Will Pa change his behavior as a result of his day at school in "Split Cherry Tree"?

Pa goes to school with Dave because he is angry and feels Professor Herbert is out of place. He doesn't agree with the educational activities and techniques being used at the school and doesn't agree with Dave's punishment for breaking the cherry tree. His intention is to "look into bug larnin', frog larnin', lizard and snake larnin', and breakin' down cherry trees!"

Upon arriving at the school and beginning to talk with Professor Herbert, Pa is at first resistant - "I don't see what bugs has got to do with a high school!" - but becomes curious and willing to learn.

I want to see th' germs off'n my teeth. I jist want to see a germ. I've never seen one in my life. 'Seein' is believin',' Pap allus told me.

Pa open to new ideas and new ways of doing things once he comes to understand the reasons for the changes.  His perspective toward the school and the Professor's methods changes, and he comes away from his visit with a new respect for the Professor and the education Dave is getting.

What lessons does Pa learn from his school day in "Split Cherry Tree"?

Pa has learned that modern day education's a lot different to how it used to be in his time. When he was a boy, Dave's dad received only a very basic education: reading, writing, and arithmetic. There was certainly no time for science in Pa's day; he had no time for studying bugs, or "bug larnin" as he contemptuously calls it. So it's not surprising that Pa developed such a hostility to an education that involves more than just the basics. The way he figures it, if a rudimentary education were good enough for him, then it's good enough for his son Dave.

After Professor Herbert graciously gives Pa a guided tour of the school and its facilities, Dave's dad changes his tune. In a moment of epiphany he realizes that he's out of step with modern education; he's a "dead leaf" who simply doesn't belong inside a modern classroom. But that doesn't mean that Dave doesn't. No longer hostile to Professor Herbert and his teaching, he instructs Dave to do what his teacher tells him.

Due to his newfound understanding of modern education Pa realizes that Professor Herbert was right to punish Dave for breaking the cherry tree. In fact, he agrees with Herbert so much that he even volunteers to help Dave carry out his punishment of sweeping up leaves.