In order to emphasize the engineering design process, we were thinking of trying to solve the staircase problem twice. The first time, we will focus on a qualitative understanding of the problem, via filming the staircase or interviewing students, and a non-technological solution. Then, we can assess the success of the color-coding etc. solution of the first intervention.
The re-design process can involve using NXT sensors or counting the video tape cross overs to track how many times students cross over to the wrong side, focusing on a quantitative understanding of the problem. Then, we can have the students put in a technological solution, using motion sensors with alarms, etc.
With this rough outline, we can highlight each of the steps of the engineering design process, while also showing how technology can be used in a re-design.