Selecting Problem-Solving Strategies. Problem-solving strategies are methods that can be
used to solve problems of various types. Teachers who use relevant and meaningful problemsolving
experiences as the focus of their mathematics class help students to develop and extend
a repertoire of strategies and methods that they can apply when solving various kinds of problems
– instructional problems, routine problems, and non-routine problems. Students develop
this repertoire over time, as they become more mature in their problem-solving skills.
Eventually, students will have learned many problem-solving strategies that they can flexibly
use and integrate when faced with new problem-solving situations, or to learn or reinforce
mathematical concepts. Common problem-solving strategies include the following: making a
model, picture, or diagram; looking for a pattern; guessing and checking; making an organized
list; making a table or chart; making a simpler problem; working backwards; using logical
reasoning