The division technique works by dividing a product or its components functionally or physically and then rearranging them back into the product. Division is a powerful technique because it forces you to break fixedness, especially structural fixedness. Division forces you to create configurations by rearranging components in ways you were not likely to have done on with on your own.
You've heard that old adage. Don't judge a book by its cover. The same holds true in creativity. We want to resist the temptation of judging ideas depending on where it came from. Yet, its very difficult for us to do this. If we like the person, we tend to like their idea. And if we don't like that person, well, let's just say we might see a few more flaws than we might have otherwise.
As a teacher of creativity, I agree that persistence is an important success factor when producing new ideas. As the researchers point out, when creative challenges start to feel difficult, most people lower their expectations about the performance benefits of perseverance, and consequently, underestimate their own ability to generate ideas. But other factors can boost...or inhibit innovation...motivation, hope, and anxiety (yes, you read it correctly - anxiety).