Problem solving is a skill that has been in evidence throughout the ages, from ancient to modern times. Problem solving helps students learn mathematics by giving them an opportunity to ôsolidify and extend what they knowö by using problems that come from the world that they understand (NCTM 52). As a significant facet of mathematics education, problem solving has gone through an evolution, culminating in todayÆs standard as presented in Principles and Standards for School Mathematics, by the National Council of Teachers of 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 century, Sir Isaac NewtonÆs and Gottfried Wilhelm LeibnizÆs discovery of differential and integral calculus enabled mathematicians to solve many problems that had been insoluble previously (ôThe Invention of Calculusö), and in the 18th century, the discovery of analytic geometry and the invention of calculus enabled scholars to apply mathematics to a wide range of problems (ôMathematicsö). These discoveries helped to forge the approaches and curricula of modern math...