We compute ko_*(K(Z/2,2)) and ko^*(K(Z/2,2)), the connective KO-homology and -cohomology groups of the mod 2 Eilenberg-MacLane space K(Z/2,2), using the Adams spectral sequence. The work relies heavily on work done several years earlier for the (complex) ku groups by the author and W. S. Wilson. We illustrate an interesting duality relation between the ko-homology and -cohomology groups. We deduce a new result about Stiefel-Whitney classes in Spin manifolds.

We thank the referee for comments which led to improvement of exposition.