Middle School Students' Reasoning about Geometric Situations

Abstract

Along with an increased emphasis on reasoning, communication, and problem solving, the National Council of Teachers of Mathematics has called for a change in assessment techniques (1989, 1991, 1995). In contrast to short-answer questions, assessments that elicit writing, diagrams, and other representations offer better windows into students' understandings and misconceptions about mathematics. This article describes some short geometry tasks that go beyond the simple recognition of figures and properties. Because they have been field-tested with students using various mathematics curricula, we have collected hundreds of student responses to these questions that seem to represent a good range of students' geometric thinking and development. From these responses, along with ideas about the development of geometric thinking (Fuys. Geddes, and Tischler 1988), we have developed scoring rubrics to go along with many of these questions. The rubrics and questions might be useful to middle school teachers who are developing short openended questions that encourage and assess students' thinking.