Based on our limited experience, the templates do seem to open avenues for student thinking and create opportunities for discussion not only about the mathematics but about strategies for using the template to reason about the mathematics. For example, some teachers made deliberate changes in what they can move and record the results; Using the number line template (Figure 3), some held the x-value constant, increased the y-value by 1 unit at a time, and recorded the output then changed the x-value by 1 and repeated the process; others looked at extremes, what happens to the difference between the expressions when x is large or when x is small. Helping students understand how to think in these ways is a fundamental part of learning to do mathematics, and it will be important for teachers to recognize this.
The next phase of the work is to formally pilot the templates and to consider the implications for research related to both the design and implementation. The potential is clearly present to make a difference in what students learn; the challenge is to make this happen in ways that can be replicated across the teaching communi