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I would definitely agree that the WHAT has to come before the HOW. Here's how our brainstorming sessions work.
We start by going up and down the rows of people as they are seated, and every person says one idea about what the robot can do. Noone is allowed to say a second idea until everyone has given their first idea. This continues until all the WHAT ideas have run out.
Next is a discussion about those ideas. We eliminate the few ideas that have no possible way of working, such as those that violate the rules, but anything that might just work is saved and written down for later reference. You never know what those crazy, off-the-wall ideas could become. Once we finish the discussion, we have a pretty good idea of what the robot could or should do.
The next step is to figure out HOW these ideas could be used in our design. We make columns on the board, dividing it into segments for each of the main components of the game and robot (balls, goals, drive train, etc.). We use the same "1 idea at a time" format and come up with every possible way of acheiving the WHAT ideas. These get written down, and we break for the day. Everyone gets a chance to think overnight, and come up with new ideas.
The next day, we pull out yesterday's work, add any new ideas, and begin to think about what the robot will actually do and look like. After a few days of this, and some preliminary work, we decide, and the build begins.
We usually get a few oddball ideas, like "The robot should fly and make pizza" but overall, it is a very efficient and productive way to brainstorm our ideas as a group.
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