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Betamale:

Could you just put it in Laymans please?

you 

weebecka:

Could you tell me which bit you'd like me to explain?...

..I prefer to use ethnographic examples

I appreacite you went on to explain this on but I find often I have no idea what the bottom lesson message is.

Anyway, I true believe on developing teachers. I am with you on that, couldnt agree more but I believe we differ in direction.

I want to educate pupils in maths, raise attainment and get on with solid teaching where I can push mathematical thinking.

I seem to find many of those in teacher training or Ofsted are driven more towards avoiding teaching subjects and making fluffy teachers to justify  poor behaviour management, having to be politically correct and falling standards

If mathematics teaching is evolving why are we chucking out GCSE papers that half decent pupils could do by the end of year 8/9?

 Weebecka I noticed you use a lot of jargon and allude to other sources. Usually it is done to obfuscate matters for no reason other than to obfuscate. Usually, but not always.

Anyway...

To cut a long story short I decided to download anything by Carol Dweck, and some of the things she says are quite interesting.

Have you actually done some research on this, and if so, any chance that we could have a look at it?

 I did try and see if I could find any research papers that you had published as being a member of staff at MMU, but you don't seem to be on their staff list. 

Karvol:

Weebecka I noticed you use a lot of jargon and allude to other sources. Usually it is done to obfuscate matters for no reason other than to obfuscate. Usually, but not always.

Hello Karvol,

I don't use jargon to pull the wool over people's eyes.  I use it when other language doesn't clearly express what I'm trying to say.  I also use it because it comes naturally to me from my international and philosophical work.

If people probe something in particular I'm always happy to try and explain or give real life examples.

Karvol:

To cut a long story short I decided to download anything by Carol Dweck, and some of the things she says are quite interesting.

Have you actually done some research on this, and if so, any chance that we could have a look at it?

I've never researched on Carol Dweck - as I said we had INSET on her provided by Barry Hymer.   If you haven't done so already it's quite nice to watch a youtube of Carol by the way. 

Karvol:

I did try and see if I could find any research papers that you had published as being a member of staff at MMU, but you don't seem to be on their staff list. 

Thanks for that reminder - I need to log in and do my staff list profile.  I've only been there a year and haven't published with this team.  My main articles on maths education have been in MT (and before that MicroMath).  I've written as Rebecca Hanson and Rebecca Teasdale.  You could look, for example, at MT210 and MT211.

weebecka:

If you look at the POSs Betamale you could say the objectives fall into two categories.

Some relate to students acquiring the core curriculum - that is learning and becoming fluent in the mathematical processes and vocabulary which have been agreed and written down by others.

The other relate to students 'connecting up' their mathematical knowledge - they are learning how to mathematise the world for themselves.  The are working on extended problems and contextualised problems.  They are often working with originality and significant indendence when they are working in this way.

Would you agree that this split exists?

If I said I think you are the kind of teacher who want to ensure your students are doing the first reliably and effectively before introducing a bit of the second would that be fair?

Im not sure what POSs are although may know them under a different name.

Essentially what you have said is correct and I will summarise:

Maths should be taught in terms of content AND process/context. We sit in the same corner there.

Now where I oppose your views is the shift towards the latter when there is no solid skills in numeracy being built.

I cannot do 'rich tasks' anywhwre close to what I would call interesting or challenging as a result of poor numeracy and simple understanding of maths, much of which comes from poor primary education, much of which you are advocating, along with all the other factors.

Pupils should only explore maths, be cross curric and do all that 'fluffy' stuff WHEN and only WHEN they are fluent in basic operations and mental/written maths.

I also strongly disagree with the maths room being a fairground of group work/exploring/sharing and doing f'all work yet 'find themselves'

If you want those skills, fine waste the time in lifeskills, tutor time but please, get the pupils numeracy sorted before this is pushed on to trainee teachers.

Watching new PGCE students is painful as they walk into tough schools with their bag of big dice and A4 size playing cards only to actually do 5 minutes of pure maths and get eaten alive by idiotic children.

I am still teaching numeracy to my year 10 C/D border kids....why?

So yes, I like rich and functional stuff WHEN pupils are equipped to do it and not at the expense of real mathematical learning. you have 20-22 hours to do fluffy cack somewhere else in the time table

weebecka:

So you feel that the heart of a mathematics education should be about the acquisition of the fundamental axioms of mathematics and that is students acquire these they will then be able to mathematise the world.

Where have I said 'the fundamental axioms of mathematics'? I'd just expect as a minimum that students should be able to count, add, subtract, multiply and divide before they apply such concepts to real life problems. As Betamale describes, many teachers are still trying to get 16 year old students to be able to calculate basic products of numbers because they've been taught through a subjective philosophy from primary school.

weebecka:

You believe that mathematics is an objective philosophy.  It exists, out there in the world.  The rules of mathematics are fixed and unchanging.  We learn them, we use them, that's it?

 Now you're misquoting me. Objectivism for me is that idea that within the philsophy that is Mathematics, you are right, or you are wrong. Obviously statistics is a caveat to this, but then again the calculations in statistics are either one way or another and it's the interpretation that is subjective.

If you take the approach that you, and bgy1mm, and others on here take, then you lose the objectivity - i.e. the all encompassing idea that a mathematical theory is only useful if proven - and Mathematics itself is just another subjective philosophy. 

The pride people have in Mathematics - and the pride all the great mathematicians have had in their career (right from Pythagoras, through Al-Kwarizmi, Fibonacci, Newton, and so on) is that Mathematics is THE objective philosophy. Lose that, and we might as well stop, now.

weebecka:

If so could you tell me a bit about your experiences of working with students on rich and extended investigations (or any work where they've had plenty of opportunity and encouragement to go beyond the syllabus) - have you found that they way students have learned through these activities has backed up your view?

I've actually done a lot of work in this area. During my two periods at university I worked with school groups in investigating the structure of bridges, and investigating and developing principles that determined which designs would take the strongest loads; in another session with a different school I led a project investigating the mechanics of bungee jumps, and how to design the rope structures to have the most 'thrilling' bungee jump without damaging the body; In my time as a teacher I've used the Bowland Mathematics materials to investigate the reduction of Road Traffic Accidents in a town; developing a new Smoothie drink for the health food market; that just touches the surface.

Whilst these were all fun, and the students learned a lot in applying their knowledge of Mathematics - the one thing that stood out is that whilst students had sound ideas, they did not have the concrete Mathematics (in whatever form: arithmetic, algebra, geometry...) to execute them.

In any field, ideas are all well and good - but if you don't have the concrete tools to develop, formalise and execute them, then they're useless.

And to quote a great man 'Nothing useless can be truly beautiful'.