Can a child be smart without a teacher?
In order to determine whether or not a child is "smart," you must first define "smart" in your own terms. Do you mean smart in the academic sense, or the worldly sense?
As for the question, a child can be "smart" without attending elementary school, yes. Children are very much the type to learn from the examples set before them. If they are not set with the example of say a kindergarten teacher, but they are exposed to an environment at home that is nurturing of their growth and such, they will learn just as well as a child in a traditional classroom. The important thing is that the child is being stimulated and engaged in their work, rather than "taught."
What a shame that people are not actually answering the question or not paying attention to it, like the response about the appendectomy. You asked if it was critical that a student learn the K-12 basics from a teacher that holds a college degree. The answer is no. Elementary level teachers do not have core subject specializations especially since programs can change every 5-10 years. Their training consists of how to present information to 30 different kids, keep them interested and in line, how to set up evaluations needed for 30 kids, etc. Besides, most parents can probably do just fine with elementary math and language arts and everything else is just extra. For junior high and high school, thinking back to my own school experiences, I can honestly say that the best teachers were not the ones who knew the most about their subject matter but were the best at getting us to think. That was a personality trait on their part or something they picked up from somewhere, not something cove
