They observed that primary grade students’ initial representations of growth were typically focused on endpoints, for example: “How tall do plants grow?” Students’ questions about plant height led to related concerns about identifying the attributes of a plant that could best represent height and how those attributes should be measured. As one might expect, students’ resolutions to these problems varied by grade.

First-Grade Representations

First graders represented the heights of plants grown from flowering bulbs, using green paper strips to depict the plant stems at different points in the growth cycle (see Figure 6-3). Consistent with the claim that young children try to create models that closely resemble real or known objects, the students at first insisted that the paper strips be adorned with flowers.

However, as the teacher repeatedly focused students’ attention on successive differences in the lengths of the strips, students began to make the conceptual transition from thinking of the strips as “presenting” height to “representing” height (see Figure 6-4). Reasoning about changes in the height differences of the strips, students identified times when their plants grew “faster” and “slower.” Their study of the plant heights was firmly grounded in prior discussions about what counted as “tall” and how to measure it reliably.

FIGURE 6-3 A display with detailed drawings of individual plants that include flowers and colors.

FIGURE 6-4 Displays of plant height depicted in bar graphs.

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