I recommend giving Thoreau's Walden a read. Whilst the vast majority of the novel do not pertain to the discussion at hand, he does address the issue at various points. He made a point that many students at Harvard, intellectuals no doubt, are not at all familiar with English classics with most students prefer 'Little Reading' (material which do not require much mental activity).
Keep in mind, this was written in 1854. Nevertheless, as OP's article pointed out, geniuses were still being churned out back then, as well as today.
Whether students are becoming dumber is really hard to say. Considering that IQ is constantly rising (Flynn Effect), you could easily argue the opposite. However, a recent study showed that an impact the internet has on people (not exclusive to teenagers) is that it could easily re-wire your brain. As other posters pointed out, this led to a decrease in attention-spam and long-term memory (I can attest to this as I currently have about 20 tabs open in my internet explorer and can move among them faster than my mum could type a sentence). Is this making kids dumber? I wouldn't think so. For one, the amount of information (while most of it useless) they receive and process is infinitely greater than what students in the past would handle. Such is the workings of the internet.
Personally, the reason why students appear dumber solely rests on the education system. According to Wikipedia, Learning is defined as 'Learning is acquiring new knowledge, behaviors, skills, values, preferences or understanding, and may involve synthesizing different types of information'. Frankly, I see a waned use of learning in the current education system. Learning is most effective when a person is interested in the topic at hand and willingly understands the information presented. Whilst completely anecdotal, I believe this has some credibility. When I visit my school's library, most of the older books appeared to be checked out by students circa 1980-1990 with little or no borrows post 2000 (so I decided to help myself to some of their books but that is another story). Now, is this because students were reading more? Probably. However, I noticed that a number of these books (mostly economic and political theory related) were replacements for textbooks. Is it possible that the shift from books to textbooks explains the possible decline in education?
I believe it makes perfect sense. Students are not learning from school anymore. Rather, they are fed information, in large, dense chunks (I mean, that is what a textbook is, a book detailing absolute facts, isn't it?) So what I propose is, keep the textbooks. Teach most of the students basic math, english, science or history through the use of textbooks. However, after 6 years or so, scrap it. Students who wish to continue learning may continue, others may leave. Students will then be required to conduct their own education the 'natural' way, through direct and personal acquisition, not feeding.