Iowa Core Curriculum - ....Problem Solving

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Home

Mathematics

Essential Skills

Problem Solving

All students should be able to:

Build new mathematical knowledge through problem solving
Solve problems that arise in mathematics and in other contexts
Apply and adapt a variety of appropriate strategies to solve problems
Monitor and reflect on the process of mathematical problem solving

"Problem solving means engaging in a task for which the solution method is not known in advance. In order to find a solution, students must draw on their knowledge, and through this process, they will often develop new mathematical understandings. Solving problems is not only a goal of learning mathematics but also a major means of doing so. Students should have frequent opportunities to formulate, grapple with, and solve complex problems that require a significant amount of effort and should then be encouraged to reflect on their thinking. By learning problem solving in mathematics, students should acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations that will serve them well outside the mathematics classroom. In everyday life and in the workplace, being a good problem solver can lead to great advantages." (NCTM, 2000, p. 52)

Implications for Curriculum, Instruction, and Assessment
Problem solving is not just a skill that all students must develop, it is also the means for effectively teaching and learning mathematics. Problem-based instructional tasks should be used in the classroom to teach important mathematics. These tasks should be chosen carefully, addressing real-world problems that allow students to have multiple ways to solve the problems, centered on an important mathematical idea, concept, or skill that is part of a course of study. These tasks should encourage the connection across curricular strands of mathematics. Teachers should choose tasks that require a high level of cognitive demand to promote the development of a deep knowledge of mathematics. Assessments designed to check for understanding should allow for problem solving to be demonstrated. Assessments should focus on the process of solving the problems as well as on correct solutions. (Adapted from Teaching Mathematics through Problem Solving, Schoen, NCTM, 2003)

"Problem solving is an integral part of all mathematics learning, and so it should not be an isolated part of the mathematics program. Problem solving in mathematics should involve all [mathematical strands]. The contexts of the problems can vary from familiar experiences involving students' lives or the school day to applications involving the sciences or the world of work. Good problems will integrate multiple topics and will involve significant mathematics." (NCTM, 2000, p. 52)