You'd be surprised at how often point #2 cannot be assumed to be true. There are some personality types that just cannot see big picture stuff, despite how much you work on training them to see it. These are the detailed-oriented people who become fixated on minutae that they can't see big picture stuff.

Have a look at what the Motesorri style of teaching does. I have a few relatives that are teachers (active and retired) in traditional schools and the younger ones are sending their kids there, rather than through the traditional system.

Tufte's ideas are good for presenting simple information. He gets many things right (eg if the visualisation doesn't work in black and white, adding colour won't fix it). However, many in the infovis community are outright sceptical, if not dismissive of his ideas for analysing high dimensional datasets.

Where his ideas really work is once you have "the answer" that you want to present to someone else. However, the basic exploration of the data to find interesting keypoints, is not what he specialises in. There's whole communities devoted to techniques for datamining and presentation, principly infovis/Visual Analytics.

The infovis community has been dealing with these subjects for years. There's many different visualisation techniques around. Here's a list of the past conferences and the papers:

http://conferences.computer.org/Infovis/

Plenty of good products out there, but the one that I like most is from Tableau Software (http://www.tableausoftware.com/).