Sue I have a few spools that just keep splitting so i now use them in my bobbin. Hope this helps. Waste not want not :)
All of your answers are excellent. Have done all these. I also bought a thread stand that stand beside my machine & sew with thread from it. This helped me when I was having problems. Also thread will dry out sometimes & become brittle. Bought some at a yrd sale once & it was that way. I peeled off a few yrds & threw away. the rest of the thread did fine. I always do everything else the other have told you first. Starting with changing my needle./Lillian
It could also be the quality of the thread. Smoother strands of thread tend to has less fuzz and break less. Also a burr (protruding, ragged edge) on your needle could be breaking your thread. Try a new needle with the same thread and see if that helps.
I just watched a tutorial about this the other day & she said if your thread shreads chances are it is one of 4 things, tension to tight, tension to loose, needle needs to be replaced & the last one is to clean the lint from under your switch plate & under your bobbin casing. Hope this helps
Try adjusting the tension on your machine;sometimes that helps. Also check your needle, it might not be the right kind for the project you are doing; match needle to fabric type. Are you using the right stabilizer? Any of these can affect results.Good luck!
Try using All Purpose Sewers Aid, just run a bead down the spool of thread, or try a Top Stitch Needle
Have you tried putting in a new needle with a bigger eye? Also take unwaxed dental floss and pull it through the tread path for incase there is some unwanted fluff. I do not have the unwaxed floss so I took topstitch thread and pulled it through and it worked. Hope something helps. If it keeps breaking throw it out then it is a bad spool.