Problem solving is a critical component of learning mathematics in the early years. Young students who are engaged in meaningful problem solving develop basic skills, higher-order thinking skills, and a repertoire of problem-solving strategies.

Children make sense of mathematical ideas by actively engaging in solving a variety of rich mathematical problems. Traditionally, worded problems in which students practiced skills ("story problems") were considered "problems." For example, a lesson on beginning addition was followed either with words or with pictures that gave students a chance to apply what they had learned. We now understand that children need a variety of problems -- such as traditional story problems, non-routine problems, problems with addition patterns, and problems they write themselves -- to focus their thinking around a particular concept.

The process of problem solving encompasses mathematics far beyond completing examples presented with words or pictures. In fact, a problem is actually a task for which the means to a solution is not known in advance. In other words, the "problem" at the end of that lesson on beginning addition was actually an "exercise" for practicing the skill, rather than a problem. Even young children soon figure out that the type of problems at the end of the page on addition just require more adding. They do not have to think about the situation in order to solve the problem -- they can do so by applying the procedure taught in the lesson.

As we think about problem solving for young students, we should consider two purposes for embedding problem solving into mathematics lessons: (1) Problem solving affords children opportunities to make sense of the mathematic concepts they are learning by using their own strategies as they decide how to proceed. (2) Rich problems can be solved in many ways, often have more than one correct answer, and encourage students to think beyond applying their basic skills. This kind of teaching encourages a problem-solving disposition that will serve children well past the primary grades.

  Opportunities for problem solving