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
Dr. Amy J. Hackenberg taught mathematics to middle and high school
students for 9 years in L.A. and Chicago, prior to earning a Ph.D.
in mathematics education from the University of Georgia. Amy is
currently an associate professor of mathematics education at
Indiana University-Bloomington. She conducts research on how middle
school students construct fractions knowledge and algebraic
reasoning and on how teachers can learn to develop productive
student-teacher relationships. In her current project she is
investigating how to differentiate instruction for diverse middle
school students (see https://idream.sitehost.iu.edu/), studying her
own teaching as well as working with practicing teachers. She is
the proud co-author of the Math Recovery series book, Developing
Fractions Knowledge.
Dr. Anderson Norton is a professor in the Department of Mathematics
at Virginia Tech. His research focuses on building models of
students’ mathematical development. This work has generated
interdisciplinary collaborations with psychologists and
neuroscientists. Prior to this volume, Norton served as chair of
the steering committee for the North American Chapter of the
International Group for the Psychology of Mathematics Education,
co-editor on a pair of publications bridging psychology and
mathematics education, and co-author of the Math Recovery series
book, Developing Fractions Knowledge.
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
internationally 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
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