  In this paper, we prove that the mean curvature blows up at the same rate as
the second fundamental form at the first singular time $T$ of any compact, Type
I mean curvature flow. For the mean curvature flow of surfaces, we obtain
similar result provided that the Gaussian density is less than two. Our proofs
are based on continuous rescaling and the classification of self-shrinkers. We
show that all notions of singular sets defined in \cite{St} coincide for any
Type I mean curvature flow, thus generalizing the result of Stone who
established that for any mean convex Type I Mean curvature flow. We also
establish a gap theorem for self-shrinkers.
