Education doesn't make people smart.
Of course education makes people smart. Nothing else will.
He never said education = learning in a classroom.
Education can take many forms. But, at the end of the day, all education is, "the act or process of imparting or acquiring general knowledge, developing the powers of reasoning and judgment, and generally of preparing oneself or others intellectually for mature life." Dictionary.com
Mr. Miyagi provided Daniel with an education in a dojo setting. He made him smarter. Nothing else will make someone smart other than an education, which can take many forms. you can become educated by going to school, volunteering in a soup kitchen, taking karate, learning a hobby.