extremely difficult to create a pencil-and-paper task that allows the teacher
to follow the processes used by students. Furthermore, traditional assessment's
approach to peer collaboration complicates our task (see
Hawkins and Sheingold, 1986). Most of the high school teachers we have worked with now
grade for individual achievement. At the same time, when using our
approach to geometry they have students work extensively in pairs.This paper represents our early efforts at assessing a small range
of higher-order mathematical thinking skills. We focused mainly on conjecturing, verifying, and generalizing skills. We described two practical ways to
assess the performance of students who have worked collaboratively. Both
assessment instruments are designed to be administered with paper and
pencil to individual students; one results in individual scores. We hope that
these ideas will be helpful to those teaching other topics; for example, we
believe that much of the analysis in this paper is relevant to suitably posed
APPENDIX 1: DETAILED LIST OF INQUIRY SKILLSThe items in the following lists provide details for the nine
categories shown in Figure 2 in the text. They indicate the kinds of
behaviors, skills, questioning strategies, and beliefs that "good explorers"
exhibit. There are areas where these lists overlap, and no one student will
exhibit all of these strategies when solving a single problem.These lists were developed by Harvard Educational Technology
Center's Geometry Labsites group.
|Using knowledge about geometry--Checking the types of relationships
discussed in class.|
|Looking for patterns other than equality.|
|Remembering that conjectures are "for all" statements.|
|Adding to the diagram--drawing auxiliary lines.|
|Has it been shown before?|
|Is it a direct consequence of a known relationship?|
Questia, a part of Gale, Cengage Learning. www.questia.com
Book title: Assessment of Authentic Performance in School Mathematics.
Contributors: Richard Lesh - Editor, Susan J. Lamon - Editor.
Publisher: AAAS Press.
Place of publication: Washington, DC.
Publication year: 1992.
Page number: 111.
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