Topic: Does the nature of mathematics change as students get older or is it only the teaching methods that change?
As it happened on Thursday, 14th October 2010, 23:30 - 00:30 GMT
11:31 pm
ColinTGraham:
Hello everyone, welcome to today's #mathchat
11:32 pm
republicofmath:
Math, & student, development cannot be separated from content. Real nature of math IS change -> no change in "nature" of math. #mathchat
11:32 pm
ColinTGraham:
If it's your first time, don't try to follow everything, just interact with one or two people, and don't forget the hashtag ---> #mathchat
11:33 pm
ColinTGraham:
Tonight's topic has already prompted some discussion, so I guess we are in for a 'bumpy ride' ... ;-) #mathchat
11:34 pm
ColinTGraham:
The topic is: Does the nature of mathematics change as students get older or is it only the teaching methods that change? #mathchat
11:34 pm
republicofmath:
Smooth sailing all the way! #mathchat
11:35 pm
ColinTGraham:
Let's start with an 'easy' question: When, or if, you think about mathematics, what do you actually imagine mathematics is? #mathchat
11:35 pm
seyfert6:
RT @jasontbedell: How would you respond to this math teacher who thinks blogging is a "colossal waste of time" for kids? http://goo.gl/2nCo #mathchat #edchat
11:37 pm
republicofmath:
that's not easy &, IMO, it's been discussed to death. My take: science of number, space, arrangement , #mathchat
11:39 pm
ColinTGraham:
@republicofmath That's why I put the 'scare quotes'... ;-) My take is maths is the language of abstraction #mathchat
11:39 pm
republicofmath:
Oh yes it has, and recently, and often. @mathheadinc Math hasn't changed #mathchat
11:41 pm
republicofmath:
I worry that some #math teachers see math as static. Bodes ill for students IMO #mathchat
11:41 pm
mathheadinc:
@republicofmath There's MORE, yes. The basics are the same. #mathchat
11:41 pm
ColinTGraham:
Over 50% of the maths we know about now has been invented or discovered since 1945 - eg chaos theory, fractals, ... #mathchat
11:41 pm
LizDk:
@ColinTGraham math is making sense and order of the world around us. Analysing it too. Then we are able to advance technology #mathchat
11:42 pm
ColinTGraham:
@mathheadinc What do you see as being the basics, or essence if you like...? #mathchat
11:42 pm
mathheadinc:
@seyfert6 Didn't read but, putting what they learn into words is an important part of learning. #mathchat #edchat
11:42 pm
republicofmath:
And as @suburbanlion points out, such things as Godel's work fundamentally changed views of math #mathchat
11:42 pm
ColinTGraham:
@LizDk How do you see that as being different from science, or is it? #mathchat
11:43 pm
ghewgley:
The #mathchat Daily is out - read this Twitter newspaper on http://bit.ly/bMxifd (19 contributions today)
11:44 pm
davidwees:
@ColinTGraham While I agree that there is much new mathematics, how much of it is taught in schools? Why not? #mathchat
11:44 pm
mathheadinc:
@ColinTGraham Depends on the subject, but things like math facts, definitions and WHY they work, number patterns... #mathchat
11:44 pm
suburbanlion:
If we think of mathematics as "the language of Nature", then "Nature" hasn't changed, but our "language" for describing it has. #mathchat
11:44 pm
Year7Numeracy:
@seyfert6 #mathchat The teacher clearly has no idea the colossal power of blogging. It gives the ss a global voice beyond their 4 walls
11:44 pm
republicofmath:
Conceptions of math - neg numbers, functions, imaginary numbers, surreal numbers, hyperbolic geometry have been in state of flux #mathchat
11:44 pm
davidwees:
How many high schools teach about fractals, chaos theory & current mathematics as part of their curriculum? #mathchat
11:45 pm
ColinTGraham:
@mathheadinc Then you get into the realms of defining what numbers are... that only really happened about 100 years ago #mathchat
11:45 pm
republicofmath:
@davidwees Not enough! #mathchat
11:45 pm
mathheadinc:
@davidwees New math or new methods? #mathchat
11:46 pm
amichetti:
@davidwees I think @lissgriffin might. #mathchat
11:46 pm
mathheadinc:
RT @suburbanlion:... then "Nature" hasn't changed, but our "language" for describing it has. #mathchat
11:46 pm
davidwees:
@mathheadinc New math itself, rather than just new methods. #mathchat
11:46 pm
ColinTGraham:
@davidwees I did, at 16+, and also was asked to do a short presn about chaos when I was training... but that was to teachers! #mathchat
11:46 pm
mathheadinc:
@ColinTGraham No, in the last century. #mathchat
11:47 pm
republicofmath:
@davidwess School math is in danger of becoming totally irrelevant to modern world of math. Not just my view. #mathchat
11:47 pm
mathheadinc:
@davidwees None in this area. They're just the things that get kids fired up about math. #mathchat
11:47 pm
davidwees:
What percentage of the math we teach in schools today was learned more than 300 years ago? #mathchat
11:48 pm
ColinTGraham:
@mathheadinc We're being picky here, considering people have been working with numbers in some way for about 10,000 years probably #mathchat
11:48 pm
republicofmath:
Mathematicians didn't understand what a function was 200 years ago. Numerical analysis is relatively recent. #mathchat
11:48 pm
mathheadinc:
@davidwees There are new concepts, ideas, discoveries, but math is not new to me. #mathchat
11:50 pm
suburbanlion:
Computational #math is a new development also. Although not part of curriculum, computers are a growing part of school experience. #mathchat
11:50 pm
ColinTGraham:
What is the constancy or nature, if you will, of mathematics that makes it stand out from other areas of science/investigation? #mathchat
11:51 pm
ColinTGraham:
@suburbanlion And the N ≠ NP debate is very current too! #mathchat
11:51 pm
mathheadinc:
@ColinTGraham Just precise. #mathchat
11:51 pm
davidwees:
@republicofmath Godel's work was awesome. I took three symbolic logic courses just so I could understand his proof. #mathchat
11:52 pm
republicofmath:
@suburbanlion Yes computational math. computational science. So math evolves, sometimes rapidly. #mathchat
11:52 pm
suburbanlion:
@ColinTGraham IMO, Nature is a computer. #math is the operating system & our universe is just a program. #mathchat
11:52 pm
ColinTGraham:
@davidwees I suspect a good number of the teachers currently in schools don't understand the new ideas well enough to teach them! #mathchat
11:53 pm
republicofmath:
@ColinTGraham it is the evolving understanding of number, space and arrangement. #mathchat
11:53 pm
ColinTGraham:
@suburbanlion Nature, here, is talking about the attributes or basic defining features, rather than some kind of Earth Mother... #mathchat
11:54 pm
ColinTGraham:
Godel Escher Bach is a defining book for me... #mathchat
11:55 pm
davidwees:
Please try to leave some comments on this person's blog so we can help them grow as a math teacher. http://is.gd/g2pnQ #mathchat #edchat
11:55 pm
ColinTGraham:
Most people I ask, once they get beyond the arithmetic/mathematics confusion, tend to speak about quantifying and measuring. #mathchat
11:56 pm
peterflom:
@davidwees Godel was a fascinating guy. Greatest logician ever, and totally wacky paranoid. #mathchat
11:56 pm
suburbanlion:
@ColinTGraham my point being that #math studies truths inherent to all possible universes, while science is concerned with our own #mathchat
11:56 pm
mrich1911:
Just sharing a list of math books along with their AR pts... http://bit.ly/aOIzPk #mathchat#teachertuesday (on Thursday...)
11:56 pm
mathheadinc:
@ColinTGraham That's what it means to them and probably how they use it most. #mathchat
11:57 pm
davidwees:
@ColinTGraham Mathematics is the language we use to communicate science. Much of it will remain unchanged but always new tools. #mathchat
11:57 pm
ColinTGraham:
@suburbanlion Yes, and sometimes impossible universes too! #mathchat
11:57 pm
DJ345:
@ColinTGraham I have never gotten to talk to another living human person who has read that book #mathchat
11:59 pm
mathheadinc:
RT @davidwees Mathematics is the language we use to communicate science. Much of it will remain unchanged but always new tools. #mathchat
11:59 pm
peterflom:
@ColinTGraham What is taught as "math" changes, unfortunately. What OUGHT to be taught is constant #MathChat
11:59 pm
davidwees:
@ColinTGraham I'm going to take it as a recommendation then that I read "Godel Escher Bach" then? #mathchat
11:59 pm
ColinTGraham:
Some themes - language, quantifying, numbers, space, pattern/arrangement, concept, abstraction,... #mathchat
11:59 pm
mathheadinc:
@davidwees Same thing I said about math not being new just the way we look at it. #mathchat
11:59 pm
ilhongy:
RT @republicofmath: Mathematicians didn't understand what a function was 200 years ago. Numerical analysis is relatively recent. #mathchat
11:59 pm
republicofmath:
@davidwees That's a limited view of math. There are problems peculiar to math that now have little do do with any other science. #mathchat


davidwees:
Okay, gotta go #mathchat. Sorry to run so early. Heading to a UBC Science mentoring event. #scichat

BiancaH80:
RT @davidwees: How many high schools teach about fractals, chaos theory & current mathematics as part of their curriculum? #mathchat

ColinTGraham:
@davidwees Absolutely!! If you haven't read Godel Escher Bach or The Crest of the Peacock, then... you must! #mathchat

Year7Numeracy:
@ColinTGraham Basics are critical and need to continually be reinforced. They are a lifeskill. #mathchat

acmcdonaldgp:
I Posted my reply! RT @jasontbedell: respond to tchr who thinks blogging is a "colossal waste of time"http://goo.gl/2nCo #mathchat #edchat

Year7Numeracy:
RT @davidwees: @ColinTGraham Mathematics is the language we use to communicate science. Much of it will remain unchanged but always new tools. #mathchat

ColinTGraham:
@peterflom So what do you think ought to be taught? #mathchat

republicofmath:
@peterflom I cannot agree. Who knows what ought to be taught? Calculus once wasn't even in 20th C #mathchat
12:01 am
suburbanlion:
@ColinTGraham Very true! Reminds me of ZFC and ZF~C -- both of interest in mathematics #mathchat
12:01 am
ColinTGraham:
@Year7Numeracy Some 'facts' though fall apart, for example triangles on curved surfaces can exceed 180 degrees internally #mathchat
12:01 am
peterflom:
@davidwees Up through high school, it's 100% #MathChat
12:01 am
suburbanlion:
Do! Excellent book RT @davidwees @ColinTGraham I'm going to take it as a recommendation then that I read "Godel Escher Bach" then? #mathchat
12:02 am
republicofmath:
@matheadinc How can you maintain view that math is not new? What math are you talking about? Journals are full of new math #mathchat
12:02 am
mathheadinc:
@republicofmath You missed that tweet. Go back. #mathchat
12:03 am
ColinTGraham:
Let's shift direction towards the age factor here. Clearly you cannot 'explain' calculus to a 6yo, but you can explore it #mathchat
12:03 am
ColinTGraham:
@DJ345 I read it 20 years ago when it first came out! ;-) #mathchat
12:04 am
ColinTGraham:
RT @peterflom: @ColinTGraham Proofs, play, the wonder of abstraction, the hidden harmonies of math #mathchat
12:04 am
peterflom:
@republicofmath It's not so much the exact content, as the method ,.... or even the mood of what is taught. #MathChat
12:04 am
Year7Numeracy:
@ColinTGraham Totally agree. But that is not a skill used on a daily basis only specialised examples. #mathchat
12:05 am
republicofmath:
Colleague Nigel Smith taught code writing/breaking & Conway's Game of Life, inf yr 6-8 curriculum. Math changes, teaching can too. #mathchat
12:05 am
ColinTGraham:
It sounds like we are moving towards an idea of mathematics as a process, rather than a product #mathchat
12:05 am
mathheadinc:
@ColinTGraham Calculus CAN be taught to a 6yo. Don Cohen has done it for over 30 years. I can do it... See www.mathman.biz #mathchat
12:05 am
ColinTGraham:
@mathheadinc I was careful to say 'explain' rather than teach calculus #mathchat
12:05 am
peterflom:
RT @suburbanlion: Do! Excellent book RT @davidwees @ColinTGraham I'm going to take it as a recommendation then that I read "Godel Escher Bach" then? #mathchat
12:06 am
suburbanlion:
@ColinTGraham a point of interest might be Piaget's Theory of Development: shift from concrete to abstract thinking around age 10 #mathchat
12:06 am
peterflom:
I led a discussion of Godel Escher Bach on DailyKos, was fun, but we didn't finish #MathChat
12:06 am
mathheadinc:
@peterflom The mood must be pleasant and exciting. Yes! #mathchat
12:07 am
davidwees:
@republicofmath I wasn't trying to argue that Math is dependent on Science, rather the opposite. #mathchat
12:07 am
ColinTGraham:
@suburbanlion Yes, that's my point, although I tend more towards Vygotsky's rather than Piaget's model #mathchat
12:08 am
davidwees:
Yes! RT @ColinTGraham: It sounds like we are moving towards an idea of mathematics as a process, rather than a product #mathchat
12:08 am
peterflom:
@suburbanlion I've seen what is, essentially, proof that Piaget was wrong. Math Circlehttp://ow.ly/2TMAR #mathchat
12:08 am
mathheadinc:
@ColinTGraham Don could. I could. :) #mathchat
12:09 am
peterflom:
@mathheadinc Mood should also be participatory http://ow.ly/2TMBs #MathChat
12:09 am
ColinTGraham:
It is interesting to consider why an hour should have 60 minutes rather than, say, 100 minutes - mathematical influence...? #mathchat
12:09 am
DJ345:
math is a formal abstraction of reality that allows you to make sense of the world and do things. #mathchat
12:09 am
mathheadinc:
@peterflom Absolutely. #mathchat
12:10 am
ColinTGraham:
@mathheadinc I think I could explain too, but whether the underlying concept was grasped would be another matter... ;-) #mathchat
12:11 am
DJ345:
@ColinTGraham Reminds me of calculus teacher's joke. What is pink has scales and hangs on the wall? #mathchat
12:11 am
ColinTGraham:
@DJ345 I think I would add the word 'symoblic' too... a formal, symbol abstraction of reality... #mathchat
12:11 am
cybraryman1:
?Pure mathematics is, in its way, the poetry of logical ideas.? #mathchat
12:12 am
DJ345:
@ColinTGraham Answer: A fish. It is pink because I painted it and it is on the wall because I put it there. #mathchat
12:12 am
ColinTGraham:
@cybraryman1 I also find it interesting that mathematicians choose to label part of their area as being 'Pure'... why? #mathchat
12:13 am
mathheadinc:
@ColinTGraham OK, I'll clarify: Don and I could both explain calculus so a 6yo could understand. #mathchat
12:13 am
DJ345:
@ColinTGraham Good point. #mathchat
12:13 am
ColinTGraham:
@elephantsgerald It was me, rather than David who suggested this, @davidwees was just agreeing with me! ;-) #mathchat
12:15 am
mathheadinc:
@ColinTGraham @cybraryman1 G.H. Hardy thought the math he did would have no application whatsoever. He was wrong. #mathchat #puremath
12:15 am
ColinTGraham:
@mathheadinc I'm just being picky! I think understanding can happen but the deeper knowledge underlying the concept comes later. #mathchat
12:15 am
republicofmath:
@mathheadinc Claim you can, but am reminded of Les Steffe's comment: can teach calculus to a kid, they won't learn anything. #mathchat
12:16 am
ColinTGraham:
OK, let's refocus - do we change our teaching methods as students get older - if the nature of maths is constant, should we change #mathchat
12:16 am
DJ345:
The moment I realized that math was an abstraction of reality was like an epiphany of logical reasoning for me. #mathchat
12:16 am
mathheadinc:
@ColinTGraham Yes, you are! You didn't say anything about deeper understanding. Of course, that comes later. :) #mathchat
12:16 am
DreamBox_Learn:
The DreamBox Blog: Our First Fractions Manipulative: Rational Rods http://bit.ly/d7Cfc1 #elearning#edchat #mathchat #teachers
12:17 am
suburbanlion:
@peterflom @ColinTGraham good point. Must consider social influences as possible cause of concrete->abstract shift #mathchat
12:17 am
ColinTGraham:
@CreativeSage Our topic is "Does the nature of math change as students get older or is it only the teaching methods that change?" #mathchat
12:17 am
davidwees:
@ColinTGraham @cybraryman1 What's even funnier about the "pure" mathematicians is that much of their is now applied physics. #mathchat
12:17 am
daveinstpaul:
Does an overemphasis on practical applications of math inhibit the development of abstract reasoning skills? #mathchat
12:18 am
peterflom:
@ColinTGraham Babylonian influence, after all these millenia. #MathChat
12:18 am
aspencountry:
RT @republicofmath: Colleague Nigel Smith taught code writing/breaking & Conway's Game of Life, inf yr 6-8 curriculum. Math changes, teaching can too. #mathchat
12:18 am
CBethM:
RT @cybraryman1: ?Pure mathematics is, in its way, the poetry of logical ideas.? #mathchat
12:18 am
mathheadinc:
@ColinTGraham Students should always be taught to reason things out. That shouldn't change. This doesn't happen in general. #mathchat
12:20 am
ColinTGraham:
@peterflom I knew that, of course! But exploring why the metric system is based on 100 vs. Babylonian 360 (or 60) is maths too! #mathchat
12:20 am
CreativeSage:
RT @ColinTGraham: @CreativeSage Our topic is "Does the nature of math change as students get older or is it only the teaching methods that change?" #mathchat
12:20 am
suburbanlion:
If there is a change in teaching methods as students age, it should be from generalized instruction to personalized instruction #mathchat
12:21 am
ColinTGraham:
@daveinstpaul How or at what age do you see this application vs abstraction happening? #mathchat
12:21 am
peterflom:
@ColinTGraham Oh, yeah. I agree. Just try DOING arithmetic base 60 and it becomes clear! #MathChat
12:22 am
davidwees:
@ColinTGraham We do change our methods slightly b/c as math gets more advanced it gets more loaded w/ vocabulary & symbols. #mathchat
12:22 am
peterflom:
@suburbanlion Why? I could almost argue for the OTHER way round, but I think it should always be personalized #MathChat
12:22 am
ColinTGraham:
@suburbanlion I think maths teaching would be more successful if it started personalized and then went general, to be honest... #mathchat
12:23 am
ColinTGraham:
@davidwees Or do we think that by packing lessons with lots of formulae and jargon and theory that we are actually teaching... ? #mathchat
12:25 am
ColinTGraham:
@davidwees Do you actually think mathematics gets more advanced or is it just that more abstract concepts are being introduced? #mathchat
12:25 am
suburbanlion:
@peterflom @ColinTGraham in terms of content, isn't the early stuff common to variety of fields? #mathchat
12:27 am
ColinTGraham:
@suburbanlion My view of early years mathematics is that the teacher should be helping the child to build his or her own maths #mathchat
12:28 am
ColinTGraham:
OK, it's almost that time again! Any final thoughts? #mathchat
12:29 am
mathheadinc:
Math needs more joy of discovery at the early ages to get the fire started and to keep it burning. #mathchat
12:31 am
davidwees:
@ColinTGraham IMHO abstract = advanced. Language is definitely a barrier for some math concepts. #mathchat
12:31 am
suburbanlion:
@ColinTGraham yes, but aren't they being encouraged to discover the same mathematical tools, albeit in different ways? #mathchat
12:33 am
davidwees:
As Seth Godin would say, the language of mathematics is "deliberately broken." (see his TED talk for clarification) #mathchat
12:34 am
ColinTGraham:
Well, time to finish for tonight! Thanks everyone. Remember to follow @mathchat for updates, and come back on Monday for more! #mathchat
12:34 am
ColinTGraham:
Please remember to add some more ideas for discussion here: http://bit.ly/aOhxOU #mathchat
12:35 am
ColinTGraham:
The archive will be online in about 30 minutes or so. #mathchat
12:37 am
davidwees:
Mathematical symbols; possible precursor to Netspeak language? :) #mathchat
12:39 am
ColinTGraham:
@suburbanlion The point for me is that the discovery processes are very individual and the teacher needs to be facilitating them #mathchat
12:43 am
mathheadinc:
@ColinTGraham True, teachers NEED to do that. but sadly, it isn't how they are taught. #mathchat