Words and Worlds (Modeling Verbal Descriptions of Situations)

In this book, the reader is invited to enter a strange world in which you can tell the age of the captain by counting the animals on his ship, where runners do not get tired, and where water gets hotter when you add it to other water. It is the world of a curious genre, known as "word problems" or "story problems". It originated in the ancient civilizations of Egypt, China, and India, and is the subject of daily rituals among students and teachers in mathematics classrooms all around the world. An international group of scholars with a shared interest in this phenomenon explore multiple aspects of this world from multiple perspectives. These discussions take us deep into philosophical issues of the relationships between words, mathematical systems, and the physical and social worlds we all inhabit. Empirical investigations are reported that throw light on how students and their teachers experience and interpret this activity, raising profound questions about the nature and purposes of mathematics teaching/learning in general and how it could be improved.