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Four years of high poverty low quality schooling surely destroy any gains a kid might have made in one year of Head Start!
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...all kids show more growth in a classroom completely made up of high SES kids
Some may suggest that "more growth" occurs due to appropriate level of support in the home. Rather than academic growth, intrinsic motivation, delayed gratification, and other traits which correlate with success being directly derived from the classroom experience alone, these may be developed and sustained outside of school. For example, role modeled on family.