The value of guess and check in problem solving

Guess and check is a strategy that can be used with middle school math students to help them develop skills in mathematical thinking and problem-solving. As Guerrero (2010) points out, the guess and check lets students focus on the quantitative relationships between numbers rather than their mathematical value. Many students find word problems difficult because they have trouble seeing these relationships. Using the guess and check method, students choose a reasonable number to "plug in" to an equation to see if it makes mathematical sense and satisfies the conditions posed by the problem.

With increased emphasis on algebra in the K-8 curriculum, teachers are encouraged to foster discussions about mathematical relationships as part of their lessons and to help their students focus on "sense making rather than merely applying rote computational strategies" (Guerrero). When students are able to develop this deeper understanding of mathematics, Guerrero asserts, teachers can "potentially influence their students' approach to middle grade mathematics."

For students to successfully employ "guess and check," they must have direct instruction and then both guided and independent practice. Unlike algorithms, "guess and check" is not exact but a "skillful art and exploratory problem-solving technique" (Guerrero, 2010). By its very definition, it is the opposite of rote learning and represents a huge departure from the way mathematics was taught to generations of students before those who are in middle school today. As Guerrero writes, teaching "guess and check" helps students develop skills that will better equip them for "symbolic understanding and abstract, complex problem solving in later grades."

Today's math programs place greater emphasis than ever before on processing and understanding instead of rote learning and memorization. There is great opportunity for teachers to really instill a love of mathematics in students; at the very least, students can develop confidence in their ability to solve problems when they can break problems down into their components, understanding the relationships between values given and understanding what the unknown is supposed to represent.

A popular problem solving strategy that an increasing number of students encounter before middle school is model drawing, sometimes taught as "Singapore Math." The Singapore method, named for the Asian nation in which it was developed, teaches students how to create visuals in a systematic way to assist in solving word problems. When students learn this method and have sufficient opportunities to practice, it can go a long way toward preparing them for the guess and check strategy. The Singapore method asks students to really examine the relationship between values in a problem and carefully consider the question being asked with respect to the solution.