I get what you're saying, I'm experiencing it, too. There are limited resources (hours in the day, available teachers and learning materials, money, miles, my child's mindspace, everything has its limits, it seems), and only so much of my child's daily experience can be devoted to dedicated language learning of one sort or another (ASL, spoken English, written English, Mandarin, Spanish) -- she wants to play piano, to do gymnastics, to ride her bike and play with her friends and her dogs and chickens, to eat, to sleep once in a blue moon
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If we spread her attention too thin, sure , she may get some phrases of each language, some basic skills. But we might be sacrificing mastery of one for this sort of dabbling if we try to do it simultaneously. Most educators recommend intensive immersion in one and then another language to truly achieve mastery in 2 languages (and so on, for more languages). Sequential learning.
So, we're asking a lot of our little one to pick up 2 languages simultaneously. I'm glad that she had a foundation in ASL to start, or I think it would have gone by the wayside if learned hand in hand with spoken English.