Trying baby-led weaning, but for a baby who puts everything in her mouth (toys, my hair, etc), she just plays with the food and doesn't eat it! Should I just try the conventional way of feeding her?

Never give up mama! :-) I presume your baby is only 6 month old and you have only been trying a couple of times. At this stage, introducing solids is just for "fun" for the baby. They explore it with their hands as well as with their mouth. Don't worry if your lo does not get anything into the mouth yet. Let him/ her explore and play with it. You may show him/ her how you eat the food. Perhaps, you can include him/ her on the table when you are having your meals so your lo can take the cue from you. Remember that they still get their full nutrition from milk at this age so continue the milk as per usual. You can make your baby-led weaning a routine in the morning or for lunch and just continue to do so until the baby learns to put the food in his/her mouth. Eventually, they will get it. But of course, it's still going to be a messy affair :-) Hope this helps.
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