<p>You all are so nice to take an interest in our case. This forum is quite amazing. </p>
<p>Schools that are reputedly demanding (oft-mentioned are Chicago, Swarthmore) are reasonably seen as that for the majority of their admittees. So, the rational observer goes to the website or rankings to see who constitutes the majority of their admittees, and voila, there are either 25-75% test scores or the grid that separates 600s from 700s in math and verbal (GPA either absent or grouped, mostly). If a kid falls above the 75%, that is a good sign to start with.</p>
<p>(Note that GPA is almost always absent or vague, presumably because equating grades from even two schools is hard, and from thousands of high schools is so hard it moves into the realm of statisticians and demographers.)</p>
<p>But, from a consumer's point of view, there just isn't enough information to judge for a particular applicant how hard the school really is other than anecdotal reports from students he/she knows who appear similar to the applicant and who attend the college.</p>
<p>This is because, (source for #1 is CTY/JHU program research):
1) There is a huge difference between a 700 verbal SAT kid and an 800 kid. The verbal scores correlate much more with basic mental ability than math scores at that level, (as a contrast, Cal Tech kids who would get 1200 on a math SAT if the scoring went up that high are overwhelmingly likely to be extremely smart verbally because there is some correlation of the two scores). </p>
<p>2) Left unmeasured in any systematic way is the capacity to focus or concentrate for several months at a time on demanding material. </p>
<p>This latter, focus, is judged by necessity almost entirely on high school grades (what else is there), but I hardly need tell you that very smart kids in high school courses that they are naturally good at can get As easily. The only test is how they do in courses that they are not good at, barring learning disabilities. But for high school kids who are good at every core subject, with test scores over 1500s, there is no way to make this assessment from a distance. In other words, they haven't been really put to the focus test.</p>
<p>At the higher end of the focus spectrum, however, I believe there are huge natural differences, even for kids with nearly perfect test scores, partly because the scores don't extend high enough to measure at the top, and partly because a smart kid who focuses easily is just not going to have to spend much time studying. </p>
<p>My line of work accepts a huge span if you are talking about focus, and a smaller span if you are considering basic mental smarts. Example of high focus demand: new associates in huge law firms assigned to antitrust sections are cast aside quickly if they show signs of flagging in absolute concentration and output, because they will have to do this for most of their working lives. This means 10-12 billable hours a day of pure concentration on more complicated stuff than most lawyers have to address, six days a week usually, eleven months a year, and over a forty year period. The work load at Chicago would be nothing for such people. In fact one of my good friends many years ago was the valedictorian of the UChicago law school and spent little time studying. It was effortless for him, mildly annoying to the ordinary mortals around him, they told me.</p>
<p>As for a kid with great focus and lesser basic ability, my guess is that schools like them better than really smart kids with lesser focus, for obvious reasons. In the long run, success goes to folks who work efficiently and long, although they may have to adjust their desired field of work slightly. </p>
<p>Sorry this is so long winded. What is the point? My instinct tells me that my daughter would find the humanities courses at a place like Chicago not too demanding, but any serious math or science course would be a huge problem. We have spent thousands on trying to figure out what the problem is, with no luck. It probably has something to do with poor rote number/symbol memory, but highly paid experts disagree. So, the gloss I use is "not a grind," even though that is not, strictly speaking, accurate.</p>
<p>Whew. Sorry, folks. Too long!</p>