Problem Solving in Mathematics

Although problem solving originated with ancient thinkers and mathematicians such as Aristotle, Archimedes, and Pythagoras, mathematics education trends in recent centuries have continued to evolve. A hallmark of early math/problem solving education was the ubiquitous ôEuclid Challenge,ö a mathematical problem put forth by Euclid and used in math classrooms throughout the years as an example of a problem that that is impossible to solve. The Euclid Challenge consists of three tasks to perform using an unmarked straightedge and compass: trisect any angle, square a circle, and double a cube (Mintz). For over two thousand years, students were told that this challenge was unsolvable; however, in 2002 it was solved by Milton Mintz, whose solution marks the revolutionary thinking now characterizing math problem solving in the 21st century.

Prior to Mintz, however, math went through centuries of other approaches. In the 17th cen

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n the public schools, and by the end of the 20th century math education was in a state of flux (Klein). Problem solving has not always been a focus of mathematics education, but now in the 21st century, the new standards presented in Principles and Standards for School Mathematics provide for the development of problem solving skills at every grade level; it states: Solving problems is not only a goal of learning mathematics but also a major means of doing so. It is an integral part of mathematics, not an isolated piece of the mathematics programàBy solving mathematical problems, students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations that serve them well outside the mathematics classroom (NCTM 4). In most mathematics education standards from the past, there is no section on problem solving, or at best a small tribute to it somewhere in the back. In this resource, however, substantial space is devoted to problem solving goals, activities, and concepts in each of four grade level stagesùPre-K-2, 3-5, 6-8, and 9-12. In each of these sections, grade-appropriate information and sample problems are provided to achieve the same four goals: Building new mathematical knowledge
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Approximate Word count = 1965
Approximate Pages = 8 (250 words per page)

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