Observing Student Problem Solving
 Introduction | Building Staircases | Student Work #1 | Problem Reflection #1 | Student Work #2 | Problem Reflection #2 | Classroom Practice | Observe a Classroom | Your Journal
"Effective learners recognize the importance of reflecting on their thinking and learning from their mistakes. Students should view the difficulty of complex mathematical investigations as a worthwhile challenge rather than as an excuse to give up. Even when a mathematical task is difficult, it can be engaging and rewarding. When students work hard to solve a difficult problem or to understand a complex idea, they experience a very special feeling of accomplishment, which in turn leads to a willingness to continue and extend their engagement with mathematics."

## (NCTM, 2000, p. 21)

By the time students arrive in the high school mathematics classroom, they generally have significant experience in problem solving -- sometimes positive and sometimes negative. Students who have been successful at problem solving in earlier grades may bring a predisposition and, in fact, an expectation that they will continue this success in high school work. In a parallel way, those who have struggled with mathematical problems may be inclined to do anything to minimize engagement with a topic that has been frustrating.

For either type of student, high school mathematics work offers the chance to grow past former limitations. Problem solving can engage the natural curiosity and questioning skills of all students, despite varying backgrounds or skill levels. As the curriculum expands, some students who were reluctant problem solvers may find aptitude in new areas and use this as a basis to shore up overall mathematics skills. All learners should have the chance in high school to work on meaningful problems that increase both their problem-solving ability and their overall understanding of mathematics concepts.

We begin with an example of teacher and student work for you to consider. Ms. Nguyen's ninth-grade pre-algebra class has been working on patterns. Here she sets up a new challenge for the class. Observe what she does, how the students work on the problem, and the role of self-review in the problem solving process.

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