Why problem-centered learning? - Problem centered math

One of the goals of mathematics instruction is to prepare students to be problem solvers in a world where they will encounter complicated issues. The North Carolina Mathematics Standard Course of Study incorporates problem solving in each strand of each grade or course. A problem-centered approach provides a vehicle to achieve the goals and objectives identified in the curriculum. Evidence from research and international studies suggests that our students are proficient in procedures but do not have the conceptual understanding to solve problems. The world they will live and work in will require them to gather, organize, and interpret data in the process of finding solutions to complex problems. It would seem only logical to provide a classroom setting where they will face similar issues. In the real world, the problems they face will not be ones for which they are selecting answers from a set of multiple choices.

The authentic type of problem is found primarily in enrichment programs or activities such as Science Olympiads and Odyssey of the Mind competitions. Typical problems in school mathematics tend to provide all the information needed and often anticipate that students will use a practiced procedure or formula to arrive at a single solution. The revisions of the End-of-Grade and End-of-Course tests in North Carolina have increased the level of cognitive demand by including more items that require a variety of problem-solving strategies. Teachers who have reviewed these instruments have commented on the need to provide more problem-centered instruction.

The role of a classroom teacher is that of an active problem solver making instructional decisions with a constant influx of data from a variety of sources. An effective classroom teacher must design experiences that enable students to achieve designated objectives and must orchestrate students’ work as they progress through those experiences. These experiences must be founded on the ways in which students develop mathematical understanding. Students build mathematical understanding when they are required to build new knowledge by pondering, creating, and critiquing arguments about mathematics.

Students must experience problems where flexible use of knowledge is required. No mathematical thinking is required for tasks in which a routine is used to provide a solution that is known in advance. Directed and focused questions must challenge students to select from a variety of strategies. Students need to analyze problems, determine what information is needed to solve them, and design solutions. Appropriate tasks should engage all students and provide opportunities for extensions that encourage students to go beyond minimum expectations. The teacher becomes a tutor or coach who facilitates the students’ investigations.

Problem solving must be more than routine exercises. It cannot be viewed as an "add on" to classroom instruction but rather an important goal. Problem solving should be viewed as a means to mathematical understanding as well as a set of procedures. Engaging students in problem-centered learning will allow students to see connections within and between content areas. Students will develop the ability to employ and select appropriateness of a variety of strategies for designing solutions. Problem-centered learning creates a model where the student becomes the thinker and is engaged in a self-directed search for solutions.