Topic: What misconceptions are most common in mathematics?
As it happened on Friday, 25th February 2011 00:00 - 01:00 GMT
11:52 pm
republicofmath:
Here's a very common & persistent misconception: area stays same as perimeter changes (cause "amount of stuff" doesn't change) #mathchat
11:53 pm
republicofmath:
Whoops! Did I jump the gun? #mathchat #justsoexcited
11:59 pm
mathfour:
hmm... are we talking about common misconceptions about math itself or about teaching math? #mathchat

mathfour:
How many chats are on now? I see #mathchat, #isedchat and #artsed so far.
12:01 am
mathfour:
@republicofmath I'm #justsoexcited about it too! #mathchat
12:01 am
dansmath:
@republicofmath - sure: 2 by 30, 3 by 20, 4 by 15, 5 by 12... same area, changing perimeter! #mathchat
12:04 am
republicofmath:
Wot's happened to @ColinTGraham then? #mathchat
12:04 am
mathfour:
@dansmath Hey there! Are you in on this fun, too? #mathchat
12:04 am
EarlSamuelson:
RT @republicofmath: Here's a very common & persistent misconception: area stays same as perimeter changes (cause "amount of stuff" doesn't change) #mathchat
12:05 am
mathfour:
So whatcha think @republicofmath and @dansmath - are we talking math work misconceptions? #mathchat
12:05 am
republicofmath:
Whew! Thanks Bon & Dan. Wasn't sure anyone was there. #mathchat
12:05 am
mathfour:
@dansmath @republicofmath Or are we talking things like, "You'll use the math you learn here later in life"? Which is BS. #mathchat
12:05 am
republicofmath:
How can you measure a circle in square inches #mathchat #misconceptions
12:06 am
mathfour:
@republicofmath I think the sweet @ColinTGraham might be having the same problem as last week. Pure speculation. #mathchat
12:06 am
dansmath:
i like to remind them it's education, not training, and i'm teaching thinking and problem solving skills not just formulas. #mathchat
12:07 am
republicofmath:
(1+x)/x = 1 (cancel x's) What if x=2? No: x is not a number. Common algebra #misconception. #mathchat
12:08 am
republicofmath:
I think one of the biggest misconceptions in math is that @ColinTGraham actually exists! #mathchat
12:09 am
republicofmath:
@mathfour Well, the misconceptions go all the way up and all the way down. So ... teachers too #mathchat
12:09 am
davidwees:
Common misconceptions in math => 8/4 = 4/8, x^0 = 0, 5x = 0 has no solution, (x+3)/x = 3 b/c x's cancel. #mathchat
12:10 am
mathfour:
Most annoying misconception is "2+2 is always 4." I hear that BS a lot. #mathchat
12:10 am
republicofmath:
@mathfour Misconceptions differing from downright deception? #mathchat
12:10 am
mathfour:
@republicofmath I think the reason they think x isn't a number is because we haven't really shown them that numbers work the same #mathchat
12:11 am
TeaKayB:
#mathchat #misconception : 2x means "twenty-something"
12:11 am
davidwees:
Most of the common misconceptions I see come from students who have memorized algorithms w/o understanding concepts. #mathchat
12:11 am
mathsatschool:
@republicofmath @colintgraham He doesn't. I've checked. #mathchat
12:11 am
republicofmath:
Oh! Would it be resolved by eating licorice? @mathfour I think the sweet @ColinTGraham might be having same problem as last week. #mathchat
12:11 am
mathfour:
Teach a kid that 8(36)=8(30+6)=240+48, then they'll understand when we show x(y+z) - but we don't. We hand them calculators #mathchat
12:12 am
mathfour:
What makes me nuts is when someone tries to explain why x^0=1. Real reason: if it wasn't it would screw everything up. #mathchat
12:13 am
republicofmath:
Common teacher misconception is that kids see things as they do e.g. many young kids don't see rows & columns of arrays #mathchat
12:13 am
sacha_is_good:
RT @republicofmath: (1+x)/x = 1 (cancel x's) What if x=2? No: x is not a number. Common algebra #misconception. #mathchat
12:13 am
mathfour:
@republicofmath Have you seen deception?!? #mathchat
12:14 am
EarlSamuelson:
RT @davidwees: Most of the common misconceptions I see come from students who have memorized algorithms w/o understanding concepts. #mathchat
12:14 am
davidwees:
Students also think -2x = 4 should be solved by adding 2 to both sides, showing they understand canceling but not why we cancel. #mathchat
12:14 am
mathfour:
@davidwees And this happens with grown-ups too! I've seen oilfield hands with this same problem! #mathchat
12:14 am
EarlSamuelson:
RT @mathfour: Teach a kid that 8(36)=8(30+6)=240+48, then they'll understand when we show x(y+z) - but we don't. We hand them calculators #mathchat
12:14 am
republicofmath:
@mathfour 2+2=4 (p<0.0001) ? #mathchat
12:15 am
mikcooke:
Think it's the too-frequent use of the word "cancel" e.g. if x^2+y^2=z^2 then "cancel" the "squares" so x+y MUST = z ! #mathchat
12:15 am
mathfour:
@republicofmath Or they see things differently (and better). #mathchat
12:16 am
republicofmath:
@davidwees. Agree many misconceptions come from rote learned algorithms. But area doesn't change with perimeter isn't one of those #mathchat
12:16 am
mathednet:
@davidwees Precisely why I never, never use the word "cancel." It really lacks a good mathematical definition. #mathchat
12:16 am
mathfour:
@republicofmath My 4th grade math teacher insisted that a square WAS NOT a rectangle - even though it was clear by definition #mathchat
12:17 am
padgets:
#mathchat Hi everybody! sorry I am late catching up.....
12:17 am
mathfour:
@davidwees But do you come back and show that adding 2 would give 2-2x=2? Or do you just say that doesn't work? #mathchat
12:17 am
padgets:
#mathchat sorry I am Sharon and I ma a HS science teacher from Iowa
12:17 am
republicofmath:
@mathfour Do you mean: have I seen "Deception"? #mathchat {Answer is: No]
12:18 am
mathfour:
@mikcooke Sweet merciful crap, yes - and "cross multiply" is over used too! #mathchat
12:18 am
mathfour:
RT @mikcooke: Think its the too-frequent use of the word "cancel" e.g. if x^2+y^2=z^2 then "cancel" the "squares" so x+y MUST = z #mathchat
12:18 am
mathfour:
@mathednet @davidwees I like "they kill each other" - much more dramatic. :D #mathchat
12:19 am
mathfour:
@padgets Hey you! #mathchat
12:19 am
jessicaboehle:
@republicofmath I'm not young and I still struggle! #mathchat
12:19 am
davidwees:
@mathfour You can prove it using limits. It's more accurate to say that the limit as y approaches 0 of x^y is 1. #mathchat
12:19 am
mathfour:
@republicofmath Dunno what you mean on that one, boss. #mathchat
12:19 am
padgets:
@mathfour #mathchat Hey! how the heck are you?
12:19 am
StrongDaughter:
RT @MariaDroujkova: Non-mathematicians think that you can count things that count in mathematics. #mathchat
12:20 am
mathfour:
@republicofmath Funny - no. You wrote "misconception vs. deception" - was wondering if you've seen someone deceive students. #mathchat
12:20 am
mathheadinc:
@jessicaboehle If you struggle, how do you get help? #mathchat
12:20 am
tj007:
most common 'canceling' misconception I see is along the lines of (x+y)/x The x's cancel to leave the answer y #mathchat
12:20 am
mathheadinc:
RT @tj007: most common 'canceling' misconception I see is along the lines of (x+y)/x The x's cancel to leave the answer y #mathchat
12:21 am
republicofmath:
@mikcooke Oh yeah, & permanence of form: sqrt(a+b) = sqrt(a)+sqt(b), log(a+b)=log(a)+log(b), (a+b)^2=a^2+b^2, ... #mathchat
12:21 am
EarlSamuelson:
can I get in on this? #mathchat
12:21 am
mathheadinc:
Some Ss think to solve for x, they need to divide by "ax" in the equation ax=b. #mathchat
12:22 am
vtdeacon:
@davidwees how about 1/4= .14? #mathchat
12:22 am
mathheadinc:
@earlsamuelson Dive in! #mathchat
12:22 am
ColinTGraham:
Hi everyone, here at last! I hate roadworks.... #mathchat
12:22 am
mathednet:
Instead of "cancel," I used "unadd" and "unmultiply" to "make 0" or "make 1." Eased vocab transition to inverses and identities. #mathchat
12:22 am
padgets:
#mathchat oh my, better lurk this eve! ummmm ...somethings look familiar some oh boy!
12:23 am
mathheadinc:
@vtdeacon That reminds me: 2^-1 = .2 #mathchat
12:23 am
republicofmath:
#mathfour "square", "rectangle" are defined notions, not perceptual so, according to David Tall, belong to advanced math thinking #mathchat
12:23 am
mathfour:
@davidwees We can't go proving stuff to algebra students - they freak. Plus it's more fun to say you'd end the universe if x^0<>1 #mathchat
12:24 am
mathfour:
@padgets Doing great! Got a babysitter even. I love this time with all y'all! #mathchat
12:24 am
ColinTGraham:
Little liar! We did our PCGEs together! RT @mathsatschool: @republicofmath @colintgraham He doesn't. I've checked. #mathchat
12:24 am
mathfour:
@StrongDaughter @MariaDroujkova What? #mathchat
12:25 am
mathfour:
@tj007 This is because we don't teach them about "Multiplication World" vs. "Addition World" - they think they are the same. #mathchat
12:25 am
republicofmath:
@tj007 How about sin x/n = 6 (cancel the n's) #mathchat
12:25 am
EarlSamuelson:
referring to x^0=1......x^3 means there are 3 extra factors of x in numerator... #mathchat
12:25 am
vtdeacon:
@mathheadinc how about multiplying a fraction by whole #. Misconception is 8= 8/8 #mathchat
12:25 am
EarlSamuelson:
x^(-5) means theres are 5 extra factors of x in denominator #mathchat
12:25 am
mathfour:
@republicofmath @mikcooke Also a differentiation of the two worlds issue (addition and multiplication) #mathchat
12:26 am
davidwees:
#mathchat @mathfour I use an archer analogy to explain the distributive rule. "Each archer outside the castl? (cont) http://deck.ly/~tHPIm
12:26 am
EarlSamuelson:
x^0 means equal nmber of factors of x in numerator and denominator #mathchat
12:26 am
mathfour:
@mathheadinc Which isn't wrong, it just yeilds 1=b/(ax). They've solved for 1, not x. #mathchat
12:26 am
ColinTGraham:
Did anyone mention "carry 1" instead of "carry 10, 100, 1000..." yet, in subtraction? #mathchat
12:26 am
mathheadinc:
Wow, haven't seen that one. RT @vtdeacon: @mathheadinc how about multiplying a fraction by whole #. Misconception is 8= 8/8 #mathchat
12:26 am
republicofmath:
@mathfour I thought you were saying teachers were being deceptive (tweet way back) #mathchat
12:26 am
mathfour:
@ColinTGraham Hey there - we were wondering about you. #mathchat
12:27 am
davidwees:
@mathfour I just use this explanation with my students for x^0. 2^4/2^2 = 2^2, 2^4/2^3 = 2^1, 2^4/2^4 = 2^0 = 1. #mathchat
12:27 am
mathfour:
@mathednet Nice - I use "the big fat 1" #mathchat
12:27 am
padgets:
#mathchat ok, I need a dictionary please! LOL
12:27 am
dansmath:
i like students who rationalize the denom of a fraction by squaring the top and bottom! 2/sqrt[3] = 4/3. #mathchat
12:27 am
davidwees:
@mathfour It's "proofy" rather than being a formal proof. #mathchat
12:27 am
mathheadinc:
@mathfour It is if you want to find x the traditional way which is all most kids are taught. #mathchat
12:27 am
EarlSamuelson:
RT @davidwees: @mathfour I just use this explanation with my students for x^0. 2^4/2^2 = 2^2, 2^4/2^3 = 2^1, 2^4/2^4 = 2^0 = 1. #mathchat
12:27 am
vtdeacon:
@davidwees but how many kids don't know what an archer is? Do you have to show a picture?#mathchat
12:27 am
republicofmath:
@ColinTGraham your first task Colin is to prove you exist! #mathchat
12:27 am
ColinTGraham:
@mathfour Just happy to see that #mathchat is now self-organizing, on Thursday/Friday at least!
12:28 am
mathfour:
RT @mathednet: Instead of "cancel," I used "unadd" and "unmultiply" to "make 0" or "make 1." Ease into inverses and identities. #mathchat
12:28 am
davidwees:
@vtdeacon I actually will draw pictures of archers. :) Most of them have seen movies w/ archers in them. #mathchat
12:28 am
ColinTGraham:
@republicofmath Would you prefer a visual 'proof', inductive proof or deductive proof Gary? #mathchat
12:28 am
tj007:
@republicofmath Not come across that one yet, but it is early days... #mathchat
12:28 am
suburbanlion:
Equating "mathematics" with "calculation" is a common misconception & not just among students. #mathchat
12:28 am
republicofmath:
@mathfour If x is integer variable then x^0 is - as you say - just defined to make things work. Limits don't enter in to it. #mathchat
12:29 am
vtdeacon:
@mathheadinc i get a lot of kids who don't really get the idea of putting a whole # over 1 to make it a fraction. Gotta show them #mathchat
12:29 am
mathfour:
@republicofmath I'm with you, but I was going by the book definition-I was a 4th grader. And by its def a square was a rectangle. #mathchat
12:29 am
davidwees:
@suburbanlion ...and Presidents... #mathchat
12:29 am
dansmath:
@vtdeacon @davidwees i use "card dealer" for the distributive law. 3(x+2) deals out a 3 to each term. #mathchat
12:30 am
republicofmath:
@mathfour I'm glad you asked that _ I thought I was supposed to understand. Re MariaDroujkova #mathchat
12:30 am
POWERORGmath:
RT @republicofmath: Common teacher misconception is that kids see things as they do e.g. many young kids don't see rows & columns of arrays #mathchat
12:30 am
vtdeacon:
@davidwees i want to see these archer pics:). Are they stick figures:). #mathchat
12:30 am
davidwees:
@dansmath That works well when there is 1 term outside the parenthesis. I like mine b/c it expands to (x + 3)(x + 5)! #mathchat
12:30 am
EarlSamuelson:
the approach used for any of these depends on the target age group #mathchat calculus approach won't work for grade 10
12:30 am
mathfour:
@davidwees That's a good one - archer (or bow and arrow dude for @davidwees and vtdeacon) #mathchat
12:30 am
ColinTGraham:
Did we get 1/2 + 1/3 = 1/5 yet? Most misconceptions I see are related to fractions/algebra... most abstract parts at school maybe? #mathchat
12:31 am
davidwees:
@vtdeacon hehehe, I wonder if I have a photo of it somewhere. #mathchat
12:31 am
mathfour:
@padgets Whatcha missing, chickadee? #mathchat
12:31 am
mathfour:
@vtdeacon @mathheadinc I have them put post-it notes on their shoes with a 1 on it. "Everyone's over 1" #mathchat
12:31 am
republicofmath:
So it seems we're heading down a track of "conceptions". What about misconceptions? #mathchat
12:32 am
ColinTGraham:
@padgets Oh Sharon, wimping out, eh! #mathchat
12:32 am
vtdeacon:
@ColinTGraham i see that adding problem a lot. How about 5/8 - 1/8= 4/0. Its like multiple misconceptions:). #mathchat
12:32 am
padgets:
@mathfour #mathchat am soo lost but that is ok LOL I often get that way, probably like some would be with science :)
12:32 am
mathfour:
@davidwees Not bad. I like drama - DO IT AND YOU'LL END THE UNIVERSE! #mathchat
12:32 am
davidwees:
@mathfour Yeah, that is funny. #mathchat
12:33 am
republicofmath:
@davidwees 2^4/2^4=2^0 is begging the question IMO #mathchat
12:33 am
padgets:
@ColinTGraham #mathchat I am trying! I get some of it, I learned that way, the way you are all talking about working on it LOL
12:33 am
mathfour:
@mathheadinc And THERE lies the problem. We teach traditional ways that don't work. Kiddos need to discover! #mathchat
12:33 am
ColinTGraham:
Yes, fraction manipulation is always tricky... RT @lufcrace: @ColinTGraham ouch! that's quite a painful misconception that one! #mathchat
12:34 am
nesa_k:
RT @suburbanlion: Equating "mathematics" with "calculation" is a common misconception & not just among students. #mathchat
12:34 am
mikcooke:
@tj007 You're up late (or really early!) No school Friday? I started teaching in 1963 in Hornchurch #mathchat
12:34 am
mathfour:
@colintgraham We dig in like we own the place. Missing you the whole time of course. #mathchat
12:34 am
vtdeacon:
How about placing 1/4 closer to 1 on number line than 1/2 because 4 is greater than 2. #mathchat
12:34 am
davidwees:
@vtdeacon Yep. That's a clear sign someone does not understand fractions. #mathchat
12:35 am
padgets:
#mathchat me me me me !!!@davidwees
12:35 am
mathfour:
@padgets What's the words - I'm dying to know. #mathchat
12:35 am
davidwees:
Making dinner simultaneously as doing #mathchat so if I drop off once in a while, you'll know why...
12:35 am
ColinTGraham:
A lot of the things I see happening in early years mathematics are very similar to EFL/ESOL language probs -- overgeneralization #mathchat
12:35 am
padgets:
#mathchat I so love the metric system
12:36 am
republicofmath:
@vtdeacon Misconception that real numbers not complex numbers, rational numbers not real numbers, integers not rational numbers. #mathchat
12:36 am
vtdeacon:
@davidwees i have so many examples of kids misconceptions on fractions. That alone could take up a whole chat. #mathchat
12:36 am
Wonkderful:
RT @dansmath: i like to remind them it's education, not training, and i'm teaching thinking and problem solving skills not just formulas. #mathchat
12:36 am
padgets:
@mathfour #mathchat I do not know LOL
12:36 am
mathsatschool:
@ColinTGraham Lol. OK, you got me :-) Am lurking in the world of 'math misconceptions' tonight. #mathchat
12:36 am
ColinTGraham:
@padgets Boo! Go away!... Imperial every day... ;-) Metric system was actually suggested by an Englishman... #mathchat
12:37 am
padgets:
#mathchat I think if we all went metric this would be sooo much easier
12:37 am
republicofmath:
@earlsamuelson Don't tell @matheadinc that! "calculus approach won't work for grade 10" #mathchat
12:37 am
mathheadinc:
@mathfour We don't use the traditional process. We use discover & Socratic method to teach calculus to young people. #mathchat
12:37 am
mthman:
Looks like the #mathchat crowd is having a lively conversation. Glad to be here on a #snowday!
12:37 am
padgets:
@ColinTGraham #mathchat darn thought I had an answer
12:37 am
vtdeacon:
@ColinTGraham math itself needs to be looked at as a language in early years in my opinion. Your fraction example for instance #mathchat
12:38 am
davidwees:
@dansmath Oh that's a good way to extend your analogy. Nice. Works for me. #mathchat
12:38 am
padgets:
#mathchat he he he eh @ColinTGraham ok back to studying the chat...
12:38 am
republicofmath:
Here's a good one - counting numbers are the same as Peano natural numbers. #mathchat
12:38 am
ColinTGraham:
Parents feel comfortable about correcting "Daddy chair" to "Daddy's chair" etc. but the same doesn't seem to happen with numeracy #mathchat
12:38 am
mathfour:
@davidwees Whatcha makin'? #mathchat
12:38 am
davidwees:
@padgets There are 3 countries in the world still using the Imperial system exclusively... and one of them is the US! #mathchat #darnyankees
12:39 am
davidwees:
@mathfour Tacos! #mathchat
12:39 am
vtdeacon:
@colintgraham that example can be explained with idea of common noun (denominator). You can't add 2cats + 3dogs & get 5 catdogs #mathchat
12:39 am
tj007:
@mikcooke It is half-term this week, so I can finally try to take part in a #mathchat
12:39 am
republicofmath:
And: it's obvious that a triangle has an area #mathchat
12:39 am
ColinTGraham:
@vtdeacon My whole research interest is basically that the language used to teach mathematics affects how its learned.... #mathchat
12:39 am
mathfour:
@padgets How funny. Which shows another misconception that teachers have... #mathchat
12:40 am
EarlSamuelson:
Thanks for letting me stumble in guys!!!! I have to run for a while. #mathchat
12:40 am
mathheadinc:
@ColinTGraham Do you English vs. Chines for example? #mathchat
12:40 am
mathfour:
If kids don't ask questions, teachers often think it's because they understand. Mostly it's because they don't know what to ask. #mathchat
12:40 am
republicofmath:
Or: you can show sum of angles of triangle is 180 degrees by cutting corners and rearranging #mathchat #misconception
12:40 am
ColinTGraham:
@vtdeacon Some of my students would say that 2 cats + 3 dogs = 3 dogs, because the dogs will eat the cats! #mathchat
12:40 am
padgets:
@mathfour #mathchat see I am of some use! LOL ;0)
12:40 am
mathfour:
I ask in class, "Do you not have questions because you understand or because you haven't the faintest idea what to ask?" #mathchat
12:41 am
davidwees:
@republicofmath I did the cutting corners proofs with my students in NYC. They really understood! Worked great. #mathchat
12:41 am
padgets:
@mathfour #mathchat (hand up) both
12:41 am
ColinTGraham:
@mthman Oh Ron, I've been saying this for years! The best teachers of maths should be working in early years... <sigh> #mathchat
12:41 am
mathfour:
@padgets I have a VERY hard time with metric. Too much moving of decimals - too easy to screw up. Over confidence. #mathchat
12:42 am
vtdeacon:
@mthman @colintgraham actually thats a major PD concept in Vermont. We have the Vermont Math Initiative which offers a masters #mathchat
12:42 am
mikcooke:
@republicofmath Kids don't see as we do: 3x^2+5xy-2y^2? Not "chunking" for 3 terms, anything up to 11 "items" We start alg badly! #mathchat
12:42 am
mathfour:
@mathheadinc Good for you! #mathchat
12:42 am
ColinTGraham:
@mathheadinc Well English and Chinese have similar grammars, but Chinese numbers are basically not a place system... #mathchat
12:42 am
republicofmath:
Well there's a reason to reject it! @ColinTGraham Metric system was actually suggested by an Englishman. #mathchat
12:42 am
padgets:
@mathfour #mathchat I am sorry for me that is the easy part :0)
12:43 am
mathfour:
@davidwees Is @dansmath not using the hashtag? Egad, Dan! #mathchat
12:43 am
vtdeacon:
@mthman @colintgraham the intent of VMI is to get teachers k-12 to understand math. Its not about teaching but rather knowing math #mathchat
12:43 am
ColinTGraham:
I think the biggest misconception is that mathematics is about numbers and counting... #mathchat
12:43 am
davidwees:
@ColinTGraham @mathheadinc When I lived in Thailand, I learned how to count to 999 b/c the Thai numeric system is so easy. #mathchat
12:43 am
republicofmath:
Snowday, snowday? There's noday like a snowday! @mthman #mathchat
12:43 am
mathfour:
@davidwees Yum! Soft shell or hard? #mathchat
12:44 am
mathheadinc:
@ColinTGraham So, are you comparing different languages or speech patterns within a language? #mathchat
12:44 am
mathfour:
@vtdeacon @colintgraham That's a great way to do it! #mathchat
12:44 am
ColinTGraham:
@davidwees Also if you count from 1 to 10 in Thai you get all five tones of the language... cool! #mathchat
12:44 am
davidwees:
@ColinTGraham @mathheadinc For example 164 is Roi Hok Sip See which means literally "hundred 6 tens four" #mathchat
12:44 am
mathednet:
Metric? I'm shooting higher: change counting in English to "...nine, ten, ten one, ten two,..., ten nine, two ten, two ten one" #mathchat
12:44 am
tj007:
@republicofmath I've seen this mentioned before - what method is preferred for proving triangle angle sum? #mathchat
12:44 am
dansmath:
@MathEdnet - oh it confuses them alright. but they also have 'thou shalt not distribute an exponent.' #mathchat
12:45 am
davidwees:
@ColinTGraham Ning, song, sam, see, haa, hok, ... #mathchat
12:45 am
mathfour:
@ColinTGraham @vtdeacon And they should be praised for their creativity. Don't we have some group theory stuff that runs like that #mathchat
12:45 am
dansmath:
@davidwees yes the (x+3) can be dealt out to the x and to the 5. i guess everyone gets two cards. #mathchat
12:45 am
dansmath:
@republicofmath @mathfour how about limit(x->0+)of x^x = 1. proved in calc1. That swings the vote for 0^0=1: [0^b=0, a^0=1] #mathchat
12:45 am
mathheadinc:
@davidwees Sounds similar to Chinese. #mathchat
12:46 am
vtdeacon:
@davidwees @colintgraham @mathheadinc its interesting how so many other languages involve the place value in the name #mathchat
12:46 am
ColinTGraham:
@davidwees Asian systems in writing do reinforce the idea of grouping, with special symbols. Certainly Japanese does. #mathchat
12:46 am
mathfour:
@ColinTGraham @mthman Pay well, and they will. #mathchat
12:47 am
mathheadinc:
@mathfour Where we started www.mathman.biz #mathchat
12:47 am
davidwees:
@mathheadinc @vtdeacon @ColinTGraham Personally I think we should modify English to do the same... #mathchat
12:47 am
dansmath:
@mathfour @davidwees there. hashtagged, deleted, and reposted. #mathchat
12:47 am
mathfour:
@padgets But I also have the most difficulty multiplying by 9. #mathchat
12:47 am
vtdeacon:
@mthman @colintgraham very nice. I do think though it needs to be presented to lower groups in nonthreatening manner #mathchat
12:47 am
mathfour:
@vtdeacon @mthman @colintgraham What's VMI? #mathchat
12:48 am
davidwees:
Strong relationship between math & language. #mathchat
12:48 am
mathheadinc:
11, 12, 13... 1ten1, 1ten2, 1ten3...20, 21, 22...2ten, 2ten1, 2ten2...RT @davidwees: @mathheadinc@vtdeacon @ColinTGraham #mathchat
12:48 am
mathfour:
@ColinTGraham The biggest misconception is that it's NOT about numbers and counting. It should be that simple! #mathchat
12:48 am
ColinTGraham:
@mathfour I don't think it's pay, I think it's much deeper than that, Bon. Read my most recent post!http://bit.ly/f8P96f #mathchat
12:48 am
vtdeacon:
@davidwees @mathheadinc @colintgraham i think there is a lot we need to "modify" with English :) #mathchat
12:49 am
mthman:
@davidwees Speak the language of math every day in class? Ask students to do the same? #mathchat
12:49 am
davidwees:
When languages do not include unique numbers past 2, research has shown people using those languages to struggle with math. #mathchat
12:49 am
davidwees:
Even if those people later learn a language which does include number concepts. #mathchat
12:49 am
mthman:
RT @mathfour: @ColinTGraham The biggest misconception is that it's NOT about numbers and counting. It should be that simple! #mathchat
12:49 am
RushaSams:
Tchr used Prezi in math for examining vocab in problems n tchg vocab! N Asheboro MS! #mathchat
12:49 am
davidwees:
Math teachers spend 50% of their time teaching vocabulary to math concepts. #mathchat
12:50 am
davidwees:
@mathheadinc Exactly! #mathchat
12:50 am
vtdeacon:
@mthman @davidwees also important to write the language of math. Really need kids speaking and writing their math thoughts #mathchat
12:50 am
mathfour:
@dansmath @davidwees Why not married couples shaking hands? No need to shake each others' hands, right? (3+x)(5+x) e.g. #mathchat
12:50 am
tj007:
Am I being overly concerned with trying to say multiply all the time, rather than saying 'this times this' or am I right... #mathchat
12:50 am
davidwees:
So students who struggle with language & vocabulary often face similar issues in math class. #mathchat
12:50 am
mathheadinc:
@davidwees Got it! Learned that from @Gladwell 's book Outliers. #mathchat
12:51 am
padgets:
#mathchat so where could I find a dictionary of math vocab? I really want my students to learn it so it is easier in their math class
12:51 am
mthman:
@davidwees ...and the problem is many teachers teach math vocab like in a LA class. Memorize, write a sentence, etc. #mathchat
12:51 am
RushaSams:
Tchr used prob re internet cafe use to bring real life to math @ N Asheboro MS! #mathchat
12:51 am
mathfour:
@dansmath Woohoo! You've got the hashtag workin'! #mathchat
12:52 am
mathheadinc:
@padgets Any decent bookstore. Try Oxford Press. #mathchat
12:52 am
ColinTGraham:
@davidwees So 2 questions: Is the vocabulary actually necessary? Secondly, if it is, Is it taught before the concept is 'found'? #mathchat
12:52 am
padgets:
@mathheadinc #mathchat thanks!
12:52 am
davidwees:
@mthman Well, no most LA classes don't teach vocabulary that way anymore, that's how it USED to be taught. #mathchat
12:52 am
vtdeacon:
@mthman @davidwees i think math vocab just needs to be used all the time by teacher and kids. Not tested by writing sentence etc #mathchat
12:53 am
republicofmath:
@tj007 One that works! Through a point not on line, can draw parallel to given line. Then use alternate angles. #mathchat
12:53 am
mathfour:
@ColinTGraham Will read and comment later - gotta focus here now. :D #mathchat
12:53 am
davidwees:
@mthman A common practice is to embed the vocabulary in context & give students chances to connect vocab to what they know. #mathchat
12:54 am
mathheadinc:
Proper vocab! RT @vtdeacon: @mthman @davidwees i think math vocab just needs to be used all the time by teacher and kids....#mathchat
12:54 am
mathfour:
@mthman @davidwees Or translate to plain language. No sense in using fancy math terms if they didn't grow up with 'em! #mathchat
12:54 am
ColinTGraham:
Post of mine from July 2010... Mathematics for speakers of other languages http://bit.ly/fNlqag #mathchat
12:54 am
davidwees:
@vtdeacon @mthman I generally start with teaching concepts in math and introduce vocabulary gradually w/ verbal definitions. #mathchat
12:54 am
republicofmath:
I'm in favor, but it proves nothing. @dansmath how about lim(x->0+) of x^x = 1. Proved in calc1. That swings vote for 0^0=1 #mathchat
12:55 am
mathfour:
@davidwees And yet they should just use plain words - I can't stand it! #mathchat
12:55 am
RushaSams:
Math stdnts know Tier 1,2 and 3 words in math classes @ N Asheboro MS! #mathchat
12:55 am
jbrtva:
@davidwees I have many students that struggle with language and some of them find math a reprieve where they struggle less #mathchat
12:55 am
republicofmath:
Hmm! @mathfour @ColinTGraham I happen to think that VERY large chunks of math ARE about numbers and counting. #mathchat
12:55 am
davidwees:
@mathfour Some of our students will go onto further math where plain words take too much time to use to explain concepts. #mathchat
12:55 am
mathheadinc:
Let's not underestimate children's intelligence and just use proper terminology. Otherwise, we're dumbing it down. #mathchat
12:56 am
mathfour:
@mthman @davidwees Exactly - if they would interchange the fancy math term with cutesie terms, they could transition them. #mathchat
12:56 am
ColinTGraham:
@tj007 If kids are ok with "times" fine... but there comes a point when precision is required, I think. It's about discourse... #mathchat
12:56 am
davidwees:
@mathfour The purpose of math vocabulary is to embed complex concepts in a minimum amount of words. #mathchat
12:56 am
republicofmath:
What language you talkin? @RushaSams Tchr used Prezi in math for examining vocab in problems n tchg vocab! N Asheboro MS! #mathchat
12:56 am
vtdeacon:
@davidwees @mthman thats reasonable. I tend to include one or two vocabulary terms in my notebook items and then use them. #mathchat
12:56 am
davidwees:
@jbrtva Ask those same students how well they do in geometry, and other language rich areas of math. #mathchat
12:56 am
tj007:
@republicofmath Cutting the triangle into three works though, but is by no means the only method (but one easily remembered) #mathchat
12:56 am
padgets:
#mathchat we have had this conversation with science vocab, decided to use what is right, not alternatives
12:57 am
jbrtva:
@davidwees we still spend a lot of time on vocab, but a lot of math can be understood without the ability to read/write English #mathchat
12:57 am
mathheadinc:
RT @ColinTGraham: @tj007 If kids are ok with "times" fine... but there comes a point when precision is required...#mathchat
12:57 am
davidwees:
@mathfour @mthman Right, start with plain language the students know, and move into unfamiliar language. #mathchat
12:57 am
ColinTGraham:
@republicofmath I'm stirring again, Gary! However, the way mathematicians see numbers and counting is not the same as Joe Public! #mathchat
12:57 am
mathfour:
@padgets There's a great one that's tiny and wonderful. But that was 15 years ago. maybe an online dictionary? #mathchat
12:57 am
johnnybevacqua:
Really appreciate this topic. Its an area we are working through at my school. @davidwees #mathchat
12:57 am
republicofmath:
I think Springer has one. Let me check. @padgets #mathchat where could I find a dictionary of math vocab?
12:57 am
dansmath:
my prealgebra book has a crossword puzzle in each chapter for vocab review. http://t.co/4iAyv1w#mathchat
12:57 am
davidwees:
@jbrtva I'd argue that type of math is purely computational and those same students will struggle with "real life" situations. #mathchat
12:58 am
davidwees:
Anyway, the reason I bring up language is that I think it is a common reason why students have misconceptions in math. #mathchat
12:58 am
mathheadinc:
@ColinTGraham Mathematicians should make the extra effort for Joe Public to get it. #mathchat
12:58 am
padgets:
@republicofmath thanks!! #mathchat
12:58 am
mathfour:
@ColinTGraham The only reason vocab is necessary is because they next teacher might use it. If we all agreed to facilitate learnin #mathchat
12:58 am
davidwees:
They hear "cancel the -2 from both sides of the equation" and miss the type of operation they should use. Eg. -2x = 6, hence x=8. #mathchat
12:59 am
mthman:
@davidwees Agreed...they become intimidated by the language if it isn't kid-friendly, or used in everyday discussions. #mathchat
12:59 am
mathfour:
Amen! RT @davidwees ...embed the vocabulary in context & give students chances to connect vocab to what they know. #mathchat
12:59 am
ColinTGraham:
Knowing the vocab is not the same as understanding concepts. Can you explain the difference between light and illumination? #mathchat
12:59 am
tj007:
RT @mathfour: The only reason vocab is necessary is because they next teacher might use it. If we all agreed to facilitate learnin #mathchat
1:00 am
mathheadinc:
If Ss R expected to go to college, their profs won't be using 'married pairs' in algebra class. But some tchrs do in high school. #mathchat
1:00 am
ColinTGraham:
I think teachers should use mathematical vocabulary from early stages, and they should do so consistently (very diffcult!) #mathchat
1:00 am
soingirl:
RT @ColinTGraham: I think teachers should use mathematical vocabulary from early stages, and they should do so consistently (very diffcult!) #mathchat
1:00 am
davidwees:
@mathheadinc Yes, we need to move students from language they know to useful math vocabulary. #mathchat
1:00 am
republicofmath:
@padgets Springer has an online encyclopedia of math http://eom.springer.de/ #mathchat
1:00 am
vtdeacon:
@davidwees i agree. In part because kids sometimes get multiple definitions from different teachers. For instance times, multiply #mathchat
1:00 am
mathfour:
@padgets But science is really different from math in that. #mathchat
1:01 am
padgets:
@republicofmath #mathchat thank you soooo much!!!!
1:01 am
mthman:
If vocab isn't seemlessly integrated into your teaching, students will learn it for a test, then mentally dump the information. #mathchat
1:01 am
davidwees:
In terms of teaching math vocabulary we should be looking at what expert foreign language teachers do. #mathchat
1:01 am
davidwees:
@mthman Especially if that vocabulary has no connection to what they know. #mathchat
1:01 am
dansmath:
@tj007 @mathfour yes i subbed for a lin alg class and the teacher got mad at me for showing the 'matrix twitch' for multiplying. #mathchat
1:02 am
republicofmath:
How did a discussion on misconceptions transmogrify into one on language? #mathchat #IblameTwiiter
1:02 am
mathfour:
@davidwees Which destroys discovery. Discovery is opening and dissecting - which can't be done with minimal words. #mathchat
1:02 am
davidwees:
@jbrtva Yeah, I've seen those students who are experts in algebra but can't do much non-algebraic stuff. I teach one now. #mathchat
1:02 am
ColinTGraham:
@davidwees Or even teachers of EFL (like me!) #mathchat
1:03 am
republicofmath:
@tj007 What happens if you cut a triangle on a sphere into 3? #mathchat
1:03 am
ColinTGraham:
Most misconceptions in mathematics happen because a child's cognitivie development is trying to make 'rules' or see patterns #mathchat
1:03 am
LizDk:
re language: command of terms like expression, equation, linear, constant all really help understanding in hs courses #mathchat
1:03 am
mathfour:
ARG! My Hootsuite tweets aren't going through #mathchat
1:03 am
jessicaboehle:
@mathfour or because we are afraid of looking stupid in front of ppl! What if I'm the only one who doesn't get it. #mathchat
1:03 am
ccampbel14:
Just got home. Did I miss the whole #mathchat?
1:04 am
mathfour:
@mathheadinc That's ridiculous - how about we let them decide. The vocab is our hangup not theirs. #mathchat
1:04 am
padgets:
@republicofmath #mathchat is that even possible? oh my......
1:04 am
ColinTGraham:
I think it behooves us all (he says in a formal register!) to recognize misconceptions are a natural part of learning #mathchat
1:04 am
vtdeacon:
@davidwees @jbrtva how much of that do you attribute to the idea of algebriac learners vs geometric learners? #mathchat
1:04 am
mathfour:
@davidwees And when they do, they can use the right words - which they will discover in their own time. #mathchat
1:04 am
LizDk:
hello everyone, I am in, sort of... watching over class quiz #mathchat
1:04 am
jbrtva:
@republicofmath sorry....I jumped off on a tangent that I saw. #mathchat
1:05 am
mathfour:
@dansmath And she should be pummled. #mathchat
1:05 am
davidwees:
@scieducation Exactly. I'm certain the same issues jump up in science education too. #mathchat
1:05 am
mathfour:
@dansmath Or pummeled. Either way. #mathchat
1:05 am
republicofmath:
@CoinTGraham We had a very poor light so the room was illuminated #mathchat
1:05 am
mthman:
@jessicaboehle A battle I fight every year teaching algebra 2 eighth graders. That's why I'm considering "flipping my classroom" #mathchat
1:05 am
davidwees:
Every teacher should learn about how languages are taught, so they can apply similar instructional strategies to their own area. #mathchat
1:05 am
ColinTGraham:
The challenge is guiding students towards reformulating their misconceptions by providing them with the context/vocab to do so #mathchat
1:05 am
mathfour:
Crap - time to pay the babysitter and let her leave. It's been fun, y'all! BATHTIME! #mathchat
1:05 am
padgets:
@republicofmath ohhhh you are good! #mathchat
1:06 am
mathheadinc:
@mathfour Kids are smarter than you think. Any moderately intelligent & knowledgeable teacher could explain the terms. #mathchat
1:06 am
davidwees:
RT @ColinTGraham: I think it behooves us all (he says in a formal register!) to recognize misconceptions are a natural part of learning #mathchat
1:06 am
vtdeacon:
@ColinTGraham so that begs the question ... Should we point out common misconceptions when we introduce a topic #mathchat
1:06 am
LizDk:
@ColinTGraham vg point: misconceptions are a part of learning. Writing tasks explaining errors or sample work are helpful #mathchat
1:06 am
mikcooke:
Fascinated to find you here! It was the old PS12 that drew you here, right? Welcome @johnnybevacqua #mathchat
1:06 am
republicofmath:
A triangle, by any other name.... #mathchat
1:06 am
davidwees:
@ColinTGraham That is the truth for sure. Best math teachers know the misconceptions students will have in advance & prepare. #mathchat
1:07 am
mathheadinc:
SURE, why not? @vtdeacon ...point out common misconceptions... #mathchat
1:07 am
padgets:
@mathheadinc #mathchat ummmm...are you sure?...do not know if I could....LOL
1:07 am
cindykbuchanan:
@republicofmath on't mean to jump into your conversation = but here's a great online math dictionaryhttp://bit.ly/QpoMR #mathchat
1:07 am
ColinTGraham:
OK, that's a wrap for today! Thanks everyone for your contributions, and for getting going without me! Archive online in 30 mins #mathchat
1:07 am
mthman:
@jessicaboehle Check out @vtdeacon's "Flipping the Math Classroom" http://j.mp/f4pFNj #mathchat
1:08 am
mathheadinc:
@padgets YES! YOU! COULD! #mathchat
1:08 am
Jena_Sherry:
At least! :) "@davidwees: Math teachers spend 50% of their time teaching vocabulary to math concepts. #mathchat"
1:09 am
tj007:
@republicofmath Ah, I see - we're talking about diffrnt levels then. As with a lot of maths, we can't always dive in2 the deep end #mathchat
1:09 am
vtdeacon:
@mathheadinc oh i do. Sometimes people believe we shouldn't "put the thought in their head" #mathchat
1:09 am
ColinTGraham:
Next week is world book day, so we will be sharing recommendations on reading. Watch out for the "How do I..." series too! #mathchat
1:09 am
mthman:
Thanks everyone for the great #mathchat...can I get a snow day every Thursday? I'll try to make the next one!
1:09 am
padgets:
@mathheadinc #mathchat ok.......I am willing to try so if I mess up you will have to straighten them out :)
1:09 am
mthman:
RT @ColinTGraham: Next week is world book day, so we will be sharing recommendations on reading. Watch out for the "How do I..." series too! #mathchat
1:09 am
republicofmath:
@ColinTGraham Right! like "if it's got 3 numbers then it's hundreds" but then write one hundred and four as 1004 #mathchat
1:10 am
mathheadinc:
@padgets Just ask the math Twitterverse. We love to help. #mathchat
1:10 am
ccampbel14:
Just jumping in, not knowing what was said already: When you multiply 2 numbers the product is always larger. #mathchat
1:11 am
padgets:
@mathheadinc #mathchat yep you guys are AWESOME!!!!!
1:11 am
mathheadinc:
@vtdeacon Keep doing what you're doing. #mathchat
1:11 am
republicofmath:
What be that? @padgets #mathchat is that even possible? oh my......
1:11 am
mathheadinc:
@padgets I'll settle for 'pretty good'. #mathchat
1:11 am
ColinTGraham:
Feel free to aruge/chat... ;-) we'll be coming back to this topic again on Monday! #mathchat
1:12 am
republicofmath:
They're not smarter than I think. I've studied them long & hard. @mathheadinc Kids are smarter than you think #mathchat
1:12 am
padgets:
RT @mathheadinc: @padgets I'll settle for 'pretty good'. #mathchat thanks! :0) LOL
1:12 am
republicofmath:
What I do? @padgets ohhhh you are good! #mathchat
1:13 am
LizDk:
@vtdeacon @ColinTGraham or steer them through experiences where misconceptions are featured, eg "Explain what is wrong here." #mathchat
1:13 am
republicofmath:
Excellent! @cindykbuchanan here's a great online math dictionary http://bit.ly/QpoMR #mathchat
1:13 am
davidwees:
Loved that we had so many people jump in on #mathchat today. Thanks everyone for a wonderful discussion.
1:14 am
remi_collins:
@davidwees absolutely, there should be math word walls. How many different terms are there in geography alone? #mathchat
1:14 am
jbrtva:
@vtdeacon @davidwees not much. For my students I feel its mostly language and undeveloped higher order thinking skills #mathchat
1:14 am
ccampbel14:
Think Ss have many misconceptions as they go through school which become barriers to later learning. #mathchat
1:15 am
ccampbel14:
Sorry I missed #mathchat again :-( Will check the archives.
1:15 am
ColinTGraham:
@LizDk @vtdeacon Yes, I've found 8/9/10yo want to know the 'big' words and "spot the mistake" always goes down well #mathchat
1:15 am
republicofmath:
@tj007 What different levels? #mathchat
1:16 am
ekendriss:
RT @davidwees: @ColinTGraham That is the truth for sure. Best math teachers know the misconceptions students will have in advance & prepare. #mathchat
1:17 am
ccampbel14:
@mathheadinc Agree about terminology. If 5 year olds can memorize names of dinosaurs they can use proper math vocabulary #mathchat
1:18 am
ccampbel14:
@ColinTGraham Agree about the misconception about #s & counting. People think it's arithmetic which is a piece of mathematics #mathchat
1:18 am
ColinTGraham:
@republicofmath Yes, seen that many times with Japanese students... 1004 is one hundred and four... Long live the place system! #mathchat
1:18 am
mathheadinc:
@ccampbel14 Exactly! Thank you. #mathchat
1:18 am
ColinTGraham:
Make it snow? RT @mthman: Thanks everyone for the great #mathchat...can I get a snow day every Thursday? I'll try to make the next one!
1:20 am
ClaudiaCostin:
RT @Rafael_Parente: RT @republicofmath: Excellent! @cindykbuchanan here's a great online math dictionary http://bit.ly/QpoMR #mathchat
1:20 am
davidwees:
@dloitz Yeah that was the point. :) So many students will add in that equation b/c of their misconceptions. #mathchat
1:20 am
tj007:
@republicofmath A triangle on a sphere is not something that 11-13yr olds will come across here, I believe. Beyond them... #mathchat
1:21 am
ekendriss:
RT @ColinTGraham: Make it snow? RT @mthman: Thanks everyone for the great #mathchat...can I get a snow day every Thursday? I'll try to make the next one!
1:21 am
davidwees:
@tj007 @republicofmath Triangles on spheres in real life are most commonly seen in flight paths of long distance flights. #mathchat
1:23 am
ColinTGraham:
@tj007 Don't they get the triangles on the globe with 3 right angles? I always used to 'screw' with Yr8's minds that way! #mathchat
1:24 am
ColinTGraham:
@tj007 Of course, the Geography teacher used to hate me for it! Geographical surveys have to reset every 9 miles w/ triangulation #mathchat