I don't know what research teachers think they are quoting. But I think "some" kids will appear to even out and these are the ones they are talking about. Kids who are average or bright but didn't have preschool and the parents never talked about letters, read to them, or do or anything academic at home. These kids show up at kindergarten or first grade completely clueless but they are cognitively ready to learn the concepts, so they make big gains fast. They might jump from the low reading group to the middle reading group within weeks or months. Then there are the kids who will probably always be in the low reading group unless they get special help. They either have a disability, or they are simply "slow". I tutored reading and worked with about 18 kids in first to third grade. With most of them there was NO WAY I would have been able to teach them at age 4 or 5 to read. I would have rather banged my head against a wall. Most of these kids made gains with help, but tended to fall back down when the help was withdrawn. I had the most success with the very young kids who just hadn't been exposed to anything in the past. Those are the kids that had parents who did nothing, and just needed a little more 1 on 1 attention. Then they "evened out".