Dave demonstrates growth because he acquires a more mature attitude about his father after Pa comes to the school and meets with Professor Herbert.
As the first of his family to attend high school in what is most likely rural Kentucky in the 1930's (the story was published in 1939), Dave starts to feel that his father is rather backward in his attitudes about certain things. For instance, he fears telling his father that he has had to stay after school and work to pay for a tree he and others have damaged while on a science class outing, knowing that he will probably get a whipping. Dave knows that his father will not understand what happened, nor will he approve of Dave's staying after school when he has chores to do in the afternoon.
When Dave explains his tardiness, Pa is originally angry with him; however, when he hears that Dave alone stayed late because the others were able to pay for the damages, Pa's sense of pride is ignited,
"Poor man's son, hun,..I'll attend to that myself in the mornin'....He ain't from this county nohow....What kind of school is it, anyhow?
Dave pleads with his father to not go, but his father vows to "straighten this thing out" and insists upon accompanying Dave to school the next day with his "long blue forty-four" pistol. Fortunately, Professor Herbert remains calm when accosted by Pa and speaks reasonably with the big man. Then, in an effort to explain why the class goes outdoors, Herbert shows Pa around, speaking of incubators, germs, and other things. When Professor Herbert tells Pa that he has a black snake that the class will chloroform and dissect to view his germs, Pa becomes upset:
"Don't do it....I believe you. I just don't want to see you kill the black snake. I never kill one. They are good mousers and a lot o' help to us on the farm...."
Overhearing his Pa, Dave begins to perceive a different side of his father, a kinder part. After school, Dave notices something different about Pa. He sees that his father
...looked lost among us. He looked like a leaf turned brown on the tree among the treetop filled with growing leaves.
Then, when Dave begins to sweep the classroom floor as he works off his fine, Pa comes to his aid, telling Dave that the teacher, Professor Herbert, is a good man. School has changed, he adds, calling himself a "dead leaf," and confirming what Dave has observed. Further, when Herbert tells Pa the debt is "on me" and they can go, Pa refuses,
"We don't do things like that...we're just and honest people. We don' want somethin' for nothin'....I ain't got much larnin' myself but I do know right from wrong atter I see through a thing."
Pa apologizes to Dave, saying that he has misjudged Dave's teacher and the school; moreover, he encourages Dave to further his education because he can do better than his father. But, he reminds Dave to always be honest and kind to animals.
While Pa has called himself "a little man," meaning he is unimportant in society, Dave realizes that his father is really no "little man." For, he now perceives in his father a reasonableness, a sense of fairness, and a certain dignity in the pride that he takes in being honest and knowing right from wrong. In this new perception of his father, Dave grows in his understanding, of this man as well as in his recognition of those values that really count in life.