Other pasts are certainly worth attentions, but are better studied in the context of a prior acquaintance with personal-local, national. And global history. That is because these three levels are the ones that affect most powerfully what all other groups and segments of society actually do. The answer is yes, if teachers administrators try hard to put first things first and achieve a modicum of clarity about what everyone ought to know. What is needed is a vision of the whole, warts and all.
Global history is perhaps more difficult.
Certainly our traditional training sidesteps the problem of attaining a satisfactory vision of the history humanity, since few historians even try for a global overview. Still, some have made the attempt. Moreover, every scale of history has its own appropriate patterns which, once perceived, are as definite and as easily tested by the evidence as are the meaningful patterns that emerge on any other scale. This means, I think, that careful and critical world history is attainable just as surely as is a careful and critical national history that does no omit the important and newly self-conscious groups that were previously overlooked. But consensus is slow to come, and may never be achieved.