The problem is that they already don't end up with practical applicable skills, and this method (teaching with an emphasis on discovery over lecture) is known t

The problem is that they already don't end up with practical applicable skills, and this method (teaching with an emphasis on discovery over lecture) is known to have results. See, for example, this lengthy technical document describing (in more scientific terms) teaching math like art [1] [1]: http://www.ams.org/notices/201308/rnoti-p1018.pdf http://www.ams.org/notices/201308/rnoti-p1018.pdf