In this book, Cathleen Heil addresses the question of how to conceptually understand children’s spatial thought in the context of geometry education. She proposes that in order to help children develop their abilities to successfully grasp and manipulate the spatial relations they experience in their everyday lives, spatial thought should not only be addressed in written or tabletop settings at school. Instead, geometry education should also focus on settings involving real space, such as during reasoning with maps. In a first part of this book, she theoretically addresses the construct of spatial thought at different scales of space from a cognitive psychological point of view and shows that maps can be rich sources for spatial thinking. In a second part, she proposes how to measure children’s spatial thought in a paper-and-pencil setting and map-based setting in real space. In a third, empirical part, she examines the relations between children’s spatial thought in those two settings both at a manifest and latent level.
There was a time when the family Künstler lived in the fairy-tale city of Vienna. Circumstances transformed that fairy tale into a nightmare, and in 1939 the Künstlers found their way out of Vienna and into a new fairy tale: Los Angeles, California, United States of America. For years Mamie Künstler, ninety-three-years-old, as clever and glamorous as ever, has lived happily in her bungalow in Venice, California with her inscrutable housekeeper and her gigantic St. Bernard dog. Their tranquility is upended when Mamie’s grandson, Julian, arrives from New York City. Like many a twenty-something, he has come to seek his fortune in Hollywood. But it is 2020, the global pandemic sweeps in, and Julian’s short visit suddenly has no end in sight. Mamie was only eleven when the Künstlers escaped Vienna in 1939. They made their way, stunned and overwhelmed, to sunny, surreal Los Angeles where they joined a colony of distinguished Jewish musicians, writers and intellectuals also escaping Hitler. Now, faced with months of lockdown and a willing listener, Mamie begins to tell Julian the buried stories of her early years in Los Angeles: her escapades with eminent émigrés like Arnold Schoenberg, Christopher Isherwood, Thomas Mann. Oh, and Greta Garbo. While the pandemic cuts Julian off from the life he knows, Mamie’s tales open up a world of lives that came before him. They reveal to him just how much the past holds of the future.
The story of Trenton begins in 1678, when 20 Quakers left Yorkshire, England to travel to America. They wintered in the fort at Burlington, New Jersey, and, in the spring of 1679, set sail for the lands they had purchased at the head of the navigable waters of the De La Warr River. Approaching rocky outcroppings in a sharp bend of the river, they stopped and began to build the village that would become the capital city of New Jersey. Trenton traces the city from these beginnings to more recent times, and just about everything in between, concentrating on the era of photography: from 1850 to 1960. The authors have masterfully compiled this volume, which blends images of the places and people that make Trenton so unique, with the stories of the important, timely events that helped to shape the history of Trenton.
In this book, Cathleen Heil addresses the question of how to conceptually understand children’s spatial thought in the context of geometry education. She proposes that in order to help children develop their abilities to successfully grasp and manipulate the spatial relations they experience in their everyday lives, spatial thought should not only be addressed in written or tabletop settings at school. Instead, geometry education should also focus on settings involving real space, such as during reasoning with maps.In a first part of this book, she theoretically addresses the construct of spatial thought at different scales of space from a cognitive psychological point of view and shows that maps can be rich sources for spatial thinking. In a second part, she proposes how to measure children’s spatial thought in a paper-and-pencil setting and map-based setting in real space. In a third, empirical part, she examines the relations between children’s spatial thought in those two settings both at a manifest and latent level.
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