This is the second time in a few months I have seen a question come up about this experiment.
As I have explained before, I am not a chemist, and know only a little about crystal growth. But I hate to see inquiries go for several days without a reply.
In general, chemical reactions, which include crystal growth, are affect by temperature. Rate of reaction generally doubles for every 10 degrees C of the material. This experiment has you study crystal growth at three temperatures - room temperature, roughly 21C, in an ice bath, roughly 0C, and in the refrigerator, roughly 10C. A reasonable hypothesis would be the room temperature crystals should grow about 4 times as fast as in the ice bath, and the refrigerator crystals about 2 times as fast as the ice bath.
If you got no crystal growth from the refrigerator sample, you should review your sample preparation and storage. If you prepared your super saturated borax solution as one bulk batch, and then separated it into each of the samples for the different temperature storage, then sample preparation is probably not the issue. If, however, you prepared each saturated solution batch separately, perhaps the degree of saturation of the refrigerator sample was not quite right.
If the solutions were prepared properly and all temperature samples were the same then you might consider the one phrase in step 11 of the procedure - "be sure not to disturb them". If the refrigerator door was opened during the crystal growth period, mechanical vibrations could have easily disturbed the crystal growth.
As I said, I'm no expert in this field, but perhaps my comments can lead you to a successful completion of this experiment.
I'm happy to see a parent engaging in their child's science education. Keep up the good work and...
Have fun with science!