The yin and yang of maths education - Part 1.

Many authors have written about the need to move from a curriculum which teaches an established curriculum to one which encourges students to mathematise their experiences of the world for themselves.

I see things a little differently.

I believe that both forms of mathematics education are justified and of great importance.

Modern technology offers students a wide variety of ways by which they can efficiently and effecitvely acquire orthodox knowledge.  Teachers who utilise this technology can create more time in the classrooms on the types of tasks which effectively develop students' abilities to interpret real life situations, struggle with connected and extended task and to learn to express and develop their own thinking. 

Modern technology can also enhance the quality and relevance of the experience a students has when they explore mathematics for themselves because they can rapidly interact with established thinking, notation and invididuals who are interested in their area of enquiry.

So it is natural both that more constructivist teaching can and will occur and also that such teaching will lead to a greater coverage of core concepts.  But I prefer not to think of the outcome as being a shade of grey although that's how my lessons might appear to others. I prefer the visualise black and white, yin and yang.

Here is an analogy.
Which is better - pop music?  classical music?  something which is halfway between the two?  or something which is unashamedly both, black and white, yin and yang with no compromise to either?  Here's a video to illustrate my preference.
http://www.youtube.com/watch?v=jTcNlcefAQ0

More orthodox justifications for and desriptions of this perspective will follow as and when I have time.