I doubt that most of us have had the need to root pole beans, so...I can only suggest two methods to try.

1. Fill a clear glass with water, cover the top with plastic wrap, poke a few holes in it and insert tip cuttings (cut below a leaf removing any leaves that will be below water)) through each hole to see if they will root in water.

2. Place several small pots of soil around a mother plant, bending a leader into each one covering the stems with soil and allowing the tip ends to be exposed. They may root along the buried parts of the stem and can be severed from the original plant after developing a good root system.

I rather doubt that the pole beans are going to root for you. They are an annual, are they not? Why can't you get more seeds?

And, if you do get more seeds, why not wait until the growing season to germinate them?

I'm not trying to be rude, but why did you plant them at the end of season, instead of at the beginning of the growing season?

What kind of pole beans are these?

Janie