Assessment plays a critical role in all aspects of teaching and learning mathematics. Assessing student work in a problem-solving environment is quite different from traditional methods of evaluating computational skills. Through the use of open-ended problems (that is, problems that can be solved using a variety of approaches, or problems that have multiple solutions), we give students the opportunity to make sense of the situation and the mathematics involved. Likewise, a rich problem-solving environment provides the teacher with a variety of assessment opportunities.

With so many potential aspects to problem solving, how can we best assess this skill? We can gather evidence in two key ways -- by observing students' work and by listening to their discussions and explanations of their thinking. What we observe and hear then guides our decisions in further planning to meet each student's needs.

As you think about the students' work with How many Vehicles? problem, use these questions to gather evidence about their mathematical understanding:

• Do students determine their own strategies for solving problems, or are they dependent on others to tell them what to do?
• Do students articulate their strategies and work to make sense of the strategies used by others?
• How effectively do students use materials as tools to help them solve problems?
• How do students keep track of and record their work?

It is difficult, if not impossible, to assign a grade to this type of mathematical learning. Keep in mind that the purpose of this type of assessment is to gain a clearer picture of each student's level of understanding and to help you, as the teacher, know where to go next. It is important to look for changes in students' work, habits, or dispositions as evidence of growth. For instance, if a student doesn't use an organized way to collect data or share information in October but does so consistently by January, that is assessment information that can be seen and noted as student progress in problem-solving situations.

Watch the video segment (duration 0:21) in the viewer box on the upper left to hear a reflection from Judy Darcy, an elementary school mathematics teacher.

  The teacher's role in developing a culture for problem solving in grades pre K-2