So I looked at the pedals today in class. The ones I can clip into say shimano. The pedals I can't clip into say WAM-S1. We took the shoe off and placed them into the WAM-S1. It looks like the front end is going in fine, but it's like the cleat is not long enough vertically to securely clip in on the back - hence the reason I can slip out easily. As some posters have mentioned, I think my shoes require SPD-SL cleats, as it is written on the sole of the shoe. We found some SPD cleats that my instructor had in storage and she's going to try installing them Thursday. Hopefully no adaptor required.

These look like the ones I CAN clip into.
I can't post urls so just put the http part in.
drivemybike.files.wordpress.com/2009/05/spdpedal.jpg