Hierarchical Ordering of Schematic Knowledge Relating to Area-of-Rectangle Problems.

Schematic knowledge was assessed by asking 195 9th- and 10th-grade students to classify area-of-rectangle problems in terms of whether the text of each problem provided insufficient, sufficient, or irrelevant information for solution. Problems involving adjacent sides information were most accurately classified, followed in increasing order of difficulty by problems involving one side and the ratio of sides, one side and the perimeter, and one side and the diagonal. Students rarely demonstrated awareness of the structure of a more difficult problem after having failed on classification of a less difficult problem. When confronted with a problem for which they lacked the relevant schema, students often attempted to meet task requirements by inappropriately using a lower order template