Increased attention has been given to issues of assessment in recent years. Teachers of mathematics have been working to change both the way they elicit evidence of their students' mathematical thinking and the way they use that evidence to monitor students' progress and guide instructional decision making. This publication is based on work done with teachers and administrators in the Classroom Assessment in Mathematics network and the Assessment Communities of Teachers project. This book presents guidelines for designing and facilitating these investigations. Emphasis is placed on experiencing a task, observing problem solving, examining students' work, developing tasks, developing rubrics, and planning assessment. Half of the text is comprised of appendices. (Contains 35 references and resources.) (ASK)