Paul Lockhart has stated that real mathematics (the process of discovering new facts/creating your own conjectures, i.e something that mathematicians have to do) is not widely taught to students. Paul Lockhart's "A Mathematician's Lament" is only that however, a lament and not a detailed proposal or plan for educators.

This begs the question: what do you suggest as a better mathematics education program /sci/? How should we teach students to do Maths properly?