You needn't have full-time experience in Education if you want to a graduate degree especially for Ph.D. Because they care much more for your research background and how much you want to devote into the EDUCATION RESEARCH. Yet, experience would be very helpful if you have any, but it could only be used to explain why you want to choose education as your major, how you find education is important and useful, the importance of the education RESEARCH. And you should also explain clearly your transfermation of your interest from your teaching experience to education research.
So, the more "academic" the major is, the less teaching experience it would require. Just like the difference between the doctoral of Business and the MBA, the latter of course need more working experience