The oxidation state of Sc in ${\mathrm{Sc}}_2{\mathrm{Si}}_2{\mathrm{O}}_7$ is 

The charge of ${\mathrm{Si}}_2{\mathrm{O}}_7^x\text{ is }{\mathrm{Si}}_2{\mathrm{O}}_7^x\equiv {\left({\mathrm{SiO}}_4^4\right)}_2-{\mathrm{O}}^{2-}\equiv {\mathrm{Si}}_2{\mathrm{O}}_7^{6-}\text{. }$- Hence, the charge on Sc is $(6+)/2=3+$Alternatively, $2x+2(4+)+7(-2)=0\Rightarrow x=3+$