Cutting mats are NOT "just" plastic mats!! The better ones, the proper ones, are of a special substance that "closes" after the slight indentations of the cuts are made. One "best brand" calls theirs a "space age" self-healing material.
Gosh, the safety issues of using glass surfaces for rotary cutting just scare me to pieces!!
Would you cut up your meat with a razor blade? Would you cut your daughter's hair with a rotary cutter? There is a reason there are particular tools for a particular purpose! Please encourage her to use the "real thing".
Jan in VA