My personal favorite are Frogglez, which have a neoprene strap that stays in place. I like these because even small kids can operate them without help, they do not pull hair, and unlike most goggles, they do not sink to the bottom of the pool. (Some kids become very alarmed to see their belongings drifting down to what they think are impossible depths, never to be seen again!)
You can purchase the entire goggle or add a Frogglez strap to any goggle that has a loop on each side. (Types that hold the strap on with a peg that goes through a hole in the strap cannot take a Frogglez strap.)
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I have also extensively tested this style as “loaner” goggles. They are inexpensive, easy to adjust, and comfortable for a range of face sizes and shapes. They also seem to be pretty durable, and the straps are not horribly slippery. (Some styles are prone to sliding down the back of the head, which causes leakage.)
The question of whether to get the kind that cover the eyes only or the kind that cover the nose is one of the child’s comfort. In fact, some kids with sensory issues tolerate goggles poorly altogether. A goggle lens that is too small will cause discomfort, one that doesn’t seal well will leak, and some kids feel smothered with a nose covering while others find it more comfortable than risking water up the nose. Individual preference is the best guide! Please let me know if you’d like me to bring a selection of goggles to a lesson for your kid to explore before you make a purchase.