The field of mathematics is complex, areas such as arithmetic, and geometry each consist of several sub-domains and encompass many cognitive processes. Achievement tests for elementary pupils assess a wide range of arithmetic skills such as number sense, procedural knowledge, and using problem solving strategies. Although mathematical tests often…

Portions of interviews with children who are engaged in a problem solving activity are presented. The problem used is an "eel question" taken from the work of Piaget. The verbal responses of children are seen as a part of effective teaching, and this method of assessment is encouraged. (MP)