Young Mathematicians at Work

This third volume in a series of three focuses on how children in grades 5-8 construct their knowledge of fractions, decimals and percents. It explores the historical development of fractions, decimals, and their equivalents and the ways in which children develop similar ideas and strategies. In our efforts to reform mathematics education, we've learned a tremendous amount about young students' strategies and the ways they construct knowledge, without fully understanding how to support such development over time. The Dutch do. So, funded by the National Science Foundation and ExxonMobil, Mathematics in the City was begun, a collaborative inservice project that pooled the best thinking from both countries. In Young Mathematicians at Work, Catherine Fosnot and Maarten Dolk reveal what they learned after several years of intensive study in numerous urban classrooms. In this third volume in a series of three, Fosnot and Dolk focus on how children in grades 5-8 construct their knowledge of fractions, decimals, and percents. Their book: - describes and illustrates what it means to do and learn mathematics. - contrasts word problems with true problematic situations which support and enhance investigation and inquiry. - provides strategies to help teachers turn their classrooms into math workshops. - explores the cultural and historical development of fractions, decimals, and their equivalents and the ways in which children develop similar ideas and strategies. - defines and gives examples of modeling, noting the importance of context. - discusses calculation using number sense and the role of algorithms in computation instruction. - describes how to strengthen performance and portfolio assessment. - focuses on teachers as learners by encouraging them to see themselves as mathematicians.

In our efforts to reform mathematics education, we've learned a tremendous amount about young students' strategies and the ways they construct knowledge, without fully understanding how to support such development over time. The Dutch do. So, funded by the NSF and Exxon, Mathematics in the City was begun, a collaborative inservice project that pooled the best thinking from both countries. In Young Mathematicians at Work, Catherine Fosnot and Maarten Dolk reveal what they learned after several years of intensive study in numerous urban classrooms. The first in a three-volume set, Young Mathematicians at Work focuses on young children between the ages of four and eight as they construct a deep understanding of number and the operations of addition and subtraction. Rather than offer unrelated activities, Fosnot and Dolk provide a concerted, unified description of development, with a focus on big ideas, progressive strategies, and emerging models. Drawing from the work of the Dutch mathematician Hans Freudenthal, they define mathematics as "mathematizing" - the activity of structuring, modeling, and interpreting one's "lived world" mathematically. And they describe teachers who use rich problematic situations to promote inquiry, problem solving, and construction, and children who raise and pursue their own mathematical ideas. In contrast to other books on math reform, Young Mathematicians at Work provides a new look at the teaching of computation. It moves beyond the current debate about algorithms to argue for deep number sense and the development of a repertoire of strategies based on landmark numbers and operations. Sample minilessons on the use of the open number line model are provided to show you how to support the development of efficient computation.