahrzehnten akademischer Laufbahnen mit Kurven, Ecken und Kanten. Tipps und Tricks, Dos and Don’ts, um wissenschaftliche Karrieren an Universitäten und anderen Forschungseinrichtungen zu starten, zu überleben und erfolgreich voranzutreiben. Von der Forschungsplanung bis zur Bewerbung um Stipendien und Stellen, von der Netzwerkbildung bis zur Work-Life-Balance, aber auch Exit-Strategien – dieser Survival Guide liefert die entscheidenden (Über-)Lebenstipps für ein Leben in Academia.

The book is made up of 21 chapters from 25 presentations at the 23rd MAVI conference in Essen, which featured Alan Schoenfeld as keynote speaker. Of major interest to MAVI participants is the relationship between teachers' professed beliefs and classroom practice. The first section is dedicated to classroom practices and beliefs regarding those practices, taking a look at prospective or practicing teachers' views of different practices such as decision-making, the roles of explanations, problem-solving, patterning, and the use of play. The focus of the second section in this book deals with teacher change, which is notoriously difficult, even when the teachers themselves are interested in changing their practice. The third section of this book centers on the undercurrents of teaching and learning mathematics, what rises in various situations, causing tensions and inconsistencies. The last section of this book takes a look at emerging themes in affect-related research. In this section, papers discuss attitudes towards assessment.

Epistemological beliefs-i.e. beliefs on the nature of knowledge, its limits, sources, and justification-play an important role both in everyday life and in learning processes. This book comprises several studies dealing with such beliefs in the domain of mathematics; amongst others a qualitative interview study, and quantitative studies for which a new questionnaire has been developed. In this new instrument, belief position (e.g. "mathematical knowledge is certain" vs. "uncertain") and belief argumentation (the way those positions are justified) are differentiated. Additionally, a test for mathematical critical thinking has been designed.The results show significant correlations between sophisticated belief argumentations and high scores in the critical thinking test, but no correlations regarding belief positions.