Representation construction
In this section, we examine representation constructions by comparing instructional
tasks in six U.S. lessons (from US3 to US8), totalling around 300 minutes, with four
Chinese lessons (from CH1 to CH4), totalling around 180 minutes. These lessons were
chosen because of their extensive coverage of linear relations. The six U.S. lessons
include 10 instructional tasks, and the four Chinese lessons include 23 instructional
tasks. To examine the kinds of representations used, we looked at the total duration for
solving each task as a whole. The proportion of different representations for each task
in the U.S. classroom is depicted in Figure 1.