  We consider the wave maps from $\mathbb{R}^{1+2}$ into $\mathbb{S}^2\subset
\mathbb{R}^3.$ Under an additional assumption of $k$-corotational symmetry, the
problem reduces to the one dimensional semilinear wave equation:
\begin{equation*}
  \partial_t^2 u-\partial_r^2 u-\frac{\partial_r u}{r}+k^2
\frac{\sin(2u)}{2r^2}=0. \end{equation*} Given any integer $k\ge 1$ and any
integer $m\ge 2k,$ we exhibit a set of initial data $(u_0,u_1)$ with energy
arbitrarily close to that of the ground state solution $Q$, such that the
corresponding solution $u$ blows up in finite time by concentrating its energy.
To be precise, the solution $u$ satisfies \begin{equation*}
  \lim\limits_{t\rightarrow T}
\left\|\left(u(t,r)-Q\left(\frac{r}{\lambda(t)}\right)-u_1^*(r), \partial_t
u-u_2^*(r)\right)\right\|_{H\times L^2}=0 \end{equation*} with a quantized
speed \begin{equation*}
  \lambda(t)=c(u_0,u_1)(1+o_{t\to
T}(1))\frac{(T-t)^{\frac{m}{k}}}{|\log(T-t)|^{\frac{m}{k(m-k)}}},
\end{equation*} where $\|u\|_{H}:=\int_{\mathbb{R}^2}\left(|\partial_r
u|^2+\frac{|u|^2}{r^2}\right).$
