Counting and Measuring : An Approach to Number Education in the Infant School

The teaching of numbers in the primary grades is seen in this book as the foundation of the beginnings of mathematical understanding. Mathematics is taken to be a language, and the aim of its teaching is to make the pupil, so to speak, bilingual, or so to increase his understanding that he is able to translate a concrete numerical problem into the symbolic language of calculation. For a child taught along these lines, how much easier, for example, would be the transition from arithmetic to algebra! Miss Churchill is fully conversant with the works of Piaget, Cuisenaire, Cassirer and other leading thinkers in educational philosophy, psychology, and linguistics. She has synthesized their concepts with her own experience and research at Leeds University, and, though written within the contexts of British education, her book should also have a marked influence on the teaching of young children in North America. Contents 5 Plates 6 Figures 7 Foreword 9 Preface 13 Chapter One. About Caroline and Others 15 Chapter Two. The Beginnings of Numbering 25 Chapter Three. The Growth of Number Systems 38 Chapter Four. The Beginnings of Understanding 59 Chapter Five. The Origins of Symbolism 68 Chapter Six. From the Concrete to the Abstract 89 Chapter Seven. From Comparison to Measurement 122 Chapter Eight. From Counting to Calculation 145 Chapter Nine. An Exploration of Space 184 Chapter Ten. The Role of the Teacher 218 Bibliography 228 Index 231