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.