Analyzing student work can help teachers improve the teaching and learning of mathematics. Fortunately, the four authors have experienced professional development that supports teachers' professional growth and provides tools to begin the challenge of analyzing student work. However, as they began to assume leadership roles in their schools and…

Relates Cognitively Guided Instruction (CGI) with anecdotes of learning-disabled students in primary grades. Message of CGI is that when teachers begin listening to children, they realize how much more students know than they recognized previously. Teachers can achieve goals of compensatory mathematics education by building on this knowledge. (SKS)

Suggests that algorithms, both traditional and student-invented, are proper objects of study not only as tools for computation, but also for understanding the nature of the operations of arithmetic. (Author/NB)

Describes the work that students and teachers do to develop computational fluency for subtraction. Examines the orchestration of whole-class discourse and presents a collection of common strategies. (Author/NB)

Suggests ways to increase students' computational fluency using concrete materials, engaging tasks, and reflection time to increase number automaticity, flexibility in thinking about numbers, and use of efficient problem-solving strategies to find sums and differences. (Author/NB)

Illustrates how an activity called Incredible Equations was used to develop 2nd grade students' number sense and number concepts. Includes student-created equations and an analysis of the mathematics they learned. (Author)

Describes a pattern-based approach to subtraction that enables students to find the amount of change from a purchase "faster than a cash register." (Author/YDS)

Provides an alternative to traditional instruction in multiplication and division to develop computational fluency in students. (Author/NB)

Presents activities using the Three Pigs to increase students' understanding of addition and subtraction. Argues that addition and subtraction are something that students can view and participate in when using the Three Pigs instead of just the manipulation of numbers. (ASK)

Presents a problem of triangular tiles that involves counting and probability. Includes instructor guiding questions. (KHR)

Presents several alternatives to customary algorithms for whole number arithmetic. Includes a brief history of each algorithm and discusses why each might be useful for particular kinds of children. (KHR)

Discusses a content-integration program in which Spanish is introduced while mathematics and other subjects are reinforced, creating a winning combination for students, teachers, and preservice teachers alike. (Author/NB)

Discusses how teachers can help English-language learners develop computational fluency. (Author/NB)

Focuses on children making sense of multiplication. In an activity called "Silent Multiplication," students use what they know about easier multiplication problems to solve increasingly difficult, related problems mentally. (Author/NB)

Presents mathematical calculator activities used by students individually, in small groups, or as problems of the week. Suggests using calculators to enhance and stimulate student learning. (KHR)