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weebecka:

And when God created the universe he also created wikipedia.

You asked me to say what multiplication is. I gave you a definition. I didn't say that wikipedia was the be all and end all. 

I've listened to your viewpoints, I've questioned them, disagreed with them, debated your choice of references and I hope proferred a coherent argument against them. However with comments like

weebecka:

And lo maths was done and the objective reality was created.

you've seemed to have got fed up with my questioning of your ideas and just gone for plain sarcasm.

I'm not trying to be morally superior in this discussion - I'm just coming from principle of Mathematics being objective. If you can't accept that, fine. But what you have to agree that a debate about the social construct concept of Mathematics has no place in a child's classroom, as the effects of it can be catastrophic. You've even admitted that you'd ignore your own priniciples in exam revision, so basically you're saying that at this point you'd teach to a test?

The issue there is that you've basically spent two years deconstructing a student's concrete belief in mathematics, and then in the space of a few weeks decided to try and reconstruct it along the lines of where I, and many other objective people come from. 

So, if that's your goal, where does your teaching style actually get you?

scentless_apprentice:

The issue there is that you've basically spent two years deconstructing a student's concrete belief in mathematics, and then in the space of a few weeks decided to try and reconstruct it along the lines of where I, and many other objective people come from. 

So, if that's your goal, where does your teaching style actually get you?

A much more robust, secure and flexible understanding of mathematics for my students.

They don't just accept what they are told, they challenge it, connect it to other ideas and, most importantly, discuss and describe it. Describing your own understanding of mathematics is well established as being one of the most powerful tools for learning.

And an environment of confident mathematical creativity and invention.  Of course most of what is being invented has already been established and proven by others.  But interestingly not all of it.

weebecka:

And an environment of confident mathematical creativity and invention.  Of course most of what is being invented has already been established and proven by others.  But interestingly not all of it.

I'm far from persuaded that this is can be a reality. Maybe in the top set at Eton you can sometimes coax children into deriving basic mathmatical theorems by themselves, but even there I'd guess it's a difficult thing to do.

In other subjects, yes, but there creativity isn't such a high bar.

Maths_Mike:

Of course you could say actually its not the resources - they are truely superb - it the ability of the teachers to deliver them - well that might be the case - as with Weebecka's ideas - they may be brillaint for her - that does not mean they are the best way for everyone.

Very good point Maths_Mike,

You may have noticed I'm very cautious of telling other teachers how to teach (although I'm sure it doesn't seem so to some).  I've only referred to a few activities to illustrate conversations.

I believe students should be taught (in a critical way if possible) a robust curriculum.

However I also believe students should spend some time working on activities which start from where they are and build from there.   There a many, many ways this can be done.  It is important the teacher has significant freedom in the way they choose to do this, both to best utilise their own strengths, but also because it's hard enough to construct activities which start from the child in this way when you've got a class of 30 different students to deal with.  If you're being told what to do from above as well it's damn near impossible.

What's needed instead is that teachers have access to inspiring examples of such teaching.  ATM has always been very good at this, but ethonographic videos (where you see good lessons and the teacher is interviewed so that the viewer can understand their context, motives and perception as to what's going on) and well constructed training can also be helpful.  The aim of such training and resources should not be to 'tell the teacher what to do' but to give them a taste of what is possible, communicated in a way so that they can take what they want from it and leave what doesn't suit them.

scentless_apprentice:

I'm quite happy with the Wikipedia definition:

"Multiplication (symbol "×") is the mathematical operation of scaling one number by another."

I'll have another go at responding to this one, since I messed it up last time.

Scentless_apprentice,

Even with a very simple concept like multiplication, there is substantial variation over time and confusion now as to what it actually is.  I can explain this further if you like (it helps if you spend sometime thinking about what you personally think multiplication is as part of this), or we can move on to a different theme.