You need to recompile the module, which would require not only a compiler and build environment, but the kernel source itself. I don't know if BackTrack ships with a compiler, but even if it does I doubt it includes the kernel sources; they are simply too large to put on a live CD.
The problem is, you need the kernel sources that were used to compile that kernel specifically. That needs to be made available from the developers, is there any online repository for BackTrack packages?
Once you have the kernel sources, and are able to compile a new version of the module, you are still looking at a temporary solution. You would need to remaster the BackTrack ISO to add in this new module, or else you will need to repeat the procedure at each boot.
My personal suggestion would be to use a more general-purpose distribution to learn on, and actually install it to a spare drive. Live CDs are good learning tools to a point, but eventually their temporary nature becomes more of a hindrance than anything. If you can't spare a drive to install to, you could even run it in a VM from your desktop machine.