ABSTRACT
Teachers argue that there is no room in the curriculum for additional topics; they can barely “cover” everything as it is. The research on which this book is based was carried out in real classrooms, fully integrated with multicultural students and disabled students, by teachers who had a full syllabus in their mathematics classes. It is important to emphasize the difference between changing instruction and adding to the mathematics curriculum. Fraction, ratio, and other multiplicative ideas are psychologically and mathematically complex and interconnected. It is impossible to specify a linear ordering of topics that can be used to plan instruction. Their fraction operations were strong; they had developed the conventional algorithms for fractions operations, or some equally good alternative algorithms of their own invention. Finally, the elusive by-product of fraction instruction, proportional reasoning, was strong among these children.
