CHILDRENS MATHEMATICS AGES 4 15 LEARNING FROM ERRORS AND MISCONENCEPTIONS

THE MISTAKES CHILDREN MAKE IN MATHEMATICS ARE USUALLY NOT JUST 'MISTAKES' - THEY ARE OFTEN INTELLIGENT GENERALIZATIONS FROM PREVIOUS LEARNING. FOLLOWING SEVERAL DECADES OF ACADEMIC STUDY OF SUCH MISTAKES, THE PHRASE 'ERRORS AND MISCONCEPTIONS' HAS RECENTLY ENTERED THE VOCABULARY OF MATHEMATICS TEACHER EDUCATION AND HAS BECOME PROMINENT IN THE CURRICULUM FOR INITIAL TEACHER EDUCATION. THE POPULAR VIEW OF CHILDREN'S ERRORS AND MISCONCEPTIONS IS THAT THEY SHOULD BE CORRECTED AS SOON AS POSSIBLE. THE AUTHORS CONTEST THIS, PERCEIVING THEM AS POTENTIAL WINDOWS INTO CHILDREN'S MATHEMATICS. ERRORS MAY DIAGNOSE SIGNIFICANT WAYS OF THINKING AND STAGES IN LEARNING THAT HIGHLIGHT IMPORTANT OPPORTUNITIES FOR NEW LEARNING. THIS BOOK USES EXTENSIVE, ORIGINAL DATA FROM THE AUTHORS' OWN RESEARCH ON CHILDREN'S PERFORMANCE, ERRORS AND MISCONCEPTIONS ACROSS THE MATHEMATICS CURRICULUM. IT PROGRESSIVELY DEVELOPS CONCEPTS FOR TEACHERS TO USE IN ORGANIZING THEIR UNDERSTANDING AND KNOWLEDGE OF CHILDREN'S MATHE