Topic (follow-up to Thursday 26th July): What is the problem with fractions? How can we fix it?
As it happened on Monday, 2nd August 19:30 - 21:00 GMT
7:34 pm
ColinTGraham:
Hello everyone, welcome to the repeat of last week's topic What is the problem with fractions? How can we fix it? #mathchat
7:34 pm
ColinTGraham:
#mathchat
7:35 pm
ColinTGraham:
If it is your first time, feel free to lurk and jump in when you are ready! Try to focus on one or two conversations only! #mathchat
7:35 pm
MmeVeilleux:
For the next 90 minutes my tweets will be related to #mathchat
7:37 pm
ColinTGraham:
Maybe we should start by talking about what we mean when we say "fraction" #mathchat
7:37 pm
MmeVeilleux:
Who facilitates #mathchat? I once saw an episode of the Bernstein Bears where the girl was suffer from an attack of mathphobia b/c of frctns
7:38 pm
MmeVeilleux:
#mathchat part-to-whole relationship - is that too simple a definition?
7:40 pm
ColinTGraham:
@MmeVeilleux I think it is just you and I at the moment Ingrid! #mathchat
7:41 pm
MmeVeilleux:
RT @ColinTGraham #mathchat ColinTGraham Part to whole is one definition, but how about decimal numbers, ratio, algebraic...?
7:41 pm
MmeVeilleux:
@ColinTGraham #mathchat Lol! I was thinking the same. I RT'ed bc there was no hashtag. I agree w/your comment.
7:42 pm
MmeVeilleux:
#mathchat Aren't decimals, ratio, algebra under the part-to-whole umbrella?
7:44 pm
ColinTGraham:
@MmeVeilleux Yes part-to-whole covers everything, but is that what you think of when someone says fraction? #mathchat
7:45 pm
MmeVeilleux:
MmeVeilleux @kelalford Isn't the = sign for teaching equivalency? Do U mean bc the parts are equivalent to each other? #mathchat
7:45 pm
jagkise:
@ColinTGraham I like the Chinese emphasis on area, set and length models for fractions to deepen part-to-whole #mathchat
7:46 pm
MmeVeilleux:
@ColinTGraham #mathchat I like to start with geometry and lines and fold lines bc then it's not as 'messy' as cutting apples or sthg.
7:47 pm
ColinTGraham:
@MmeVeilleux For example 2/4 and 27/9 are both fractions symbolically... #mathchat
7:47 pm
MmeVeilleux:
#mathchat I did not know that the Chinese use length. I wd like to know more about their representations.
7:47 pm
jagkise:
#mathchat I like to start with three students on their feet as a set. Have them describe themselves in fractions. 1/3 wearing jeans, etc.
7:47 pm
ColinTGraham:
@jagkise Do you have any examples of this Chinese approach? #mathchat
7:48 pm
jagkise:
@MmeVeilleux #mathchat Division: If half a length is 1 and 3/4 feet, how long is the whole?
7:48 pm
MmeVeilleux:
@ColinTGraham #mathchat I mostly teach primary so I like to start off first with 1/1 or 2/2 whole numbers into fractions
7:49 pm
jagkise:
@ColinTGraham #mathchat Singapore does it too. Area...coloring shapes, working with tiles, etc. Sets...boys out of all students, etc.
7:50 pm
MmeVeilleux:
@jagkise #mathchat For reasonableness (estimation), I'd take a strip of paper that length and fold in half then word w/pictures
7:50 pm
jagkise:
@ColinTGraham #mathchat They ensure students understand multiple models for fractions. I find US students don't recognize all as fractions
7:51 pm
MmeVeilleux:
@jagkise #mathchat I had heard of Singapore math a little and I have read some obscure articles about Vygotskian math w/out numbers
7:52 pm
MmeVeilleux:
#mathchat I sometimes de-emphasize numbers to start and give names or letters to pieces so that primary stu are thrown off by numbers
7:52 pm
ColinTGraham:
One of the 'issues' we identified last Thursday was the idea of equivalent fractions. 2/4 is not seen as 'the same' as 4/8 #mathchat
7:54 pm
MmeVeilleux:
#mathchat Y do U think this confusion about equiv fractions exists? I think it might be b/c we often privilege only 1 solution method &
7:54 pm
Sundayteatime:
#mathchat I tend to play a lot of equivalent fraction snap on the interactive whiteboard
7:55 pm
MmeVeilleux:
#mathchat con't & it is probably good to start with more expansive definitions. Example of pre- and post-assmt I like to use in a moment
7:56 pm
ColinTGraham:
Equivalency maybe confusing if we introduce the symbolic notation too early or use terms like 'reduce' when values don't change #mathchat
7:56 pm
jagkise:
@ColinTGraham #mathchat We have six students stand. Students "see" how 3 of 6 is half of the whole group. Really effective.
7:56 pm
ColinTGraham:
@Sundayteatime What ages are you working with? #mathchat
7:56 pm
MmeVeilleux:
@Sundayteatime #mathchat Is it a timed game? Do U find snap to B effective?
7:57 pm
jagkise:
#mathchat Just finishing research on how students with different #MBTI types learn fractions. Statistically significant www.edcoaching.com
7:58 pm
ColinTGraham:
@jagkise Seeing 3 out of 6, though, is not the same as seeing 4 out of 8, which is where some of the confusion may arise #mathchat
7:58 pm
MmeVeilleux:
@ColinTGraham #mathchat In Grades 2&3, I don't intro terms like 'reduce'; reducing seems to be needed 4efficiency later on
7:58 pm
jagkise:
#mathchat Many students need to work with physical tools like fraction strips to see equivalencies as well as the labels.
7:58 pm
ColinTGraham:
@jagkise What is MBTI for those unfamiliar with it? #mathchat
7:59 pm
jagkise:
@ColinTGraham #mathchat We do groups of 3, 4, 6 as a matter of fact. Then repeat concepts with color tiles and drawings
7:59 pm
MmeVeilleux:
#mathchat One stumbling block in Math is to teach number as usually being discrete objects (3 apples) instead of liquids, lengths,etc Agree?
8:00 pm
jagkise:
@ColinTGraham #mathchat #MBTI refers to Jungian learning preferences for being energized and how we process information
8:01 pm
jagkise:
@MmeVeilleux #mathchat Agree! I even get teachers saying "You can't divide 3 by 2." Well yes you can!!
8:01 pm
ColinTGraham:
@MmeVeilleux So you see some of the problem with fractions being related to countable and 'uncountable' things? #mathchat
8:02 pm
malcolmbellamy:
@ColinTGraham explore equivalency then use scales..... two smaller cubes is equivalent to one larger #mathchat
8:02 pm
ColinTGraham:
Imprecise use of language seems to be a recurrent factor in confusion in mathematics #mathchat
8:02 pm
MmeVeilleux:
@ColinTGraham #mathchat I think it is inherently confusing to think about 3 apples div by 2 b/c the last one U cut in half whereas it is
8:03 pm
MmeVeilleux:
@ColinTGraham #mathchat more 'natural' (to me) to take 3cm and divide in half or 3 litres and pour into 2 equal amts
8:03 pm
ColinTGraham:
I use Smarties or M&Ms or packets of coloured sweets... to get away from cutting things! #mathchat
8:04 pm
MmeVeilleux:
#mathchat I think the whole apple prob is that the first two apples are not cut in halves, only the last 1 which gets a dif name, ie. 1/2
8:04 pm
mthman:
A lil' boy keeps me from #mathchat 2day http://twitpic.com/2b1oxv
8:04 pm
ColinTGraham:
RT @Sundayteatime: @MmeVeilleux by reduce do you mean simplify? In uk we tend to use that term. Can still cause confusion though. #mathchat
8:04 pm
ColinTGraham:
@Sundayteatime Don't forget the hashtag! #mathchat
8:05 pm
ColinTGraham:
@mthman It's ok Ron, no point in spoiling his summer! #mathchat
8:05 pm
MmeVeilleux:
@Sundayteatime Yes, I mean simplify. #mathchat
8:06 pm
Sundayteatime:
@ColinTGraham #mathchat oops yes sorry. I'm a first timer.
8:06 pm
MmeVeilleux:
@mthman Adorable and those shapes remind me of a logic game whose name escapes me! argh on tip of my tongue #mathchat
8:07 pm
ColinTGraham:
@Sundayteatime Yes, I much prefer 'our' term, rather than reduce to lowest terms.... ;-) #mathchat
8:07 pm
POWERORGmath:
@ColinTGraham #mathchat The M&Mks get their attention too.
8:07 pm
malcolmbellamy:
by simplify can we say "see it in a different way"? (visualisation) #mathchat
8:08 pm
MmeVeilleux:
#mathchat And it occurs to me that simplifying is easier when you U know ur multiples v. well. Requires lots of prior number experience.
8:08 pm
mthman:
@ColinTGraham LOL. He keeps me on my toes! #mathchat
8:09 pm
jagkise:
@malcolmbellamy #mathchat We've said, "Is there another fraction name that describes that amount?"
8:09 pm
POWERORGmath:
RT @ColinTGraham: Imprecise use of language seems to be a recurrent factor in confusion in mathematics #mathchat <~Yes at K-16 level.
8:09 pm
MmeVeilleux:
#mathchat Simplify does sound more motivating than reduce to the lowest terms!!
8:09 pm
ColinTGraham:
@POWERORGmath The thing I do with sweets/candies is get them to count various fractions... they are not allowed to eat of course! #mathchat
8:10 pm
mthman:
@MmeVeilleux It started as a simple game of red-light, green-light...6 pieces of sidewalk chalk later... #mathchat
8:10 pm
jagkise:
@MmeVeilleux #mathchat We provide very accurate fraction strips (which bridge to the most iimportant numberline model) They "see" multiples
8:10 pm
malcolmbellamy:
@jagkise name or picture? #mathchat
8:10 pm
MmeVeilleux:
@jagkise That is lovely wording! Must use that. #mathchat
8:10 pm
ColinTGraham:
@POWERORGmath Then I go round and steal a sweet from each group, eat it, and they have to start again.... evil teacher! #mathchat
8:10 pm
POWERORGmath:
RT @jagkise: @MmeVeilleux #mathchat Agree! I even get teachers saying "You can't divide 3 by 2." Well yes you can!! <~*frown* but true
8:10 pm
jagkise:
@POWERORGmath #mathchat Catch Deborah Ball at any math conference and her talk on teacher knowledge, precision of language
8:11 pm
MmeVeilleux:
@mthman #mathchat What a hoot. My competitive husband likes to make racetracks. The kids add parking lots etc so much fun!!!
8:11 pm
jagkise:
@malcolmbellamy #mathchat at that stage they would have a picture or manipulative in front of them. Concrete-pictorial-abstract sequence
8:12 pm
ColinTGraham:
Write another way maybe better? RT @malcolmbellamy: by simplify can we say "see it in a different way"? (visualisation) #mathchat
8:12 pm
POWERORGmath:
@jagkise #mathchat Yes. Color tiles are good for tactile & visual learners (esp w/fractions)
8:12 pm
MmeVeilleux:
@jagkise #mathchat Do you think the numbers are confusing or helpful for them? Wd numberless #lines be useful?
8:12 pm
POWERORGmath:
RT @jagkise: #mathchat Just finishing research on how students with different #MBTI types learn fractions. (cont) http://tl.gd/2stg28
8:12 pm
malcolmbellamy:
@jagkise gr8 good practice for everyone #mathchat
8:13 pm
MmeVeilleux:
@ColinTGraham #mathchat That is really really funny! I will have to try that!!! haha
8:13 pm
ColinTGraham:
@POWERORGmath Give two teachers $3 and tell them to divide it by two... oh no, you can't, no money for you then... They get it! #mathchat
8:14 pm
jagkise:
@MmeVeilleux #mathchat I like the concrete-pictorial-abstract sequence. But the strips are labeled from the start.
8:15 pm
ColinTGraham:
So let's try another question: What problems do your students have with fractions? #mathchat
8:15 pm
POWERORGmath:
RT @ColinTGraham: Equivalency maybe confusing if symbolic notation is intro'd too early #mathchat
8:15 pm
POWERORGmath:
RT @ColinTGraham: Equivalency maybe confusing if we use terms like 'reduce' when values don't change #mathchat
8:16 pm
ColinTGraham:
For example: Students understand what fractions are, but cannot manipulate (4-rules +-x/)...) #mathchat
8:17 pm
MmeVeilleux:
@ColinTGraham #mathchat My primary stu confuse numerator & denominator & s.times get MAD if we use 6/2
8:17 pm
MmeVeilleux:
@ColinTGraham #mathchat My primary stu confuse numerator & denominator & s.times get MAD if we use 6/2 #mathchat
8:17 pm
mthman:
@MmeVeilleux The cul de sac is my canvas all year long. We buy large (80 piece) boxes of chalk 2-3 times per year. #mathchat
8:18 pm
Cassyt:
Why the emphasis on simplifying fractions? Don't we force students to focus on the wrong skill? #mathchat
8:19 pm
mthman:
@MmeVeilleux That's how he learned his alphabet, numbers, & shapes. Who says learning has to be boring?! #mathchat
8:19 pm
ColinTGraham:
@MmeVeilleux Is this because 6/2 is difficult to name or label... 21/9 twenty-one ninths seems ok, but not six halves? #mathchat
8:19 pm
MmeVeilleux:
@mthman #mathchat I should buy shares in sidewalk chalk too. I'd like to get up the nerve to post inspirational quotations in chalk!
8:20 pm
MmeVeilleux:
@ColinTGraham #mathchat Because they tell me the smaller number always has to go on top!
8:20 pm
jagkise:
@Cassyt #mathchat I think equivalency, not simplifying, is maybe the learning objective.
8:20 pm
ColinTGraham:
That is a question for the curriculum designers! Maybe for algebra...? RT @Cassyt: Why the emphasis on simplifying fractions? ... #mathchat
8:21 pm
ColinTGraham:
@MmeVeilleux Ah, so for your students their concept of "fraction" is "less than one", whereas yours is part to whole relationship #mathchat
8:22 pm
MmeVeilleux:
@ColinTGraham #mathchat Now that you say that, yes, that is exactly it.
8:22 pm
ColinTGraham:
@Cassyt I also think it is another way to 'test' if kids know their times tables... :( #mathchat
8:26 pm
POWERORGmath:
@ColinTGraham #mathchat The money examples always work & reinforce decimal rules too!
8:27 pm
mthman:
@MmeVeilleux Yes, only in our neighborhood the signs are for the REAL cars!! #mathchat
8:27 pm
POWERORGmath:
RT @ColinTGraham: Another 'trick' is that 1 pack is shared between three or four. There are often leftover sweets... for teacher! #mathchat
8:28 pm
ColinTGraham:
@POWERORGmath How many people see decimal numbers such as 1.50 as being 'mixed numbers': whole number+decimal fraction though? #mathchat
8:28 pm
POWERORGmath:
@ColinTGraham Food examples and items in class help students visualize the math #mathchat
8:28 pm
MmeVeilleux:
@mthman #mathchat LOL!! UR inspiring me. Next time, I think I will make crosswalks, bike lanes, etc I think it's time2get more elaborate!!
8:29 pm
jagkise:
@POWERORGmath #mathchat U of Mich Deborah Ball's NCSM talk Learning to do mathematics as a teacher. at http://tinyurl.com/2bq7n3o
8:29 pm
ColinTGraham:
@mthman What's your son's favourite fraction Ron? #mathchat
8:30 pm
POWERORGmath:
@jagkise #mathchat U of Mich Deborah Ball's NCSM talk Learning 2 do mathematics as a teacher. athttp://tinyurl.com/2bq7n3o <~Thx
8:30 pm
ColinTGraham:
@POWERORGmath Scaling recipes can work very well too, especially if you have cups and spoons as well as weights #mathchat
8:30 pm
MmeVeilleux:
@ColinTGraham #mathchat Mixed numbers has always confused me as have all the terms: natural #s, real #s. I can't remember which is which.
8:31 pm
mthman:
@MmeVeilleux How can you create the illusion of a speed bump w/sidewalk chalk? #mathchat
8:31 pm
jagkise:
@ColinTGraham #mathchat Yes but if "strip families" are in different colors numbers don't seem dstracting. For ex http://tinyurl.com/2v4zk2t
8:31 pm
POWERORGmath:
@jagkise #mathchat We need more practice with teaching fractions at the pre-service level!
8:31 pm
MmeVeilleux:
#mathchat Do you think it is acceptable for me to say numbers when I mean mixed numbers? eg. in name #s btw 1 & 2 Thoughts?
8:32 pm
ColinTGraham:
@MmeVeilleux Yes, terminology can be a big problem when all you students see is a number... 3/2 1.5 and 3:2 aren't seen as related #mathchat
8:32 pm
jagkise:
@POWERORGmath #mathchat I teach fractions to teachers any chance I get!
8:32 pm
MmeVeilleux:
@mthman Now that is going to require some shading. However, what about using pieces of leftover wood as mini-ramps? #mathchat
8:32 pm
mthman:
@ColinTGraham 1 1/2 - His and half of everyone else's...! #mathchat
8:32 pm
POWERORGmath:
@ColinTGraham #mathchat I do. Knowing place value, decimal names help with converting to fractions
8:34 pm
POWERORGmath:
RT @ColinTGraham: @POWERORGmath Scaling recipes can work very well too, especially if you have cups and spoons as well as weights #mathchat
8:34 pm
MmeVeilleux:
@ColinTGraham #mathchat So would you call 1.5 a mixed number? Shd I rephrase my prob to What mixed #s are btw 1&2?
8:34 pm
jagkise:
#mathchat For summary of student learning need differences see "Why are These Students 2 Years Behind" at http://tinyurl.com/3xbbb42
8:34 pm
MmeVeilleux:
#mathchat Most disastrous fractions lesson I did was in Gr5/6 & require Ss to make circles divided in 100 sections to represent %
8:35 pm
ColinTGraham:
@jagkise Similar concept to cuisenaire rods, or using Lego as I do! #mathchat
8:35 pm
MmeVeilleux:
#mathchat Eventually we all seemed to understand % but I'm sure there is an easier way, eg. sliding % into daily convo more often etc
8:36 pm
ColinTGraham:
@MmeVeilleux I think 'names' for things should only be introduced when the name has a clear function or purpose #mathchat
8:36 pm
MmeVeilleux:
@ColinTGraham #mathchat So do you use Cuisenaire rods a lot? I have tried but w/out much success.
8:37 pm
POWERORGmath:
@MmeVeilleux instead of having looking at fractions as how many pieces, you see full + partial packs #mathchat
8:37 pm
MmeVeilleux:
#mathchat Another essential concept in fractions seems to be: What is 1? b/c "1" can change from context2context
8:37 pm
ColinTGraham:
@MmeVeilleux Cuisenaire rods cannot really be 'introduced' but for reinforcing concepts, I find them useful. Lego seems easier! #mathchat
8:38 pm
mthman:
@MmeVeilleux If I could pull off the speed bump just once...maybe, just maybe...ya think? #mathchat
8:38 pm
MmeVeilleux:
@POWERORGmath #mathchat That is gd language: full & partial packs. I like that.
8:38 pm
ColinTGraham:
@POWERORGmath Yes and you can put three packs together and then do a sharing activity or use average pack size as the unit #mathchat
8:39 pm
MmeVeilleux:
@mthman #mathchat Go for it Michaelangelo!
8:40 pm
ColinTGraham:
@MmeVeilleux I used the idea of sharing out packs when we talked about Egyptian fractions, were there was a 'little bit' ignored #mathchat
8:40 pm
jagkise:
#mathchat We found that Singapore Model Drawing, combined with fraction strips, was huge in helping students understand mixed numbers
8:40 pm
POWERORGmath:
RT @jagkise: @POWERORGmath #mathchat I teach fractions to teachers any chance I get! «Awesome. We need many ways to C the math! :)
8:41 pm
ColinTGraham:
@jagkise Do you have an online reference for the Singapore model... for the archive! #mathchat
8:41 pm
MmeVeilleux:
@ColinTGraham #mathchat Q: To clarify, are we talking about packs as 1 full pack = 1 or 2/2? Q2: What R Egyptian fractions?
8:41 pm
POWERORGmath:
RT @jagkise: #mathchat student learning need differences see "Why are These Students 2 Years Behind" at http://tinyurl.com/3xbbb42
8:42 pm
mthman:
@MmeVeilleux Okay...this is going to take some planning! Any tips? #mathchat
8:43 pm
ColinTGraham:
Egyptians expressed fractions as sums of parts but numerator was always 1, except for 'special' fractions #mathchat
8:43 pm
MmeVeilleux:
#mathchat Has everyone here read the Teaching Gap by Stigler & Hiebert? Explains Y Ss are behind. It changed my math teaching.
8:43 pm
ColinTGraham:
@MmeVeilleux For example: 7/8 = 1/2 + 1/4 + 1/8 #mathchat
8:43 pm
POWERORGmath:
@MmeVeilleux #mathchat I don't emphasize proportion %. Can b confusing. But moving dec & chgng to dec equiv helps!
8:44 pm
ColinTGraham:
@POWERORGmath A big confusion with % is that increase by 200% = multiply by 3... EEK! #mathchat
8:44 pm
mthman:
@MmeVeilleux No, but I'll add it to my list! Thx. #mathchat
8:45 pm
POWERORGmath:
@MmeVeilleux #mathchat Partial & full lang is familiar; helps trans to formal terms; easy to connect 2 prior knowldge
8:45 pm
MmeVeilleux:
@ColinTGraham #mathchat The numerator was always 1??? Now that I visualize it, that makes sense! That is sooo awesome!!!
8:45 pm
POWERORGmath:
RT @ColinTGraham: @POWERORGmath Yes & U cn put 3 packs tgthr & then do a sharing activity or use average pak size as the unit #mathchat
8:46 pm
MmeVeilleux:
@ColinTGraham The Egyptian math fractions made my day. #mathchat
8:47 pm
ColinTGraham:
Personally, I think early fractional notation was developed by/for engineers, dividing things until 'error' was negligible... #mathchat
8:47 pm
POWERORGmath:
@jagkise #mathchat Haven't used Singamore math but models always make 4 meaningful connections. Esp when studs draw model
8:48 pm
MmeVeilleux:
@ColinTGraham #mathchat I had also not thought about 200%increase as X3. I had never thought about that B4.
8:48 pm
POWERORGmath:
@ColinTGraham #mathchat See www.greatsource.com for Singapore Math info
8:48 pm
Cassyt:
Crikey! 1 phone call and suddenly I can't keep up! #mathchat
8:49 pm
jagkise:
@POWERORGmath #mathchat Singapore model drawing a powerful heuristic through algebra. "Why wasn't I taught this" is common reaction
8:49 pm
MmeVeilleux:
@Cassyt #mathchat LOL!!
8:49 pm
ColinTGraham:
I have also used tangrams and origami for fractions. Origami can be very useful for geometric 'proof', too. #mathchat
8:50 pm
jagkise:
RT @ColinTGraham: I have also used tangrams and origami for fractions. Origami can be very useful for geometric 'proof', too. #mathchat
8:50 pm
Cassyt:
I train teachers on Singapore Math - model drawing can be powerful. @POWERORGmath: #mathchat
8:50 pm
POWERORGmath:
@MmeVeilleux #mathchat full pkg=3/3 All parts present out of total original in pkg to make 1 whole.
8:50 pm
ColinTGraham:
@Cassyt Don't worry, the archive will go online after about 30 minutes and the discussion often continues through the week! #mathchat
8:51 pm
POWERORGmath:
RT @ColinTGraham: Egyptians expressed fractions as sums of parts but numerator was always 1, except for 'special' fractions #mathchat
8:51 pm
MmeVeilleux:
#mathchat I'm making my own archive by favoriting thgs I really want2 remember.
8:52 pm
Cassyt:
That's my favorite moment in a training! @jagkise: @POWERORGmath #mathchat Singapore model drawing-Teachers ask"Why wasn't I taught this?"
8:53 pm
Cassyt:
Great idea - I'll need to check out the archive this time. RT @MmeVeilleux: #mathchat I'm favoriting thgs I really want2 remember.
8:53 pm
jagkise:
@Cassyt #mathchat do you have the Singapore Min of Ed's most recent book on model drawing? Algebra great http://tinyurl.com/jmbmf
8:53 pm
MmeVeilleux:
#mathchat I understand Xfractions. Eg: I need 2/5 of 3/4 or sthg (licorice - a personal fave) but I don't get dividing fractions.
8:54 pm
POWERORGmath:
@MmeVeilleux Haven't read that. Thanks for sharing. #mathchat
8:54 pm
MmeVeilleux:
#mathchat I may be beyond help for dividing fractions as I've asking this Q many X in the last decade. It could be me hitting the wall.
8:54 pm
Cassyt:
@jagkise I've got every book, from the Ministry's to Ban Har Yeap's. #mathchat
8:55 pm
MmeVeilleux:
@jagkise Must get my hands on some Singapore Math bks. Have heard about them but have not seen them. #mathchat
8:55 pm
jagkise:
@MmeVeilleux #mathchat Read Ma's "Knowing and Teaching Mathematics" to see needs in division of fractions.
8:56 pm
ColinTGraham:
@MmeVeilleux I demo the dividing of fractions buy having say 20 lego bricks, which I give to 2 groups of 2 (8 +12) then they share #mathchat
8:57 pm
MmeVeilleux:
@jagkise #mathchat Thx. Is Ma the author? Also is it an article or bk? TY so much. I certainly will look it up.
8:57 pm
ColinTGraham:
@MmeVeilleux so one group has 12/20, another has 8/20 which they divide into two parts, not necessarily 1/2 each though #mathchat
8:57 pm
ColinTGraham:
Did I say buy and not by...? Money on the mind! #mathchat
8:59 pm
POWERORGmath:
@jagkise #mathchat So sad the number of teacher prep institutions that only show limited ways of solving problems. Failing kids/teachers
8:59 pm
ColinTGraham:
In the last couple of minutes... any 'burning' questions or thoughts about fractions? #mathchat
8:59 pm
jagkise:
@MmeVeilleux #mathchat A book. Ma is author http://tinyurl.com/29f9ubu Scholarly but important
8:59 pm
Cassyt:
Read Ma and Wu. RT @jagkise @MmeVeilleux #mathchat Read Ma's "Knowing and Teaching Mathematics"
8:59 pm
MmeVeilleux:
@ColinTGraham #mathchat I'm flabbergasted. That makes sense! I have been on this quest for a decade. I need a moment!!! sharing lego...
8:59 pm
POWERORGmath:
RT @Cassyt: I train teachers on Singapore Math - model drawing can be powerful. @POWERORGmath: #mathchat <Awesome.
9:00 pm
jagkise:
@POWERORGmath #mathchat We first need to adapt the truth that everyone can learn math. Too many teachers math phobic
9:00 pm
ColinTGraham:
@MmeVeilleux @tcash uses an eggbox and a piece of string to divide holes... #mathchat
9:01 pm
ColinTGraham:
Another topic! RT @jagkise: @POWERORGmath We 1st need to adapt the truth that everyone can learn math. Too many teachers phobic #mathchat
9:01 pm
POWERORGmath:
@Cassyt #mathchat Yes. That's a gr8 intro to open their minds! "Why wasn't I taught this?"
9:01 pm
MmeVeilleux:
@jagkise #mathchat TY for the link. I will get my hands on it. Scholarly is good!
9:02 pm
jagkise:
@ColinTGraham #mathchat Start with Gladwell's great chapter in Outliers on cultural attitudes toward math. Powerful with teachers.
9:02 pm
ColinTGraham:
OK thanks everyone for another stimulating chat! Follow @mathchat for updates. And don't forget to vote for the next topic! #mathchat
9:03 pm
iDianne2:
RT @ColinTGraham: Another topic! RT @jagkise: @POWERORGmath We 1st need to adapt the truth that everyone can learn math. Too many teachers phobic #mathchat
9:03 pm
MmeVeilleux:
@ColinTGraham #mathchat I like the eggbox & string idea too. So the string cuts each box in half by threading thru lengthwise?
9:04 pm
MmeVeilleux:
#mathchat TY for a gr8 conversation. I don't know if others lrned but I am good at asking questions & I lrned a lot. TY for yr insights!!!!
9:04 pm
ColinTGraham:
@MmeVeilleux Yes and you can use it width-wise too to give 1/4 holes... #mathchat
9:05 pm
ColinTGraham:
Vote for the next topic here: http://mathschat.wikispaces.com/Current+Poll Catch you all next time! #mathchat
9:05 pm
MmeVeilleux:
@ColinTGraham #mathchat Gr8. Just wanting to confirm that I understood correctly.
9:07 pm
POWERORGmath:
@MmeVeilleux #mathchat Multiple by recip of 2nd frac. "Keep 1st frac, Change Oper to mult, Flip 2nd frac"
9:10 pm
jagkise:
#mathchat Thanks everyone for new ideas. Fractions are so key to algebra that we really can't overdo chatting about the topic!!