I think it's a generational difference. I whistled it to my mother (in her eighties) and she said "Itsy Bitsy". I believe I grew up with that and did a double-take in my daughters' childhood when they sang "Incy Wincy/Eency Weency" (Eency Weency is the spelling in the Playschool Useful Book publishe 1979). I switched in order to avoid confusing them.
My mother swear she knew Incy Wincy Spider at school - but she is a very old lady and might be wrong. I, on the other hand, am only a fairly old lady, and I'm pretty sure we learnt it at school in the very early sixties - and the spider was definitely Incy Wincy!
Spider
Re: Spider
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My childhood is flashing before my eyes!
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Re: Spider