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#mathchat Wiki
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! guided tour
001 Differentiation
002 'Real' maths
003 Fractions
004 Manipulatives
005 Assessment
006 What technology?
007 Adult curriculum
008 Reflective Learners
009 Engagement
010 Class Time Use
011 Why I hate maths
012 Terminology
013 'Mathphobia'
014 The Nature of Maths
015 Show and Tell
016 Vertical Integration
017 Product to Process
018 Investigation Length
019 Preparation for Work
020 Success in Mathematics
021 Groupwork
022 Effective lessons
023 Impact of ICT
024 Mathematics Websites
028 Why under 16?
2010.07.15 Differentiation
2010.07.19 Differentiation (2)
2010.07.22 'Real' maths
2010.07.26 'Real' maths (2)
2010.07.29 Fractions
2010.08.02 Fractions (2)
2010.08.05 Manipulatives
2010.08.09 Manipulatives (2)
2010.08.12 Assessment
2010.08.16 Assessment (2)
2010.08.19 What tech?
2010.08.23 What tech? (2)
2010.08.26 Adult maths
2010.08.30 Adult maths (2)
2010.09.02 Reflective learner
2010.09.06 Reflective learner 2
2010.09.09 Engagement
2010.09.13 Engagement 2
2010.09.16 Class Time Use
2010.09.20 Class Time Use 2
2010.09.23 Why I hate maths
2010.09.27 Why I hate math 2
2010.09.30 Terminology
2010.10.04 Terminology 2
2010.10.07 'Mathphobia'
2010.10.11 'Mathphobia' (2)
2010.10.14 Nature of Maths
2010.10.18 Nature of Maths (2)
2010.10.21 Show and Tell
2010.10.25 Show and Tell (2)
2010.10.28 Vertical Integration
2010.11.01 Vertical Integratn 2
2010.11.04 Product to Process
2010.11.08 Product to Proc. 2
2010.11.11 Investigation length
2010.11.15 Investigation leng 2
2010.11.18 Prepn for work
2010.11.22 Prepn for work 2
2010.11.25 Success in Maths
2010.12.03 Groupwork
2010.12.06 Groupwork 2
2010.12.10 Effective lessons
2010.12.13 Effective Lesson 2
2010.12.17 Impact of ICT
2010.12.20 Impact of ICT 2
2010.12.24 Maths Websites
2011.01.03 Maths Website 2
2011.01.07 Ideal curriculum
2011.01.10 Ideal curriculum 2
2011.01.14 Short or longterm
2011.01.17 Short or longterm2
2011.01.21 Continuing PD
2011.01.24 Continuing PD 2
2011.01.28 Why under 16?
2011.01.31 Why under 16? (2)
2011.02.04 Which is more fun?
2011.02.11 Blended learning
2011.02.14 Blended learning 2
2011.02.18 Fast tracking
2011.02.21 Fast tracking (2)
2011.02.25 Misconceptions
2011.02.28 Misconceptions 2
2011.03.04 Good Reads
2011.03.07 Good Reads (2)
2011.03.11 How do I  fractions
2011.03.18 How do I  lang
2011.03.21 How do I  lang (2)
2011.03.25 How do I  curric
2011.03.28 How do I  curric 2
2011.04.01 How?  next topic
2011.04.04 How?  nxt topic 2
2011.04.08 How?  Geometry
2011.04.11 How?  Geom 2
2011.04.15 How?Investigation
2011.04.18 How?Investigatn 2
2011.04.22 How? Do vs. learn
2011.04.25 How?Do vs learn 2
2011.04.29 How?Dig deeper
2011.05.02 How?Dig deeper 2
2011.05.06 'Big Ideas'
2011.05.09 'Big Ideas' (2)
2011.05.13 High school skill
2011.05.16 High school skill 2
2011.05.20 Journals
2011.05.23 Journals (2)
2011.05.27 Studentdriven
2011.05.30 Studentdriven (2)
2011.06.03 How?  Maths play
2011.06.06 How?Maths play 2
2011.06.10 Deeper thinking
2011.06.13 Deeper thinking (2)
2011.06.17 How?  Disjointed
2011.06.17 How?  Disjointed 2
2011.06.24 How?  Problems
2011.06.27 How?  Problems 2
2011.07.01 Holiday maths
2011.10.28 Extent of plans
2011.10.31 Extent of plans (2)
2011.11.04 Authentic is..?
2011.11.07 Authentic is..? (2)
Z_1 Thursday raw
Z_2 Monday raw
Z_consolidated
2011.02.04 Which is more fun?
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Topic:
Which is more fun  Algebra or Geometry?
As it happened on
Friday, 4th February 2011 00:00  01:00 GMT
12:08 am
davidwees
:
@
ColinTGraham
Geometry is more fun, especially when you consider that much of algebra can be done with geometry. #
mathchat
12:10 am
ColinTGraham
:
Hello #
mathchat
, any other chatters today?
12:11 am
padgets
:
#
mathchat
Hi everybody!! long time gone, Sharon here am a HS science teacher from Ottumwa Iowa USA love to lurk and learn ;0)
12:11 am
ColinTGraham
:
Today's #
mathchat
topic: "Algebra or Geometry  which is more fun?"
12:12 am
millerblair
:
Where is the line between algebra and geometry? Algebraic principles are applied to a lot of geometric problems. #
mathchat
12:12 am
ColinTGraham
:
@
padgets
Hi Sharon, nice to have you back again! #
mathchat
12:12 am
peterflom
:
@
colintgraham
Algebra #
MathChat
12:13 am
padgets
:
@
ColinTGraham
#
mathchat
thanks! snow day 3 need some chatting, been stuck in snow!! I like Algebra
12:13 am
ColinTGraham
:
@
millerblair
If there is no line between Algebra and Geometry, why does almost every curriculum draw one? #
mathchat
12:13 am
millerblair
:
@
padgets
Good that I'm not the only one back after missing a lot of #
mathchat
:)
12:13 am
mathheadinc
:
@
ColinTGraham
The visual proofs in geometry make it fun. #
mathchat
12:13 am
padgets
:
@
millerblair
#
mathchat
been very intense at work :)
12:14 am
millerblair
:
@
colintgraham
Good question. I'm not saying there is no separation, but a lot of cross application of principles. #
mathchat
12:14 am
ColinTGraham
:
@
mathheadinc
There are those who would say that true mathematical proof must be done by logical reasoning, though! #
mathchat
12:15 am
millerblair
:
@
padgets
Me too, and have been teaching an after school course, which is on a couple week's break. #
mathchat
12:15 am
ColinTGraham
:
Maybe we should distinguish between our personal preferences and what Ss will see as being more fun, or should we? #
mathchat
12:15 am
padgets
:
@
millerblair
#
mathchat
yes I use algebra and geometry even in Biology, I can see who knows how and who does not
12:15 am
mathheadinc
:
@
ColinTGraham
And to that I say, "Expand your horizons!" #
mathchat
12:17 am
padgets
:
#
mathchat
well for math challenged teachers like me I just make sure I teach them the right way to do the math :)
12:17 am
ColinTGraham
:
@
mathheadinc
I certainly think the visual element of geometry can make it more appealing #
mathchat
12:17 am
millerblair
:
@
colintgraham
As to whether algebra or geometry is fun for students depends on how it is presented to them. #
mathchat
12:18 am
padgets
:
#
mathchat
My team math teacher is doing some great stuff with kids using cad wonderful cell city blueprints
12:18 am
ColinTGraham
:
OK, you have to expand on that, even though it was a binary choice question, Peter! RT @
peterflom
: @
colintgraham
Algebra #
MathChat
12:18 am
davidwees
:
I think there's scope for differentiation between strict math proofs and outlines which have the gist of a proof. #
mathchat
12:18 am
teachdig
:
Geometry is more fun, especially when you consider that much of algebra can be done with geometry. #
mathchat
via @
davidwees
I agree!!
12:19 am
ColinTGraham
:
@
millerblair
So what aspects of presentation will blur the distinction as you see it? #
mathchat
12:19 am
millerblair
:
@
padgets
That sounds really cool. Are any of the student examples posted online? #
mathchat
12:20 am
peterflom
:
@
colintgraham
Algebra, to me, is like a game. Geometry is like torture. I am not visual #
MathChat
12:20 am
padgets
:
@
millerblair
#
mathchat
no sorry to say she is just getting started with comfort in using tech she is excited to start
12:20 am
ColinTGraham
:
@
davidwees
I would agree that visual presentations which support a theorem can help with those who "don't get" the formal approach #
mathchat
12:21 am
davidwees
:
@
ColinTGraham
@
mathheadinc
Lots of algebraic concepts can be visualized with geometry though #
mathchat
12:21 am
teachdig
:
I like the visual nature and easier application of geometry... of course then you need to be using algebra to solve in the end #
mathchat
12:21 am
peterflom
:
@
colintgraham
What exactly is "proof"? No one seems to know. #
MathChat
12:21 am
padgets
:
@
peterflom
#
mathchat
I never did figure that one out :)
12:22 am
millerblair
:
@
colintgraham
I meant that neither algebra or geometry is inherently fun (or not fun). Blurring is in application to problems. #
mathchat
12:22 am
davidwees
:
I like that you can take something complicated in notation, turn it into a picture, and it becomes so much clearer. #
mathchat
12:23 am
ColinTGraham
:
@
peterflom
I believe the accepted definition is that "proof" is a convincing demonstration of 'truth' from deductive reasoning... #
MathChat
12:23 am
teachdig
:
Sorry to drop in and run. Time for some tacos with people from my new job. Celebrating someone's birthday! #
mathchat
12:23 am
davidwees
:
When I first learned about modulo arithmetic & symmetry groups, the pictures in my textbook were really useful. #
mathchat
12:23 am
ColinTGraham
:
@
teachdig
Have a good time, Dvora! #
mathchat
12:24 am
peterflom
:
@
davidwees
I hate when people "make things visual" #
MathChat
12:24 am
peterflom
:
8 year old son just learned > and < signs as "eaters". He says "= is open mouthed both sides" #
MathChat
#
math
12:24 am
mathheadinc
:
@
davidwees
That's what plots are all about. Visualizing makes concepts easier to remember. #
mathchat
12:25 am
ColinTGraham
:
I've been using LEGO digital designer to provide visual support for proofs, or mathematical statements. #
MathChat
12:25 am
padgets
:
@
peterflom
#
mathchat
yes I learn that it was called the alligators mouth
12:25 am
millerblair
:
@
peterflom
@
colintgraham
I like that puzzle/mystery element to algebra that can lead to some fun activities to hook students in #
mathchat
12:25 am
peterflom
:
@
colintgraham
Convincing to whom? What if it convinces some and not others? What if no one understands it? #
MathChat
12:26 am
ColinTGraham
:
@
millerblair
So the question may be better phrased as: Is geometry or algebra perceived as being more fun? #
mathchat
12:26 am
davidwees
:
@
peterflom
Yeah that's a personal preference. I wonder if most people prefer visual aids? #
mathchat
12:27 am
ColinTGraham
:
@
peterflom
The convincing comes from accepting the statements, axioms etc which form the basis of the deductive reasoning process #
MathChat
12:27 am
padgets
:
RT @
padgets
: @
davidwees
#
mathchat
As a visual learner, I could not have learned the math I did without picts
12:27 am
millerblair
:
@
colintgraham
I'd agree with that statement of the question, but really think that would vary from class to class. #
mathchat
12:28 am
davidwees
:
@
ColinTGraham
@
peterflom
My professor used to say that something was proved when everyone stopped arguing that it wasn't. #
mathchat
12:29 am
ColinTGraham
:
My feeling is that 'trained' mathematicians will sometimes resort to algebra in situations where they don't need to. #
MathChat
12:30 am
mathheadinc
:
Rolling Wheel with Spoke  #
WolframDemonstrations
http://goo.gl/q52ff
#
mathchat
12:30 am
padgets
:
@
davidwees
#
mathchat
I thought proofs only were in geometry? see learned something new :)
12:30 am
davidwees
:
@
peterflom
@
colintgraham
I'd argue that if NO one else understands your proof, it's not a proof. #
mathchat
12:31 am
ColinTGraham
:
OK, before we get off topic and start entering the mathematical philosophy of proof... let's talk about what we mean by 'fun' #
MathChat
12:31 am
mathheadinc
:
@
padgets
Actually every solved equation is a proof of sorts without repeating the same reason ever & over. #
mathchat
12:32 am
davidwees
:
@
peterflom
I'm LD in a different way. 0th percentile for auditory working memory. 99th percentile for visual memory. #
mathchat
12:32 am
mathheadinc
:
@
ColinTGraham
'Fun' is when what Ss learn is exciting and it makes Ss want to learn more. Fun lights a curiosity fire. #
MathChat
12:32 am
millerblair
:
@
colintgraham
By 'resorting to algebra' do you mean as an inefficient route to a solution? #
mathchat
12:32 am
padgets
:
RT @
padgets
: @
mathheadinc
@
peterflom
Gotta love my PLN! I did not think of proofs that way! #
mathchat
12:33 am
davidwees
:
@
peterflom
At least according to an online memory test I took that was created by some university psych department. #
mathchat
12:33 am
ColinTGraham
:
An example of what I mean by 'acceptance': the internal angles of triangle only sum to 180 if you accept that it is on a 2D plane #
MathChat
12:33 am
peterflom
:
@
colintgraham
"fun" = stuff you would do if you didn't have to, and weren't being paid to #
MathChat
12:33 am
mathheadinc
:
@
padgets
There are many more algebraic proofs in analytic geometry, though. most Ss don't do them. #
mathchat
12:34 am
padgets
:
#
mathchat
@
mathheadinc
wow, this is soooo cool
12:35 am
mathheadinc
:
@
padgets
I haven't answered a question in analytic geo in over 10 years, though. More & more is getting left out. #
mathchat
12:35 am
ColinTGraham
:
@
peterflom
What if what you were paid to do was also fun though? Is it not possible to have fun doing things you have to do? #
MathChat
12:35 am
padgets
:
#
mathchat
the reason I say that is I was just doing a lesson with kids on molecular orbitals and it got me thinking..
12:35 am
peterflom
:
@
padgets
What exactly is cool? #
MathChat
12:36 am
ColinTGraham
:
@
millerblair
Yes, or that algebra is seen as being a 'rigourous' method albeit inefficient in some situations. #
mathchat
12:36 am
mathheadinc
:
@
ColinTGraham
Changing nappies isn't fun but the end result is very nice :) #
MathChat
12:36 am
POWERORGmath
:
RT @
mathheadinc
: @
ColinTGraham
'Fun' is when what Ss learn is exciting and it makes Ss want to learn more. Fun lights a curiosity fire. #
MathChat
12:36 am
millerblair
:
For me the bigger question isn't what fun is,but rather how do we expose students to potential of fun in algebra & geometry? #
mathchat
12:37 am
padgets
:
@
peterflom
#
mathchat
just reading the tweets, some I get some I am not sure but someone always explains
12:37 am
mathheadinc
:
@
padgets
Start here www.mathman.biz Little kids learning higher math! #
mathchat
12:37 am
ColinTGraham
:
@
millerblair
I think you need to be aware of 'fun' as a concept before you can 'inflict' it on the students, though! #
mathchat
12:38 am
mathheadinc
:
@
millerblair
The teacher has to show them the fun parts. The challenge has to be made fun! #
mathchat
12:38 am
padgets
:
#
mathchat
@
mathheadinc
thanks!!! I love new things :)
12:39 am
millerblair
:
@
colintgraham
'Fun' isn't a concept in my mind, it's a highly variable experience for each individual. #
mathchat
12:39 am
ColinTGraham
:
My 'visual proofs'  a work in progress! 101 manipulative lessons with LEGOÂ®
http://bit.ly/bz8Z8p
#
MathChat
12:40 am
padgets
:
@
mathheadinc
#
mathchat
sounds like my kind of teacher :) math made easy
12:42 am
ColinTGraham
:
@
millerblair
This was part of my thinking too. Often when we talk about fun, maybe we mean Csikszentmihalyi's concept of 'flow' #
mathchat
12:42 am
padgets
:
@
ColinTGraham
#
mathchat
who? ooh my
12:42 am
peterflom
:
8 year old son "HOW am I supposed to do the 8 times table?" Dad helps out with a trick. #
MathChat
12:43 am
padgets
:
@
peterflom
#
mathchat
miss those times my kids are grown now enjoy while you can :)
12:43 am
ColinTGraham
:
@
padgets
Check out the Wikipedia on
http://en.wikipedia.org/wiki/Flow_
(psychology) Flow in psychology, Sharon. It's a good start #
mathchat
12:43 am
peterflom
:
@
padgets
Not "easy". "Easy" is bad. "Easy" isn't fun. #
MathChat
12:44 am
ColinTGraham
:
@
mathheadinc
"You will have fun or I'll beat you...!" Do we equate fun with enjoyment or relaxing or what? #
mathchat
12:45 am
padgets
:
#
mathchat
@
ColinTGraham
just read it, wow, that is waaaaay cool, think I will spring that on the know it alls at work he he he
12:47 am
ColinTGraham
:
If I am totally honest, I'd like to see use of the word 'fun' as a description of anything. To me, it's like 'nice'  imprecise! #
MathChat
12:48 am
mathheadinc
:
@
ColinTGraham
That's blowing out of proportion. #
mathchat
12:48 am
millerblair
:
@
colintgraham
@
mathheadinc
I think a lot of students associate fun with relaxing  school is not relaxing & no possibility of fun #
mathchat
12:49 am
mathheadinc
:
@
padgets
Mostly a big, interesting, exciting challenge. These kids are working on college level concepts #
mathchat
12:50 am
padgets
:
#
mathchat
you should have seen the "fun" kids had making my quizzler they were learning Biology at the same time
12:50 am
millerblair
:
For me fun is any experience where I am actively, passionately & fully engaged in a moment of action or connection. #
mathchat
12:50 am
padgets
:
@
mathheadinc
#
mathchat
I am going to try it, I want to get better at math
12:50 am
ColinTGraham
:
@
mathheadinc
Playing Devil's Advocate! If you have to "show the fun", it's not the same... Showing where fun may be found...? #
mathchat
12:51 am
padgets
:
@
ColinTGraham
#
mathchat
but if i had not shown the "fun" they never would have done it on their own :)
12:52 am
ColinTGraham
:
@
millerblair
I think 'fun' is also associated with a sense of achievement or victory in some way too. eg working hard to improve #
mathchat
12:53 am
mathheadinc
:
@
ColinTGraham
I hate to leave. Food is here! Later :) #
mathchat
12:54 am
ColinTGraham
:
@
mathheadinc
OK, see you next time! we're into the final stretch anyway ;) #
mathchat
12:54 am
millerblair
:
@
colintgraham
Agreed & to improve or be 'victorious' one must be engaged and active in the process. #
mathchat
12:56 am
padgets
:
#
mathchat
that is why I wear tennis shoes to work!
12:57 am
ColinTGraham
:
If we use Blair's idea of engagement/involvement in an activity as being (part of) fun... how important are clear outcomes? #
MathChat
12:58 am
padgets
:
#
mathchat
very important to me! My learning targets are on the board everyday so kids have a goal
12:58 am
ColinTGraham
:
By clear outcomes, I mean stages or moments when Ss (or we) can feel a sense of victory or achievement or success? #
MathChat
1:00 am
millerblair
:
@
colintgraham
Outcomes are still an important for 'measuring' progressunderstanding where we are, want to go & how far we've come #
mathchat
1:00 am
padgets
:
@
ColinTGraham
#
mathchat
oh....well our summative assessments are all project or problem based so I see lots of good things
1:02 am
ColinTGraham
:
Maybe more 'fun' would be had if learning outcomes/goals etc. were explicitly stated by individuals, as well as by the curriculum #
MathChat
1:03 am
ColinTGraham
:
Any parting thoughts for today's topic? #
MathChat
1:05 am
millerblair
:
Thanks for the #
mathchat
@
colintgraham
@
padgets
@
mathheadinc
1:05 am
padgets
:
#
mathchat
well, I learned some new stuff and appreciate you letting me lurk and learn take care stay safe and tweet you next time :)
1:06 am
ColinTGraham
:
OK, thanks everyone. Another lively discussion! Archive will be online in about 20 minutes or so #
MathChat
1:08 am
ColinTGraham
:
Don't forget to add some Ideas for Discussions
http://bit.ly/aOhxOU
otherwise we'll have nothing to vote on! #
mathchat
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As it happened on Friday, 4th February 2011 00:00  01:00 GMT