Topic: What terminology should we use and when - 'proper' mathematical terms or everyday language?
As it happened on Thursday, 30th September 2010, 23:30 - 00:30 GMT
11:32 pm
ColinTGraham:
Hello everyone and, in case you haven't got used to the idea yet, I am going to be spending the next hour tweeting in #mathchat
11:33 pm
ColinTGraham:
If it is your first time here, welcome! Don't try to follow everything, just interact with one or two people #mathchat
11:34 pm
ColinTGraham:
Links, URLs and so on will be extracted later, so you don't need to check them out now! #mathchat
11:34 pm
ColinTGraham:
Tonight's full topic is: "What terminology should we use and when - 'proper' mathematical terms or everyday language?" #mathchat
11:35 pm
padgets:
@ColinTGraham #mathchat Hi everyone! I am a high school science teacher lurking and learning from some great math folks!
11:35 pm
millerblair:
Introduce math terminology as students need a way to express or refer to a concept - the 'uh, uh, that thing moment' #mathchat
11:36 pm
suburbanlion:
#mathchat @republicofmath had a great post today on "Strangeness of #mathematical #language"http://wp.me/pJESd-Ak
11:36 pm
ColinTGraham:
@padgets Hi Sharon! Lurking means no-one knows you're here! ;-) #mathchat
11:37 pm
mthman:
What mathematical language/terminology do students resist using? #mathchat
11:37 pm
ColinTGraham:
Let's use this question to focus, at first: Does the introduction of terminology come before or after the concept? #mathchat
11:37 pm
padgets:
@ColinTGraham #mathchat well, I plan to talk some......:-)
11:38 pm
padgets:
#mathchat I have been in my math team mates room and she does vocabulary activities first
11:38 pm
mthman:
@ColinTGraham My preference is to come while introducing a concept...let them hear it in context first...talk about other meanings #mathchat
11:38 pm
millerblair:
For anyone who hasn't seen @republicofmath 's blog post 'The Strangeness of Mathematical Language' http://wp.me/pJESd-Ak -gd read #mathchat
11:38 pm
ColinTGraham:
@suburbanlion I already had Gary's post in the prep, before he knew! #mathchat
11:39 pm
ColinTGraham:
@millerblair It's in the prep for tonight already! #mathchat
11:40 pm
mthman:
Hmmm...that didn't sound right...I use the vocab all throughout the intro...then discuss meaning(s). Ask Ss to use it in Q's #mathchat
11:40 pm
padgets:
#mathchat we use things like semantic mapping, concept mapping, word sorts and other literacy strategies
11:40 pm
ColinTGraham:
@mthman How do you decide how much terminology to introduce, Ron? #mathchat
11:40 pm
padgets:
RT @millerblair: @republicofmath 's blog post 'The Strangeness of Mathematical Language'http://wp.me/pJESd-Ak -gd read #mathchat
11:42 pm
ColinTGraham:
For newcomers, please make sure you follow @mathchat, preparatory questions usually appear on the Wiki about 8 hours b4 Thur's #mathchat
11:42 pm
millerblair:
@ColinTGraham My bad didn't get over to the prep before the chat - thought others may not have seen it. #mathchat
11:43 pm
mthman:
@ColinTGraham The volume of terminology is determined by past experience (mine)...but I don't try to limit it or assess it all. #mathchat
11:43 pm
ColinTGraham:
@millerblair Don't worry about it, useful links are always welcome however many times they get tweeted! #mathchat
11:44 pm
padgets:
#mathchat Do you all visuals for vocabulary or just a definition?
11:44 pm
ColinTGraham:
@mthman How do you decide on 'correct' terminology... interesting differences between describing polynomials in relation to US/Uk #mathchat
11:44 pm
mthman:
If you want your students to talk the language of math, you have to lead the way! Use it, make fun of it, have fun with it! #mathchat
11:45 pm
ColinTGraham:
@padgets Depends, where do you get your definitions from? #mathchat
11:45 pm
millerblair:
@mthman I'm w/ you on introduction of terms in context, but I like to start w/ the way students describe or understand a situation #mathchat
11:45 pm
cybraryman1:
My Math Vocabulary sites: http://bit.ly/byedYS #mathchat
11:45 pm
mthman:
@ColinTGraham I expect them to follow my lead...or challenge my use of the terminology. #mathchat
11:46 pm
ColinTGraham:
@cybraryman1 Are those American math vocabulary sites, Jerry? Check out trapezium/trapezoid, for example...! #mathchat
11:46 pm
padgets:
#mathchat oh no I thought math had the same word for all the same things, not like science where some animals have 3 different names! :-)
11:46 pm
mthman:
@millerblair Exactly...let them compare & contrast their understanding to my usage. #mathchat
11:46 pm
cybraryman1:
Have your students create their own math glossaries with their own visuals #mathchat
11:47 pm
rushtheiceberg:
RT @mthman: If you want your students to talk the language of math, you have to lead the way! Use it, make fun of it, have fun with it! #mathchat
11:47 pm
padgets:
RT @cybraryman1: My Math Vocabulary sites: http://bit.ly/byedYS #mathchat
11:47 pm
ColinTGraham:
@cybraryman1 So get Ss to explain their thinking/approach/process from the beginning? #mathchat
11:48 pm
millerblair:
@padgets Wherever possible I like to intro the term with a visual - this can be difficult with some things #mathchat
11:48 pm
POWERORGmath:
RT @cybraryman1: My Math Vocabulary sites: http://bit.ly/byedYS #mathchat
11:48 pm
ColinTGraham:
@millerblair For example, where are visuals challenging? #mathchat
11:48 pm
padgets:
#mathchat I would think it would be hard to have metric in your country and the English system here, run into it many times in science
11:49 pm
ColinTGraham:
@mthman How consistent are you in your use of terminology? #mathchat
11:49 pm
millerblair:
@mthman Got you. That's why I like the moments when they are searching for a word to describe a situation-drives need for a term #mathchat
11:49 pm
POWERORGmath:
Absolutely!!!> RT @cybraryman1: Have your students create their own math glossaries with their own visuals #mathchat
11:49 pm
cybraryman1:
@ColinTGraham Yes, you want to see how students solve problems #mathchat
11:50 pm
ColinTGraham:
@padgets Technically, the 'English' system is metric... Imperial measurement is probably best term to use, US does its own thing... #mathchat
11:50 pm
padgets:
@millerblair #mathchat That is why I have trouble, cannot do the stuff in my head :-)
11:51 pm
padgets:
@ColinTGraham #mathchat yep and that drives me CRAZZZZYYYY! :-)
11:52 pm
ColinTGraham:
At what age do you think it is valuable or realistic to ask children to explain process, as opposed to describe it? #mathchat
11:52 pm
millerblair:
@ColinTGraham Abstract concepts - i.e. irrational numbers -easy to provide examples & Venn Diagram, but irrationality itself? #mathchat
11:52 pm
enlindsay:
@rushtheiceberg Amen! if you don't use the words how do you expect your students to use the words? #mathchat
11:53 pm
enlindsay:
@POWERORGmath Yes. This works really well and really helps the ELL students #mathchat
11:54 pm
padgets:
#mathchat I think as early as possible
11:55 pm
enlindsay:
@padgets I agree. #mathchat
11:55 pm
millerblair:
@ColinTGraham I've taught in UK & Canada - well aware of terminology differences. I go w/ term predominant in that system #mathchat
11:55 pm
mthman:
@ColinTGraham Sorry...custodian came in for a chat...I use the terminology whenever possible. #mathchat
11:55 pm
ColinTGraham:
@millerblair So exemplification is ok, but concept is more difficult to display... Are there situations when visuals help concept? #mathchat
11:56 pm
mthman:
Wow...my time is up...I need to pick up my 5 y/o...will catch what I can on my phone! #mathchat
11:56 pm
cybraryman1:
@ColinTGraham MathSphere Maths Dictionary (UK) has trapezium Good point. Math Vocabulary sites: http://bit.ly/byedYS #mathchat
11:56 pm
padgets:
#mathchat Is there a universal Math dictionary or like in science Latin is used?
11:56 pm
ColinTGraham:
@millerblair I prefer to go with conceptually correct terms... if properly defined... ho-hum! #mathchat
11:57 pm
ColinTGraham:
@mthman Catch you later Ron! #mathchat
11:58 pm
padgets:
RT @cybraryman1: MathSphere Maths Dictionary (UK) has trapezium Good point. Math Vocabulary sites: http://bit.ly/byedYS #mathchat
11:58 pm
ColinTGraham:
There have been examples of workbooks/methods which ask children as young as 6 to 'explain' their answer. Can they? #mathchat
11:59 pm
republicofmath:
About grade 5 @ColinTGraham What age is it valuable or realistic to ask children to explain process as opposed to describe it? #mathchat


ColinTGraham:
@republicofmath So that's about 10/11 years old, Gary? #mathchat

millerblair:
@ColinTGraham Examples of places where visuals are great - physical concepts/geometry, integers, patterns/sequence, proportions #mathchat

padgets:
RT @republicofmath: About grade 5 #mathchat < agree :-)
12:02 am
ColinTGraham:
@millerblair How do you link the terminology of a visual with a written example, eg tie geometry into algebra...? #mathchat
12:03 am
ColinTGraham:
@padgets Some maths dictionaries are listed in the preparation page for tonight, Sharon! But US/UK terminology differs... #mathchat
12:03 am
enlindsay:
@ColinTGraham My students are adding and subtracting integers and drawing two colored chips is helpful to understand the concept #mathchat
12:04 am
dendari:
@ColinTGraham Thats a good question. How old is the child? ___ is the exact right age to ask him/her to explain #mathchat
12:04 am
padgets:
@ColinTGraham #mathchat I missed them! must go back and read again thanks! :-)
12:04 am
ColinTGraham:
In Japan, early years rotational symmetry is taught as being 180-degree rotations, so an equilateral triangle has none #mathchat
12:04 am
millerblair:
@ColinTGraham I ask my 13/14 yr olds (Gr. 8) to do a lot of explaining - they get better as the year goes on. #mathchat
12:05 am
republicofmath:
That's my experience. @ColinTGraham So that's about 10/11 years old, Gary? #mathchat
12:05 am
ColinTGraham:
@enlindsay Understanding, seeing, describing and explaining are all different levels cognitively... it's important to recognize #mathchat
12:06 am
ColinTGraham:
@millerblair Explanation is 'required' (hoped for!) from age 11 upwards in the UK national curriculum #mathchat
12:07 am
millerblair:
@ColinTGraham Can be tricky to link term to examples-diagrams, pictures of problem, use of objects to represent variables/numbers #mathchat
12:07 am
ColinTGraham:
So, if explaining and describing are seen as important parts of being mathematicians... where do we get definitions from? #mathchat
12:07 am
suburbanlion:
@ColinTGraham it's not just US/UK differences. For example, "natural number" varies from textbook to textbook. #mathchat
12:08 am
millerblair:
RT @ColinTGraham: Understanding, seeing, describing & explaining are all diff. levels cognitively... it's important to recognize #mathchat
12:08 am
ColinTGraham:
@millerblair Online manipulatives can be very helpful if you get Ss to make their own #mathchat
12:08 am
mthman:
What terminology do you use to teach rotations? Most students don't wear watches! #mathchat
12:08 am
Chuck_Bell_:
Don't know a math teacher anywhere who couldn't use this! RT @cybraryman1: My Math Vocabulary sites: http://bit.ly/byedYS #mathchat
12:08 am
ColinTGraham:
@suburbanlion But whose textbook, who edited, who decides the content of the texts? #mathchat
12:09 am
ColinTGraham:
@mthman Oh Origami, if you want to find out how, check out my Skype presentation for TeachMeet Tennessee on Saturday! #mathchat
12:09 am
millerblair:
@ColinTGraham Agree - I use a lot of manipulatives - physical & virtual in class - students also create #mathchat
12:10 am
padgets:
#mathchat Well, I hate to run but have a grad paper to write, take care everyone, thanks for the chat, tweet you all next week :-)
12:10 am
MathPerch:
RT @mthman: If you want your students to talk the language of math, you have to lead the way! Use it, make fun of it, have fun with it! #mathchat
12:11 am
ColinTGraham:
@suburbanlion Yes, some people include zero as a natural number, others don't... what is a number? numbers vs numerals... ;-) #mathchat
12:11 am
millerblair:
@mthman Rotations - complete or partial turns - examples wheels on a bike/car #mathchat
12:12 am
republicofmath:
Known 4 yr olds in UK explain why something is prism ; context is critical. @ColinTGraham@millerblair Explanation from age 11 #mathchat
12:12 am
ColinTGraham:
OK, here's an "off-the-wall" as a colleague described it: Do you/should you teach the Greek alphabet and how to write it? #mathchat
12:13 am
ColinTGraham:
@republicofmath Do you believe this is actually explanation or is it just highly observant description? #mathchat
12:14 am
republicofmath:
LOL And in US how to pronounce it! @ColinTGraham Do you/should you teach Greek alphabet and how to write it? #mathchat
12:14 am
ccampbel14:
Hello everyone on #mathchat. Sorry I am sooooo late!
12:14 am
millerblair:
@republicofmath @ColinTGraham New curriculum in Wstn Canada has introduced explanation in earlier years - in context #mathchat
12:15 am
ColinTGraham:
@ccampbel14 Hi Cathy, glad you could join us! #mathchat
12:16 am
ColinTGraham:
@millerblair UK expectation is that 11 year olds should be able to notice and describe patterns in words (eg Fibonacci numbers) #mathchat
12:17 am
tperran:
#mathchat Hi everyone. Sorry I'm late! Hope you all ae havng a good week so far.
12:17 am
millerblair:
@ColinTGraham Teach Greek letters as required for functions, sequences/series, geometry & measurement in secondary not whole thing #mathchat
12:17 am
ccampbel14:
Young children can memorize names of dinosaurs, Pokemon, etc. so I know they can learn math vocabulary! #mathchat
12:17 am
republicofmath:
Good question. Have to reflect on it. @ ColinTGraham is this explanation or highly observant description? #mathchat
12:17 am
ColinTGraham:
I think children as young as 4 or 5 can say/notice things like "add 3" or "double"... but not 'generalize to the nth term'... #mathchat
12:17 am
cybraryman1:
@millerblair My Math Manipulatives page: http://bit.ly/dutc65 #mathchat
12:19 am
ColinTGraham:
@ccampbel14 Memorizing lists is not the same as being able to describe or define the object though... #mathchat
12:19 am
ccampbel14:
@suburbanlion Didn't know that 'natural numbers' have different definitions! I understood it to be the counting numbers. #mathchat
12:20 am
millerblair:
@ColinTGraham Earliest I can find in Wstn Canada curriculum guidelines is Gr. 4 (10 yrs) - explaining concept of 0 and 1 #mathchat
12:20 am
ColinTGraham:
Let me throw out an example which came up recently... If I say "binomial" what do you immediately think of? #mathchat
12:20 am
ccampbel14:
@ColinTGraham I haven't taught the Greek alphabet . Exposed students to pi, alpha, beta - ones I think they might see. #mathchat
12:21 am
ccampbel14:
@ColinTGraham You are right. I do think, though, that they can learn the terminology with understanding. #mathchat
12:21 am
millerblair:
@cybraryman1 Thanks for sharing Math Manipulatives page. Here are my bookmarkshttp://delicious.com/mr.b.miller/math+interactive #mathchat
12:21 am
ccampbel14:
@ColinTGraham Binomial to me is a polynomical with two terms. #mathchat
12:22 am
ccampbel14:
In our Western Canadian curriculum we ask kids to explain right from kindergarten - can show it if they have trouble explaining #mathchat
12:23 am
ColinTGraham:
Binomial to me conjures up the binomial theorem and rows of Pascal's triangle... #mathchat
12:23 am
republicofmath:
LOL. Known elem teachers who have trouble with this. @ColinTGraham 4-5 yr olds can say "add 3" or "double"but not generalize. #mathchat
12:23 am
suburbanlion:
@ccampbel14 main debate is whether or not to include 0. ie: number theorists like to start at 1, set theorists like to start at 0. #mathchat
12:24 am
ccampbel14:
What about the word 'and' when you say numbers? I am a stickler for only using this where you see a decimal point. #mathchat
12:24 am
ccampbel14:
@suburbanlion Don't really know what set & number theorists are. New idea for me! #mathchat
12:24 am
ColinTGraham:
@ccampbel14 Again, as I said earlier, describe and explain are not the same. I don't think kids of single-digit ages can explain #mathchat
12:25 am
millerblair:
@ColinTGraham @republicofmath It's a very fine line - isn't explanation ability to use in context & describe appropriate observ.? #mathchat
12:25 am
enlindsay:
@ccampbel14 what a great thought! #mathchat
12:26 am
ColinTGraham:
@millerblair To me, explain means "Say why... happens" or give the reason for "...." #mathchat
12:26 am
ccampbel14:
@ColinTGraham I will have to think about it...I know kids can describe more easily but I need to rethink whether they explain.. #mathchat
12:27 am
ColinTGraham:
So - some points to consider: explain/describe, define, show/tell, whose 'meaning'? #mathchat
12:28 am
ColinTGraham:
In the final few minutes... any thoughts or comments about using 'correct' terminology? #mathchat
12:28 am
cybraryman1:
RT @ColinTGraham: So - some points to consider: explain/describe, define, show/tell, whose 'meaning'? #mathchat
12:28 am
republicofmath:
Probability distribution; binomial expansion: middle term hard. @ColinTGraham If I say binomial what do you immediately think of? #mathchat
12:28 am
Sundayteatime:
@ccampbel14: What about the word 'and' when you ... #mathchat What do you mean here?
12:29 am
ColinTGraham:
@republicofmath Yes, given that I am basically a statistician... my thoughts too! #mathchat
12:29 am
enlindsay:
@ColinTGraham I would agree but students do connect a pic or idea to dinasours and so on. They don't just memorize these words #mathchat
12:29 am
suburbanlion:
Math terms are only valid within the context of the text that defines them. #mathchat
12:29 am
ccampbel14:
I like to provide correct terminology along with 'friendlier' terms but I do explect them to use correct terms over time. #mathchat
12:29 am
davidwees:
@ColinTGraham x+3 or -6x^2 + 6x for examples of binomials. #mathchat
12:30 am
ccampbel14:
@Sundayteatime Instead of saying 134 - one hundred and thirty-four it is one hundred thirty-four. 1.3 would be 1 and three tenths #mathchat
12:30 am
millerblair:
@ColinTGraham Agree, but "saying what happens" is usually in a given context. Give reasons for, is observation of math usage #mathchat
12:30 am
ColinTGraham:
In US terminology... which personally I think is confusing. RT @davidwees: x+3 or -6x^2 + 6x for examples of binomials. #mathchat
12:31 am
republicofmath:
It's a big #math world. Try to communicate effectively. @ColinTGraham thoughts or comments about using correct terminology? #mathchat
12:31 am
ccampbel14:
I think using correct terminology helps students explain their thinking which demonstrates understanding. #mathchat
12:31 am
ColinTGraham:
OK, looks like we opened another can of worms today! We'll be back to visit this topic again on Monday! #mathchat
12:31 am
millerblair:
@elenelsecchio That is a good test. Appropriate application and extension to generalisable conditions. #mathchat
12:31 am
Traveller698:
RT @ColinTGraham: So - some points to consider: explain/describe, define, show/tell, whose 'meaning'? #mathchat
12:32 am
ColinTGraham:
Thanks for your contributions everyone. Please add new ideas for discussions to the Wiki:http://bit.ly/aOhxOW #mathchat
12:32 am
enlindsay:
You know students understand the words they hear when you hear them using them in their own sentences correctly. #mathchat
12:33 am
ColinTGraham:
Remember to follow @mathchat to keep up-to-date with changes. #mathchat
12:34 am
ColinTGraham:
I will be giving a presentation to TeachMeet Tennessee on Saturday, using my experience with #mathchat
12:34 am
ccampbel14:
Thks every1 for #mathchat. Becoming increasingly challenging to participate now that I'm back at work. Will try again next week.
12:35 am
millerblair:
@ColinTGraham Thanks for moderating & pushing discussion along. Thanks @padgets@elenelsecchio @cybraryman1 @republicofmath for #mathchat
12:35 am
ColinTGraham:
The schedule is here: http://tmtn.wikispaces.com/Schedule if you want to join us virtually. If not, see you next time! #mathchat
12:36 am
ColinTGraham:
The archive will be online in about 30 minutes or so as usual. #mathchat
12:36 am
padgets:
#mathchat thanks for the kudos! :-)
12:36 am
ccampbel14:
@ColinTGraham Do you ever sleep?! #mathchat
12:37 am
mikcooke:
@glenmacpherson Did you follow #mathchat today? It was about the timing for the use of proper terminology in #mathematics
12:39 am
ColinTGraham:
@ccampbel14 No, I'm a robot! I can decide my own schedule at the moment, so that helps, and I've always been a night owl! #mathchat
12:40 am
elenelsecchio:
@millerblair Thanks for the tweet although you should know: I don't often tweet about maths! I was gatecrashing the #mathchat
12:42 am
ColinTGraham:
@elenelsecchio Gatecrashers are always welcome! #mathchat is one big party ;-P
12:43 am
millerblair:
@elenelsecchio No worries. I don't like to tweet only about maths! Like any interest. convo. - on topic gatecrashers welcome in #mathchat
12:48 am
elenelsecchio:
@millerblair @ColinTGraham Ihihi will gatecrash again then :) Thanks for chat and sharing! #mathchat
12:55 am
JillBromen:
RT @MrStephenWolfe: I don't see a need to "wait on superman" - I see superheroes on here every day #ELLchat #mathchat #lrnchat