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 LEGO® 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' progress-understanding 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