You have all seen these sorts of questions before.  They are typical school types of questions.  The first six are taken from the sample items of the Alabama high school graduation exam, and the last two are from math textbooks sent to me on the Internet by math students seeking help. 

Most competent, capable working adults probably could not answer most of these questions or a series of questions like them. Most people do not need to know how to answer them or anything like them.  On the other hand, people who can answer these kinds of school problems correctly may not be able to build anything, grow anything, repair anything, play music, create art, or solve personal relationship issues. Yet the kinds of questions shown here are the sorts of things that commonly make up the substance of schoolwork.  And it is students' ability to answer them correctly that determines whether a school or school district is doing its job properly.  Moreover, because students in culturally and economically deprived schools and school  districts score lower on these sorts of tests than do students in culturally and economically advantaged ones, courts are being asked to require states to pay more money for the education of disadvantaged students in order to give those students "equal opportunities" -- equal opportunities to learn how to do well on these tests.  Some courts are obliging.

This enterprise is misguided in many ways.

These particular questions do not measure how well anyone can solve any problems but these odd kinds.  While it is important that students learn how to reason, solving math problems of this sort is only one kind of reasoning prowess, and probably not the most important except for some scientists, mathematicians, and engineers, for whom it might be equally important as other forms of reasoning skill. 

Knowing esoteric grammar does not tell how well anyone can communicate or understand ideas.  Clear, coherent, and in some cases powerful communication, is what is important.  The study of the rules of grammar is only one way of approaching that, and probably not the best way.

Knowing specific trivial social studies facts does not show how well one understands government, political science, or philosophy of government; nor does it show what sort of citizen one is likely to be or how much one might contribute to society. 

Students without parents or other mentors who can help them understand or do many of the kinds of things required by schools are at a serious disadvantage, a disadvantage schools themselves are not likely to be able to overcome as long as these sorts of topics form or dominate the curriculum.

Students without parents or mentors to motivate them to (try to) learn these kinds of things are at perhaps an even more serious disadvantage,  a disadvantage schools themselves are not likely to be able to overcome as long as these sorts of topics form or dominate the curriculum.

The concept of an opportunity to learn, as with the concept of any "opportunity" is ambiguous.  In one sense I had the same opportunity to win Olympic gold medals as Carl Lewis did.  In another, perhaps an even more important sense, I never had any chance or opportunity to win a gold medal for speed.  (I have written about the concept of opportunity in a chapter on "Fairness" in an online book, The Ethical and Philosophical Foundations of Economics.) Now the Carl Lewis example of the ambiguity of the concept of "opportunity" probably involves inborn physical traits, and to that extent it is not appropriate as an analogy for the situation involving classroom learning. It is only meant to explain that there is an ambiguity in the meaning of the word opportunity, and that there is always a potential difference between having a realistic opportunity and having mere access to the environment where an opportunity could be found by someone. 

The point is that no matter what reason someone is not ready or is unable to take advantage of a learning situation, they have no likely realistic opportunity to learn something just by being  placed in a learning environment that might be conducive to learning for someone who is properly prepared and motivated.  Even if disadvantaged students were put into the very same classrooms with culturally advantaged students, they would still not have the same (real) opportunity to learn, because their initial and ongoing classroom needs are so different and because they will not generally have the same foundations in experience from which to absorb and assimilate the same information.  They will have the same opportunity to learn that you would have to learn advanced physics or advanced music theory if put into graduate level courses with grad students.  It is not that disadvantaged students do not have the ability to learn with the right introduction; it is that they tend to lack the kind of introduction and ongoing environment that schools simply cannot supply or make-up for, as long as the curriculum involves teaching and testing and grading on these unnecessary and irrelevant kinds of topics. 

It is not clear that money is either a necessary or sufficient to solve these particular issues.  While it is true that many schools in economically or socially disadvantaged areas are seriously underfunded and do not have decent facilities and other resources, they also have equally serious difficulties that may not be helped much by the application of money or the mere "things" that money can buy.  For example, paying inner city teachers as much as suburban teachers is not going to lure teachers from the suburbs to the inner cities.  Nor will training and hiring more teachers who are certified in their subject matter make the subject matter of these kinds of test questions more accessible or more desirable to inner city students in any realistic way. And, while having decent buildings is important for students and teachers, decent buildings (or even palatial buildings, as some wealthy school districts have) and a wealth of equipment do not insure decent curriculum or instruction.  If teachers and students do not or cannot make real and important use of their facilities or equipment, it is of no real advantage, or it is of relatively little advantage, to have it.

I have taught inner city college students, and they are just as creative, just as bright, and just as capable of learning as any other students; but the curriculum as taught and as tested is not of much interest or value to them, and they are more likely to know that than are suburban students who are more acquiescent about learning things that make no sense or have little apparent value.  In certain ways, inner city students are much more able to analyze and evaluate meaningful material than are suburban students who have mainly learned to memorize things and to figure out what the teacher is looking for, whether it makes any sense or not. 

To spend energy, time, and money improving anyone's ability to do well on high stakes kinds of tests is to waste that energy, time, and money.  It seems to me it is even a greater waste of money and of everyone's, including the students', time and energy to try to get schools to be geared toward improving test scores by putting more emphasis on teaching disadvantaged students the kinds of things tested above.  They have greater need to learn more important things, as do all students.  And they have a greater chance than most students of learning the more important things, if they were taught them by capable teachers, particularly teachers who can distinguish between what is basic as a foundation for all other learning, reasoning, problem solving, analyzing, calculating, and communicating on the one hand, and the above kinds of things states and the federal government want taught and tested, on the other.