Is Scrum possible without test driven development?

I have now witnessed two companies move to agile development with Scrum.

In both cases the standard of coding was good enough when each part of the application was only being worked on by one or two developers with the developers spending a reasonable amount of time working on one part of the application before moving to the next task. The defect rates were also reasonable.

However with Scrum the developers are expected:

to all be able to work on all the bits of the application.
to only work on one area of the application for a few days at most before moving to the next area
to mostly work on code they did not write

Code qualities became an issue in both of the Scrum projects.

So is there a way to do Scrum that does not lead to these problems, without first getting all the developers to do test driven development?

Have you seen Scrum work well on a large project without test driven development? (If so how?)

Solution

Regarless of the use of Scrum, what you were seeing was a change from a code ownership approach to a communal code approach. In order for that to work, there has to be a process change which supports it. One such possibility is TDD. There are others (Automated unit testing even if doesn't drive design coupled with Code Reviews, strong design communication, greater design up front, not developing on code without first pairing with the original author on the code, and more I'm sure you could think of).

Communal approaches work in smaller communities (in large ones it can degenerate into a tragedy of the commons) with a high sense of cohesion between the members.