Human beings have tremendous potential to acquire new knowledge, develop new skills, and improve their brains throughout life. By explicitly teaching learners about brain plasticity and malleable intelligence (the idea that they can become functionally smarter through effort) and by modeling and teaching specific learning strategies, teachers can…

There has long been dispute in mathematics between the drill and practice orientation that focuses primarily on memorizing mathematics as meaningless rote algorithms and the approach based on understanding and making creative use of mathematics. This 25-chapter book, based on a 7-year study at the University of Illinois, seeks to explain and…

This book explores what makes mathematics possible as well as what makes mathematics difficult. Included is a discussion of the definition of mathematics, mathematics in language, the meaning of numbers, calculating and measuring, notation, numbers in space, and the best ways to learn mathematics. Historical information and practical examples are…

This book is the result of the accumulated research of five researchers from the United States and Australia on a school in Coastal Australia. The research team shared a constructivist epistemology and interpreted the qualitative and quantitative data collected over a 10-week period in two classrooms from that perspective. Each chapter discusses…