As an example of the first situation, an interesting fact overshadowed by how it is presented, please see the article by Catherine Shock and Jay P. Greene, Adding Up to Failure, in the Winter edition of the City Journal. The authors did some research which turned up an interesting fact: among top ranked education schools, nearly twice as many courses are offered around multiculturalism and diversity as are offered around math.
Interestingly they lead and end the article with perfectly sound propositions.
A good education requires balance. Students should learn to appreciate a variety of cultures, sure, but they also need to know how to add, subtract, multiply, and divide.
The issue isn't whether we should be teaching cultural awareness in education colleges or in public schools; it's about priorities. Besides, our students probably have great appreciation already for students from other cultures—who're cleaning their clocks in math skills, and will do so economically, too, if we don't wise up.
One could quibble with their methodology as outlined in the article but I suspect that their key finding is materially correct. It certainly maps to experiences we have had with the teachers of our children, individuals who as a group are broadly well intentioned, motivated and effective teachers but frequently light on the analytic/scientific side of things. And I don't think this is unique to the US, we experienced it with our kids in school in the UK and Australia as well.
This hits one of my hot buttons. I view mathematics and numeracy in general to be part of a continuum with reading - they are all part of the symbolic representation of an external reality. Literacy lends itself to a fine nuanced comprehension of reality, particularly non-quantifiable aspects of reality (such as beliefs, feelings, etc.) while numeracy at the other end of the scale, lends itself to more testable aspects of reality.
So a finding such as this, that our educators are being over-exposed at one end of the continuum and underexposed at the other is a fair issue to raise and debate. The authors of the article ought to be commended for the effort to shed light on the issue.
It is unfortunate then, that the body of the article is laced with derogatory or mocking comments (e.g. "professors are a self-perpetuatiing clicque") and with belittling comments (e.g. "prospective teachers haven't cried out for more math courses because such courses tend to be harder than those involving multiculturalism".) That tone tends to overshadow the real research they have done and the validity of the point they have raised.
Fortunately, regardless of how things get reported, there are things that can be done. It is someone else's fight to figure out whether teachers in education programs need to be better trained in rigorous and analytical thinking. I leave that to them.
As parents though there is plenty we can do through the books we choose for our kids. The nonficiton wing of children's books has long been sort of a red-headed step child. None-the-less there are great books out there that stock the minds of our children with useful information and help develop the capacity for observation, measurement, analysis and constructive skepticism. TTMD is slowly beginning to build a set of book lists to that end (for example see the book list, Teaching Children to Observe.)
There is a new children's book blog as well that was just launched this month, I.N.K. (Interesting Nonfiction for Kids) that is aimed at bringing attention to the quality books in this genre that can enhance the lives of our children.