Working with the Array: Mathematical Models

In their series of professional books for teachers, Young Mathematicians at Work , Catherine Twomey Fosnot and Maarten Dolk described Mathematics in the City, an innovative project where teachers helped young children construct a deep understanding of number and operation in a math-workshop environment. Now they and two colleagues from the project have developed a flexible, video-based, digital context for inquiry into the teaching and learning of mathematics that will change how professional development is conducted. Designed for you, the workshop participant or preservice teacher, the Working with the Array CD-ROM enables you to not only watch but interact with video that depicts classroom teachers as they listen to, question, and interpret students’ thinking; develop connections between mathematical ideas and strategies; and, ultimately, develop vibrant mathematical communities in their classrooms. In Working with the Array , your workshop participants will observe fourth graders as they construct some of the big ideas related to surface area and volume, making connections between multiplication’s commutative and associative properties and uncovering landmark division strategies like halving and factoring. By studying the use of carefully crafted problems designed both to generate a range of solution strategies and to highlight the power of arrays and other models for multiplication and division, teachers will discover what a valuable tool real-life contexts are for building a solid foundation in mathematics.