Thank you for your question, Maryann.  Although you can till the straw under, left untouched it serves some of the same purposes as a cover crop.  It protects the soil from compaction (by rain and snow); it slows down the growth of weeds in spring, and, as it decomposes, it  returns nutrients to the soil for reuse in new plants.  However, because it is so fibrous, soil microbes can break it down much more slowly than turf grass, for example.
Some common mulches provide nutrients deeper in the soil, because they have nodes on their roots that convert gaseous nitrogen into a form plants can absorb.  These are the legumes, including clover, peas, alfalfa, beans and vetch.  (Fava beans are also edible!). They need to be removed or tilled under before they flower, to prevent seed production, lest they become weeds.  There are several other grasses used as cover crops, as well.  
The decision is yours as to whether you plant a cover crop, or just leave the straw, but cover crops should be in the ground to germinate ASAP.  Good luck!

Thank you so much!  Straw will go to the weedy edges of the garden and we’ll sew fave beans in active part.  

Maryann



Great!  With beans (and peas), don't remove the flowers and seed pods, or you won't have any food!  Just harvest them for the table so the beans don't sprout.  You can also save some beans and replant them next fall.