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Betamale:

• Numeracy is not maths
• Rote learn numbers and basic operations
• Explore

Not the other way round and trying to justify it with trendy words and obscure references makes it even less credibl.

Make your own subject, sit in a cornfield talking about your feelings and how to explore....fine.....just don't call it maths or suggest people should who are teaching or coming into teaching

Of course.

You can have a sensible debate about whether zero was discovered or invented.Maybe you can even have that debate with schoolchildren.

But they need to be nicely behaved, disciplined schoolchildren who are comfortable with the notation 0.002 and who can appreciate the problem when you throw 0/0 or 0^0 at them as teasers.

The decimal place value system isn't maths - in fact the vast majority of numbers are no longer represented that way. But you do need to learn it, because it's the social convention, just as it's the convention to write English in Latin characters and not in ideographs or in Hebrew letters.

 Don't debate with that idiot bgy1mm. He is a failed computer programmer from Leeds who has never set foot inside a classroom since he left school.

Rather fitting the stereotype, I suspect he lives his life through a series of online fora. Quite why he feels the need to infest this one with his asinine and ill informed vacuities I have no idea.

Brookes - yes.  Weebecka's getting a much easier ride on TES than teasdaler did when she started out on NCETM

scentless_apprentice:

Again, you're saying therefore that Mathematics is a social construct. Which, frankly bewilders me.

Well that's not surprising.  It's a totally bewildering and weird idea isn't it?  I'm certainly not sure I totally understand it myself.  I'm no idealist scentless_apprentice.  I just kind of am where I am!

I'm not sure where to begin with this - we could look at the difference between pure maths (which is entirely abstract, so we have issues as to whether it is a reality let alone an objective reality) and applied maths (which has been shown to mutate often and to be constructed in contexts).

Or perhaps we could look at the philosophical and psychological foundations of constructivism.

Constructivism is interesting because when you go on international forums it's a fundamental part of the theory of education. But when you come back to blighty and mention it the general reaction is 'burn the witch'.

Or is this all going a bit far scentless_apprentice?

Shall we just accept that you see maths as being an objective reality and I see it as being a personal, social and contextual reality (or something like that, I'm not sure I've expressed it very well)?

The implications are not major - only that I deliberately teach my students to question as much of the core curriculum as possible and that I am open to the idea that some of the types of teaching described in parts 1, 3 & 4 of the POS could be more powerful (if we are indeed constructing a personal reality for students) than one would expect them to be if we were dealing with an objective reality.

I'm not remotely interested in chucking away the core curriculum.  But I want my students to question it and to have time to work on rich extended and contextualised activities too.

Karvol:

The Dutch mathematical education system

Please tell my about your experiences with the Dutch education systme Karvol, I'm interested.  Have you been fully trained according to the Freudenthal system?  Which aspects of it did you like and which didn't you like?

scentless_apprentice:

How can any student have any faith in Mathematics if they're being taught that nothing is concrete, then be told 'but by the way, to pass the exam, you're going to have to accept it'.

I teach them to treat is as if it's not concrete so that they learn to fully understand it, not that it is not concrete.

Exams are important. 

I don't know your references in this post so I can't comment on them.