Introduction Professional Learning and Three Grand Organizers for Arithmetic Instruction From Whole Numbers to Fractions Assessing Stages of Units Coordination Teaching Students at Stage 1: Fragmenting Transitioning to Stage 2: Part-Whole Reasoning Teaching Students at Stage 2: Measuring with Unit Fractions Teaching Students at Stage 2: Reversible Reasoning Teaching Students at Stage 3: Fractions as Numbers Teaching Students at Stages 2 and 3: Equal Sharing of Multiple Items Teaching Students at Stages 2 and 3: Multiplying Fractions Teaching Students at Stages 2 and 3: Adding and Subtracting Fractions Teaching Students at Stages 2 and 3: Dividing Fractions From Fractions to Algebra
Amy J. Hackenberg is an Associate Professor in Mathematics Education at Indiana University. Anderson Norton is an Associate Professor in Mathematics Education at Virginia Tech University. Dr Robert J. (Bob) Wright holds Bachelor's and Master's degrees in mathematics from the University of Queensland (Australia) and a doctoral degree in mathematics education from the University of Georgia. He is an adjunct professor in mathematics education at Southern Cross University in New South Wales. Bob is an inter nationally recognized leader in assessment and instruction relating to children's early arithmetical knowledge and strategies, publishing six books, and many articles and papers in this field. His work over the last 25 years has included the development of the Mathematics Recovery Program, which focuses on providing specialist training for teachers to advance the numeracy levels of young children assessed as low-attainers. In Australia and New Zealand, Ireland, the UK, the USA, Canada, Mexico, South Africa and elsewhere, this programme has been implemented widely, and applied extensively to classroom teaching and to average and able learners as well as low-attainers. Bob has conducted several research projects funded by the Australian Research Council including the most recent project focusing on assessment and intervention in the early arithmetical learning of low-attaining 8- to 10-year-olds.
With its beginnings in whole-number arithmetic understanding, Developing Fractions Knowledge is the most comprehensive look at fractions learning to date. It journeys with the practitioner and learner to view fractions as part-whole concepts, measures, and ultimately as numbers with meaning. The assessment and instructional tasks and practical connections to research and Math Recovery principles make it a must-have resource for educators to use again and again! -- Carolyn Olijnek Developing Fractions Knowledge skilfully combines cutting-edge research with practical knowledge of the classroom to provide an essential resource for everyone interested in developing students' understanding of fractions. I can't wait to try some of the tasks and activities with students! -- Dr Janette Bobis, Professor in Mathematics Education, All in, it was an enjoyable book (I have to admit thinking a book on fractions is not one I would choose) and I think would be a worthwhile investment for a department. -- N. G. Macleod