By presenting students with open performance tasks, and then examining their work by listening and observing, the teacher makes assessment part of daily instruction.   Rather than being a task done quietly, alone at a desk, performance tasks allow students to learn math content by using math process tools

Research
Children need to experience mathematics as a process and use mathematics to discover things for themselves (Richardson, 1999).  According to the NCTM Standards for Mathematical Practice, teachers should seek to develop the expertise in their students to solve problems, communicate, reason, represent and make connections. Through these processes, students solve problems, apply strategies, and reflect on their learning as they acquire and use mathematical knowledge (NCTM, 2000).
 
Application
By presenting students with open performance tasks, and then examining their work by listening and observing, the teacher makes assessment part of daily instruction.   Rather than being a task done quietly, alone at a desk, performance tasks allow students to learn math content by using math process tools (Richardson, 1999). The performance task IS the lesson.  Built around problems and explorations, they span grade levels and allow for differentiated instruction.  They provide the teacher with rich information about student thinking and learning, and build new mathematical knowledge.
 
Resources
Performance Task Resources
PALM is an on-line, resource bank of mathematics performance tasks, collected from numerous sources and indexed via the  National Council of Teachers of Mathematics (NCTM).  The tasks include student directions, scoring rubrics and examples of student work.   http://palm.sri.com/palm/tasks/index.html
 
(broken link) Exemplars is a website that provides performance material for both instruction and assessment. You will find tasks, rubrics,   question guides and an   implementation guide at this site.
 
Additional Resources from the Virginia Department of Education
Facilitating Students’ Mathematical Understanding through a Focus on Process Goals for Students.   Resources are from the VDOE sponsored 2011 Math Institute that focused on facilitating students’ mathematical understanding through the process standards of problem solving, communication and reasoning.
 
References
Richardson, K.  (1999). Developing number concepts planning guide. Parsippany, NJ: Dale Seymour Publications.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston,VA:  NCTM.