Conceptual Understanding in Solving Two-Step Word Problems with a Ratio

When solving multistep word problems, children may have difficulty in either understanding concepts and relationships or organizing a solution method. Both factors of problem difficulty were studied by means of interviews with 36 children (ages 9 to 14) who solved problems having the same structure but varying in context and in the numbers used. The child's representation of a problem was probed by tasks involving repetition of the problem statement and selection of drawings. The meaning of concepts and relationships was a major source of difficulty, and levels were identified in understanding the concept of ratio. The solution method was also a source of difficulty, but its nature was less clear. The results underline the importance of a careful analysis of problem types in studying sources of difficulty.