As we can gather from reading "Blues Ain't No Mockingbird," Cathy is an inveterate storyteller. For instance, after the cameramen turn up unannounced at her grandparents' house, she starts telling a tale about a man who tried to kill himself by jumping off a bridge.

The cameramen remind her of this story because there was a camera crew filming the suicide attempt. But as Granny doesn't want to hear the rest of this gory story, Cathy starts telling another, much nicer story instead: the story of Goldilocks and the Three Bears.

Given her penchant for telling stories, then, it's not surprising that at the end of "Blues Ain't No Mockingbird," Cathy should express her desire to tell the story about what happened when her grandfather used a hammer to kill a hawk and then smashed up the film crew's camera. For her, this story will be concerned with what she calls "the proper use of a hammer."

The irony here, of course, is that the story has already been told by Cathy's distant cousin, the unnamed narrator of "Blues Ain't No Mockingbird" She has already shown us "the proper use of a hammer." Even so, it would still be interesting to see just what Cathy could do with the same material.

In "Blues Ain't No Mockin Bird," what does Cathy mean by writing about the hammer?

Cathy is presented as a storyteller, though she is still a child. The narrator, her cousin, offers her opinion of Cathy’s perspective on the situation with the two cameramen trying to record on the family’s property without permission. The men, who are white, take for granted their superior status compared to the family members, who are black. The overall tone in the story is ironic, as the two white men end up needing to be rescued from a menacing hawk. It is after Grandpa Cain rescues them, by throwing a hammer at the hawk, that Cathy makes this statement. “Proper use” can be considered to compare the hammer to a camera, as both are kinds of tools. Instead of intruding into the family’s life, the men could have used the camera in a way that helped them, as Grandpa did with the hammer. Alternately, since a hammer is not intended to be used to save people, throwing it is not “proper” use. Grandpa managed to use the situation with the hawk as a way to get the camera away from the men. Cathy may mean that her story will be about how black people can outwit white people with superior attitudes.

Cathy, in "Blues Ain't No Mockin Bird," is a third cousin with a special gift of understanding the unstated suggestions of life, for example, she knew why photographers who were photographing a man about to jump to his death would, "of course," reserve a few shots for later (for the aftermath of the event).  The four children out playing saw Granddaddy come home from hunting with a chicken Hawk slung over his shoulder. They also saw its outraged mated swooping and attacking Granddaddy. They also saw Granddaddy nail the hawk to the toolshed door and then throw the hammer at the swooping, attacking hawk.

This scenario is what inspired Cathy to utter her proclamation that she will one day write a story about “the proper use of the hammer.” Since throwing a hammer is most decidedly not the proper use of a hammer, we can conclude that Cathy may mean "proper use of a hammer" literally. Since she also understates things that are not stated, she could also mean the symbolic or metaphoric "proper use of a hammer."

Granddaddy threw the hammer to stop the enraged hawk mate from attacking him. He then promptly, upon Granny's request, broke the cameraman's camera and told the filmmakers to get off their property. property that they owned.

It may be that Cathy is thinking of the "proper use of the hammer" as the metaphor of defending yourself and your loved ones against attack by using things in slightly unorthodox ways but to good effect, such as throwing a hammer at an attacking hawk and breaking a camera while politely explaining that intruders need to vacate the premises.