Productivity, by (one of the generic) definition, is a measure of efficiency in converting an input to a desired output - but, what exactly is it in the context of CSE?
Many people have a difficult time defining productivity in a practical way, and find it particularly difficult to measure it in an objective way. For the Better Scientific Software (BSS) project, we use a pragmatic definition based on the well-known Iron Triangle model. The most familiar quote associated with this model is "Better, Faster, Cheaper, pick two of the three."
While it is true in our experience that an explicit measurement of productivity is difficult, relative comparison of the producivity difference between two approaches for conducting work can often be done well enough for practical purposes.
Given this context, we define Productivity Improvement as increasing the volume of better, faster and cheaper. In other words, as we look for ways to improve how we conduct our work, we want to consider how the change will positively impact the quantity and quality (better), the amount of time (faster) and the amount of resources (cheaper) associated with developing our scientific and engineering software.
By focusing on productivity improvement as a relative measure comparing our current software activities with a new approach, we can avoid the typical quagmire that leads to unproductive discussions on productivity.