Assessment of Authentic Performance in School Mathematics

By Richard Lesh; Susan J. Lamon | Go to book overview
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 algebra problems.
APPENDIX 1: DETAILED LIST OF INQUIRY SKILLS
The 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.
Conjecturing
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?

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