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Why Do Some Plants Have Larger leaves than other plants? Why do the overall shapes of different kinds of leaves vary? How does one determine the area of a peculiarly shaped leaf? Plant biologists are extremely interested in these questions. A biologist might wonder, for instance, which of two plant species carries out the most photosynthesis. Since the amount of light a plant can absorb for use in photosynthesis is related to its area, the biologist might investigate the photosynthetic capacity of two species by comparing the amount of chlorophyll in leaf pieces of the same area.

What might students say about the angles of the pentagonal block shown in figure 1? Children might respond in different ways, depending on their abilities and experiences with angles. Some might say that the block “has five angles” after touching each of the corners. Others might observe that “it looks like all the angles are the same size.” Perhaps a few would respond as did Luke, a bright fifth grader who is featured in this article.

A comprehensive process design, which facilitates the analysis of all events that have an impact on students’ mathematical experiences, is outlined in the Assessment Standards for School Mathematics (NCTM 1995). This process of assessment is held to six standards: Mathematics, Learning, Equity, Openness, Inference, and Coherence. These Standards represent those ideas that are valued and by which mathematical assessment should be judged.