In the first step, students read and understand all information pertaining to the math problem statement. They interpret the math problem using their own words and make sketches of the essential information. Students also may compile a comprehensive list of all the specified facts, restrictions and conditions. It is at this point that students decipher the desired goal and list other information related to the problem. They compare the given problem with any problem they solved in the past to decide the best approach to resolve the current problem.
Teachers encourage students to choose an appropriate systematic strategy to tackle the math problem based on the students' prior experience solving closely associated problems or the insight they collect from understanding the current problem statement's context. Because some problems can be solved using different strategies, students may state all of the strategies but use only the ones with which they are comfortable. Choosing a strategy involves ensuring that all the given information will be used and the desired goal fulfilled.
Students experiment systematically with the chosen strategy to determine whether or not it is applicable to the particular problem. If it isn't, then changing tact is necessary. They sketch the steps they used to arrive at the answer and analyze as if the steps are correct and can be proven. The students verify that the solution they derived suits the problem statement and answers all the questions asked. If the it does not provide viable solutions to the problem, then they change the strategy.
The students use the favored strategy consistently to solve the problem and accurately record all solutions in the appropriate form, such as graphs, lists and tables. They monitor their thinking at every step to ensure they methodically solve the problem according to the provided instructions and restrictions.
The final step is to assess the answers' validity and to analyze whether or not all the questions are comprehensively covered. Students may describe the problem-solving process orally or in writing and evaluate the approaches used by other students to gain insight of alternative strategies. To perfect their skills, students discuss the answers and use the same strategy to solve other math problems.