It is not the first time I come back on the topic: everything is a matter of perspectives.
Nothing can be really different, new, modern, innovation and so without changing our point of view. When “education” comes into play things are even more complicated. It might be that we think of teaching the right stuffs, the correct principles, good ideas in general and the outcome can be exactly the contrary.
Either we used the wrong approach or the “audience” didn’t get our perspective. In both cases the teacher and/or the student should change their perspective (or their mind?) if we want to share some knowledge, to transmit something to the future.
Unfortunately in these cases numbers and equations, potentially more objective, are of little help; words can be easily manipulated on both sides and faith is usually not enough. It is hard to say (and even more to do), but IMHO it is required modesty and work.
A perspective change may be not natural and easy as it appears on the “other side”, but I’m sure results and gratifications will come. In the end is it correct to teach to go forward (backward) or it is enough to teach to go and leave the freedom to choose the direction (eventhough we figure out the right angles)?
PS @ 09.12.15. Let me add this quote, absolutely apt:
Life can only be understood backwards but it must be lived forwards [S. Kierkegaard]