The connective KO-theory of the Eilenberg-MacLane space K(Z_2,2), I: the E_2 page

We compute the $E_2$ page of the Adams spectral sequence converging to the connective KO-theory of the second mod 2 Eilenberg-MacLane space, $k{o}_{\ast }(K(Z\mathrm{/}2,2))$. This required a careful analysis of the structure of $H^{\ast }(K(Z\mathrm{/}2,2);Z_2)$ as a module over the subalgebra of the Steenrod algebra generated by $S{q}^1$ and $S{q}^2$. Complete analysis of the spectral sequence will be performed in a subsequent paper.