Symbolism, Imagery, Allegory
One of Doug Shoemaker's final acts as head of his household before he bit it from lung cancer was to symbolically turn over his duties to Karl by writing down the tasks for maintaining the house. "He showed me how to fix everything around the house," Karl explains to Gratz. "We'd do stuff all day and he'd add it to that list" (26.104). Although Doug spent the majority of Karl's childhood either doing mayor stuff or being drunk, it's his attempt to get to know his son in his last days, and maybe pass something onto him as well so he can take care of his mother and their home.
To Karl, though, the list becomes more than just a legacy his dad has handed down to him. It's a comfort object that he clings to … well, like Darla clings to Mr. Babbitt. Okay, maybe that doesn't really work as a metaphor, but whatever.
Either way, he keeps the list tacked to his bulletin board and even takes it down at night to read as he goes to sleep. By this time, he has the tasks memorized, which means the list has outlived its usefulness. Now, it's a reminder of his father's best side and the person he became when he knew he was dying. "He was dying, but life was better than it ever had been," Karl says. "I loved that" (26.105).
So, if the list is a comfort object related to his dad, what do we make of the fact that close to the end of the book, Karl's mom busts into his room and rips the thing up? We're not totally sure, but we think it also symbolizes the mess of Karl's past and how while he and his mom have avoided talking about it, there are a lot of issues under the surface. Check out what he has to say after their conversation about Karl's dad and Karl's alleged hobby of whacking cats:
At first we thought that that sad pile of torn paper could be put back together like a puzzle. But it quickly turned out to be hopeless; the dried-out pieces broken in our hands […] After awhile we both gave up; there was no way to get it all laid out and then tape it together. (23.111)
This is like a picture of what Karl's life has been like since his dad died—dried-out, broken pieces that can't be put back together. His mom has gone off the deep end. The house is overrun with cats. Most of all, Karl tries to keep things together the way his dad wanted him to, but in the end, his efforts always fail. When he says he's "just kind of absorbing that it's really gone" (23.115), what he's really trying to do is deal with the fact that the chips—or rather, the ripped pieces of paper—are down, and he and his mom have to deal with everything they've spent the last four years covering up.