You are probably right about it being some kind of insect.

Interesting. Could be from Gordian Worms. I've never encountered them before but they live all over the world. I searched the internet but couldn't find any pictures of their egg strings. There are lots of articles on them but they all pretty much say the same thing. Check out the link below for more details.

Here is a link that might be useful: Gordian Worms

I don't know....could be dragonflies as well.

"Female "basket tail" dragonflies (Epitheca spp.) carry a batch of eggs and drag their abdomen across the water surface, depositing the eggs in long gelatinous strings. The eggs are clear to milky white with tiny spots of embryos. Toad eggs look similar but they are larger and more silty in appearance. Also, toad eggs are often right along the shoreline in weedy shallows among plant stems, and dragonfly eggs will be slightly further out in deeper water."

Found one site that said the egg strings may exist anytime between May and July. Let us know what you find out.

Thanks for the ideas. I do get many dragonflies and damselflies, however I tried googling baskettail dragonfly eggs and came up with a photo of eggs that looks quite different although you never know.(http://southwestdragonflies.net/caphotos/basketaileggstring.jpg)
I couldn't find photos on egg strings for Gordian Worms either.

I'll keep searching on the internet. In the meantime, I went outside to check on the pond and skim some floating algae scum and see that most of those eggs have disappeared. Either the goldfish ate them, or they came off when I was skimming the algae (hope it wasn't the latter).
There is still some there, so I'll be careful and keep an eye on it. Not much I can do if the goldfish decide to snack on it.