What is the Difference Between Solving a Problem and Reasoning Out an Answer?

Reasoning out the answer requires a student to examine if the final solution is logical and practical. It is not enough just to know how to solve the problem. Students should also be able to articulate why they chose a particular strategy and the steps they followed to solve the problem.

After solving the problem, students may reason out why the answer arrived at is correct and if the answer makes sense. The ability to solve the math problem and reason out the answer are both important as these help students be confident about the math they are learning.

Consider the following problem: If each bus holds 44 students, how many buses are needed so that all 154 third graders can go to the zoo?

Students need to evaluate the problem then represent it symbolically. When they complete the calculation, they will arrive at the answer 3 ½. Often students stop here. After all, they have an answer so they must be done. What’s missing is the reasoning part of solving the problem. If students reasoned, they would realize that it is impossible to have 3 ½ buses. 4 buses are needed in order to transport all the students to the zoo.

Discuss here: What kind of activities do you use to help students develop problem solving skills?

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