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! guided tour
001 Differentiation
002 'Real' maths
003 Fractions
004 Manipulatives
005 Assessment
006 What technology?
007 Adult curriculum
008 Reflective Learners
009 Engagement
010 Class Time Use
011 Why I hate maths
012 Terminology
013 'Mathphobia'
014 The Nature of Maths
015 Show and Tell
016 Vertical Integration
017 Product to Process
018 Investigation Length
019 Preparation for Work
020 Success in Mathematics
021 Groupwork
022 Effective lessons
023 Impact of ICT
024 Mathematics Websites
028 Why under 16?
2010.07.15 Differentiation
2010.07.19 Differentiation (2)
2010.07.22 'Real' maths
2010.07.26 'Real' maths (2)
2010.07.29 Fractions
2010.08.02 Fractions (2)
2010.08.05 Manipulatives
2010.08.09 Manipulatives (2)
2010.08.12 Assessment
2010.08.16 Assessment (2)
2010.08.19 What tech?
2010.08.23 What tech? (2)
2010.08.26 Adult maths
2010.08.30 Adult maths (2)
2010.09.02 Reflective learner
2010.09.06 Reflective learner 2
2010.09.09 Engagement
2010.09.13 Engagement 2
2010.09.16 Class Time Use
2010.09.20 Class Time Use 2
2010.09.23 Why I hate maths
2010.09.27 Why I hate math 2
2010.09.30 Terminology
2010.10.04 Terminology 2
2010.10.07 'Mathphobia'
2010.10.11 'Mathphobia' (2)
2010.10.14 Nature of Maths
2010.10.18 Nature of Maths (2)
2010.10.21 Show and Tell
2010.10.25 Show and Tell (2)
2010.10.28 Vertical Integration
2010.11.01 Vertical Integratn 2
2010.11.04 Product to Process
2010.11.08 Product to Proc. 2
2010.11.11 Investigation length
2010.11.15 Investigation leng 2
2010.11.18 Prepn for work
2010.11.22 Prepn for work 2
2010.11.25 Success in Maths
2010.12.03 Groupwork
2010.12.06 Groupwork 2
2010.12.10 Effective lessons
2010.12.13 Effective Lesson 2
2010.12.17 Impact of ICT
2010.12.20 Impact of ICT 2
2010.12.24 Maths Websites
2011.01.03 Maths Website 2
2011.01.07 Ideal curriculum
2011.01.10 Ideal curriculum 2
2011.01.14 Short or longterm
2011.01.17 Short or longterm2
2011.01.21 Continuing PD
2011.01.24 Continuing PD 2
2011.01.28 Why under 16?
2011.01.31 Why under 16? (2)
2011.02.04 Which is more fun?
2011.02.11 Blended learning
2011.02.14 Blended learning 2
2011.02.18 Fast tracking
2011.02.21 Fast tracking (2)
2011.02.25 Misconceptions
2011.02.28 Misconceptions 2
2011.03.04 Good Reads
2011.03.07 Good Reads (2)
2011.03.11 How do I  fractions
2011.03.18 How do I  lang
2011.03.21 How do I  lang (2)
2011.03.25 How do I  curric
2011.03.28 How do I  curric 2
2011.04.01 How?  next topic
2011.04.04 How?  nxt topic 2
2011.04.08 How?  Geometry
2011.04.11 How?  Geom 2
2011.04.15 How?Investigation
2011.04.18 How?Investigatn 2
2011.04.22 How? Do vs. learn
2011.04.25 How?Do vs learn 2
2011.04.29 How?Dig deeper
2011.05.02 How?Dig deeper 2
2011.05.06 'Big Ideas'
2011.05.09 'Big Ideas' (2)
2011.05.13 High school skill
2011.05.16 High school skill 2
2011.05.20 Journals
2011.05.23 Journals (2)
2011.05.27 Studentdriven
2011.05.30 Studentdriven (2)
2011.06.03 How?  Maths play
2011.06.06 How?Maths play 2
2011.06.10 Deeper thinking
2011.06.13 Deeper thinking (2)
2011.06.17 How?  Disjointed
2011.06.17 How?  Disjointed 2
2011.06.24 How?  Problems
2011.06.27 How?  Problems 2
2011.07.01 Holiday maths
2011.10.28 Extent of plans
2011.10.31 Extent of plans (2)
2011.11.04 Authentic is..?
2011.11.07 Authentic is..? (2)
Z_1 Thursday raw
Z_2 Monday raw
Z_consolidated
2010.08.05 Manipulatives
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Topic:
What are 'brilliant' activities with manipulatives?
As it happened on
Thursday, 5th August 23:30  00:30 GMT
11:31 pm
ColinTGraham
:
Hello everyone, welcome to this week's chat! #
mathchat
11:32 pm
ColinTGraham
:
If it is your first time, I recommend TweetGrid for #
mathchat
http://bit.ly/ca6WA4
11:33 pm
ColinTGraham
:
Don't worry about trying to follow everything if it moves too fast, you can check the archive later. #
mathchat
11:34 pm
ColinTGraham
:
Tonight's topic: "What are 'brilliant' activities with manipulatives?" Online or physical... #
mathchat
11:34 pm
ColinTGraham
:
Who wants to start us off? #
mathchat
11:35 pm
mthman
:
How do YOU define manipulatives? #
mathchat
11:35 pm
cybraryman1
:
When my site & Twitter get back up & running better: Math Manipulative cached page:
http://bit.ly/aWv4rD
#
mathchat
11:35 pm
ccampbel14
:
What percentages of teachers do you think use manipulatives regularlyl in class? #
mathchat
11:35 pm
ghewgley
:
I'm curious to see what others are doing! I'm a Smartboard user, plus I like to use real life manipulatives as well. #
mathchat
11:35 pm
MariaDroujkova
:
@
oxtralite
's National Library of Virtual Manipulatives rocks! #
mathchat
11:36 pm
ColinTGraham
:
http://nlvm.usu.edu/en/nav/vlibrary.html
#
mathchat
11:36 pm
ccampbel14
:
I think manipulatives are any tools that you can use to help think mathematically. Professionally created, homemade, etc. #
mathchat
11:36 pm
mthman
:
Do you count computerbased applets as manipulatives (virtual manipulatives)? #
mathchat
11:36 pm
MariaDroujkova
:
@
mthman
I define "manipulative" as a pedagogical tool for learning through spatial manipulation (possibly virtual) #
mathchat
11:37 pm
ColinTGraham
:
Sometimes people use the term 'maths' lab for something that provides students a chance to 'play' with something. #
mathchat
11:37 pm
ccampbel14
:
I think applets link the concrete manipulatives to the symbolic. But they could be if they are interactive. #
mathchat
11:37 pm
mthman
:
Here is a great resource for virtual manipulatives
http://www.shodor.org/interactivate/
#
mathchat
11:38 pm
ccampbel14
:
Do you think that a pencil is a manipulative? #
mathchat
11:38 pm
ColinTGraham
:
I think anything which requires the student to do something to something else and observe the effect is a manipulative #
mathchat
11:39 pm
ghewgley
:
I like the transparency mode in Smartboard 10.6. It lets a student measure/draw anything that shows up on the Smartboard. #
mathchat
11:39 pm
ccampbel14
:
I think that virtual manipulatives are manipulatives if students are using the site, not watching the teacher do it. #
mathchat
11:40 pm
mthman
:
@
ccampbel14
My point exactly...pencil? dice? protractor? unit cubes? #
mathchat
11:40 pm
ColinTGraham
:
RT @
MariaDroujkova
: I define "manipulative" as a pedagogical tool for learning through spatial manipulation (possibly virtual) #
mathchat
11:40 pm
ghewgley
:
A pencil can be a manipulative. #
mathchat
11:40 pm
ccampbel14
:
Watching someone use manips is like watching a cooking show and then being asked to make the recipe! #
mathchat
11:41 pm
ColinTGraham
:
@
ghewgley
Does this mean you think rulers, protractors etc. are manipulatives? #
mathchat
11:41 pm
mthman
:
BINGO! RT @
ccampbel14
: I think virtual MANIPULATIVES if students are using the site, not watching the teacher do it. #
mathchat
11:41 pm
ghewgley
:
Fraction bars, scales, measuring tapes, etc are all useful. #
mathchat
11:42 pm
ccampbel14
:
In the past the only the 'slower' students used manips. Has this changed? The perception changed? #
mathchat
11:42 pm
mthman
:
@
ghewgley
Exactly...can you use a pencil to measure, a straighedge, spinner? #
mathchat
11:42 pm
ColinTGraham
:
Do we all agree that a manipulative is something which gives students a handson view of mathematics? #
mathchat
11:42 pm
ccampbel14
:
I think all students should experience manips but quite often the top kids fight it. What do you do? #
mathchat
11:42 pm
ghewgley
:
If you use something, you are manipulating it. So if you measure with a ruler, it is a manipulative. It can be virtual as well. #
mathchat
11:42 pm
MariaDroujkova
:
@
ccampbel14
A pencil as a writing tool is not a manipulative by my definition. But if you build out of pencils, then yes! #
mathchat
11:43 pm
Saskateach
:
I hope so RT @
ccampbel14
: In the past the only the 'slower' students used manips. Has this changed? The perception changed? #
mathchat
11:43 pm
ColinTGraham
:
RT @
ColinTGraham
: Do we all agree that a manipulative is something which gives students a handson view of mathematics? #
mathchat
11:44 pm
mthman
:
@
Saskateach
It has in my room! I try to build every lesson around something concrete or a simulation. #
mathchat
11:44 pm
ghewgley
:
I think the brightest students use manipulatives the most. #
mathchat
11:44 pm
MariaDroujkova
:
@
ghewgley
Measuring is spatial, so measurement activities have to do with manipulatives for me... #
mathchat
11:45 pm
Saskateach
:
I think manips enhance students abilities to visualize prob/ solutions as well as understanding of math concepts. #
mathchat
11:45 pm
ColinTGraham
:
RT @
ccampbel14
: I think all students should experience manips but quite often the top kids fight it. What do you do? #
mathchat
11:45 pm
ccampbel14
:
@
ghewgley
Really? I find that most top students say the don't need to use materials, they can do it in their head. #
mathchat
11:45 pm
mthman
:
The scaffolding is more natural too! RT @
ghewgley
: I think the brightest students use manipulatives the most. #
mathchat
11:46 pm
padgets
:
#
mathchat
it has been 2 weeks since you kindly offered to help me get better at math, doing the tutorials on web, am getting better :0
11:46 pm
MariaDroujkova
:
@
ccampbel14
It depends on activity  it's hard to formulate a new topology theorem or build a math sculpture "in your head" #
mathchat
11:46 pm
mthman
:
@
ccampbel14
I agree, but they also fight writing about it, sharing, showing work, etc...need to model oral problem solving w/them! #
mathchat
11:47 pm
ccampbel14
:
@
MariaDroujkova
I agree that manips are not just for the weaker kids. Haven't heard the terms human math & ethnomath often. #
mathchat
11:47 pm
mthman
:
Yay! RT @
padgets
: has been 2 weeks since you kindly offered 2help me get better at math, the tutorials, am getting better :0 #
mathchat
11:48 pm
ccampbel14
:
@
mthman
You are SO right. They fight really having to think about mathematics. They are quite happy getting an answer. #
mathchat
11:48 pm
mathheadinc
:
@
MariaDroujkova
Math 2.0 was great last night! #
mathchat
11:48 pm
ColinTGraham
:
Great! So, who should manips be aimed at/used with? RT @
padgets
: ... doing the tutorials on web, am getting better :0 #
mathchat
11:49 pm
ghewgley
:
I'm not saying the weakest kids do not benefit from manips, I'm just saying they are worse at using them in the beginning. #
mathchat
11:49 pm
mathheadinc
:
@
ccampbel14
: @
mthman
I let my students find out the hard way that not writing discoveries slows learning. #
mathchat
11:49 pm
mthman
:
@
ccampbel14
Heard this somewhere...GIVE them the solution...make them show a correct procedure! Make them find the error & explain #
mathchat
11:50 pm
mathheadinc
:
@
ColinTGraham
Manips should be aimed at every student. Why not? #
mathchat
11:50 pm
mthman
:
@
ghewgley
Weak kids need good modeling...need to be explicitly taught to think through a situation! #
mathchat
11:50 pm
ccampbel14
:
@
mthman
I was just going to say that. It was in the past couple of weeks on Twitter. It was like a lightbulb going on for me. Wow! #
mathchat
11:50 pm
ColinTGraham
:
Me and @
coachGinsburg
! RT @
mthman
: GIVE them the solution...make them show a correct procedure! Make them find the error & explain #
mathchat
11:50 pm
padgets
:
#
mathchat
in my guided study the kids who can see the answer as well as write the answer do much better
11:50 pm
MariaDroujkova
:
@
mathheadinc
Math 2.0 was great in large part because you were there :) Come again. Alan Kay hosts this Saturday #
mathchat
11:51 pm
ColinTGraham
:
What manips would be meaningful for higherlevel students? #
mathchat
11:51 pm
mthman
:
@
ColinTGraham
@
coachGinsburg
! I knew there was a reason I like you! #
mathchat
11:51 pm
ghewgley
:
Manips should be targeted at those who are currently unable to grasp a concept. It should be used by all  in the beginning. #
mathchat
11:51 pm
jrsteach
:
@
ghewgley
manips are impt going from concrete to abstract #
mathchat
11:52 pm
mathheadinc
:
@
mthman
Have weak ones start with a simple idea, tell them to figure out a way, then build on that. #
mathchat
11:52 pm
Saskateach
:
I agree with every student until they are comfortable enough to do it without. They are a tool to aid/enhance understanding. #
mathchat
11:52 pm
ccampbel14
:
I think we have 2 support teachers on how 2 integrate manips. It isn't just giving kids the tools & letting them go! #
mathchat
11:52 pm
mathheadinc
:
@
MariaDroujkova
Thank you! I'm already thinking about the next one! :DDD #
mathchat
11:52 pm
ghewgley
:
@
mthman
Exactly. They can't picture the process  hence the manipulatives. #
mathchat
11:52 pm
MariaDroujkova
:
@
ghewgley
Weak students have most trouble connecting different representations of math, including manipulatives #
mathchat
11:53 pm
mthman
:
@
mathheadinc
Yes! Help them see learn how to learn, accept success, and grow from there! #
mathchat
11:53 pm
ColinTGraham
:
Anyone use fingers? (beyond counting of course!) #
mathchat
11:53 pm
ccampbel14
:
I have seen some teachers try using manips & it is a freeforall b/c the teacher thinks they can't help or guide. #
mathchat
11:53 pm
mathheadinc
:
@
ccampbel14
Don't you think teachers should be taught that for their degrees? #
mathchat
11:53 pm
ghewgley
:
@
jrsteach
Absolutely, especially for those who are in between and need the bridge between concrete and abstract. #
mathchat
11:54 pm
ColinTGraham
:
@
ccampbel14
What activities do you think need special attention if manips are introduced? #
mathchat
11:54 pm
padgets
:
#
mathchat
Iany visible way to demostrate a math concept helps, whether it is a paper square or a fancy flash tutorial on the web all good
11:54 pm
mthman
:
Name a topic and a favorite simulation that helps develop their skills in that area... #
mathchat
11:54 pm
MariaDroujkova
:
Finger multiplication, finger binary, counting on fingers to 10^8... Love finger math! #
mathchat
11:55 pm
ghewgley
:
@
MariaDroujkova
That's where modeling, modeling, modeling comes in  with lots of explanations and thinking outloud. #
mathchat
11:55 pm
Saskateach
:
We need to model and have students model efficient use of manips. They are math tools not free for all toys. #
mathchat
11:55 pm
ColinTGraham
:
Which teachers? Maths/Primary/All? RT @
mathheadinc
: @
ccampbel14
Don't you think teachers should be taught that for their degrees? #
mathchat
11:55 pm
ccampbel14
:
@
mathheadinc
Absolutely! I had very little experience with manips in university. We need lots of practicehow 2 set ground rules.. #
mathchat
11:55 pm
MariaDroujkova
:
@
ccampbel14
You need some "free play" time with manipulatives, but then modeling and sharing should happen within the group #
mathchat
11:56 pm
padgets
:
@
MariaDroujkova
#
mathchat
where can I learn how to do finger math?
11:56 pm
MariaDroujkova
:
@
ghewgley
"Thinking out loud" is so valuable in general :) #
mathchat
11:57 pm
mthman
:
I've become a big fan of smaller learning "centers" in class...small group sharing instead of whole class sharing... #
mathchat
11:57 pm
ccampbel14
:
Marilyn Burns has a great list of 7 "musts" to use manips effectively. Discuss why u use them, routine to hand out & collect, etc. #
mathchat
11:57 pm
TheHomeworkDog
:
RT @
cybraryman1
: When my site & Twitter get back up & running better: Math Manipulative cached page:
http://bit.ly/aWv4rD
#
mathchat
11:57 pm
ColinTGraham
:
Is there a perception that Lego/blocks/counters/cuisenaire rods etc. are toys and that they are not 'real maths'? #
mathchat
11:57 pm
mthman
:
@
MariaDroujkova
@
padgets
Would love to learn the rules for multiplication w/fingers! #
mathchat
11:58 pm
ghewgley
:
@
MariaDroujkova
You're right. It's hard to guess what someone is thinking. In math people give up when they can't follow you. #
mathchat
11:58 pm
mathheadinc
:
@
ColinTGraham
All! I've tutor math ed students, much of what they must learn for math is useless. #
mathchat
11:58 pm
TheHomeworkDog
:
RT @
mthman
: Here is a great resource for virtual manipulatives
http://bit.ly/a9Fy89
#
mathchat
11:58 pm
mthman
:
@
ColinTGraham
I hope not...I think that is why www.legoengineering.com is growing... #
mathchat
11:58 pm
padgets
:
@
MariaDroujkova
#
mathchat
thanks for letting me know!!!! :0)
11:58 pm
mathheadinc
:
@
ColinTGraham
I think they need to learn how to make complicated math simple enough for young people to understand, as Don does. #
mathchat
11:59 pm
ccampbel14
:
@
ColinTGraham
Yes, many kids think they r toys. I let them play the 1st day & say they r play toys. Next day they are thinker toys #
mathchat
11:59 pm
mathheadinc
:
@
ccampbel14
Excatly. Just ask a kid to make patterns with things and find the math in it. Exciting things will happen. #
mathchat
12:00 am
ccampbel14
:
I explain that engineers use tools to pass their exams so the manips are the tools we use to help think about math & do math #
mathchat
12:00 am
mathchat
:
Seting up Math lab
http://bit.ly/d5z0k8
#
mathchat
12:00 am
ccampbel14
:
@
ColinTGraham
I took a short course on Chisanbop math. Is that what you are talking about? #
mathchat
12:00 am
mthman
:
Sweet! RT @
ColinTGraham
Wrote a paper on finger multiplication when I was doing my training! I can dig it out for you! #
mathchat
12:00 am
mathchat
:
Math Manipulative Acitivities:
http://bit.ly/a6sZKP
#
mathchat
12:01 am
ghewgley
:
@
ccampbel14
Tying manips to the real world helps my students a lot. #
mathchat
12:01 am
ColinTGraham
:
@
ccampbel14
Basically times tables up to five (and beyond) using modular arithmetic... #
mathchat
12:01 am
mathheadinc
:
@
ccampbel14
@
TheMathman
does the same things and he teaches calculus to young people. It works extremely well. #
mathchat
12:01 am
mthman
:
Anyone use this site before?
http://www.cuttheknot.org/games.shtml
#
mathchat
12:02 am
ColinTGraham
:
@
mathchat
is tweeting out some links you can check out later! #
mathchat
12:02 am
Saskateach
:
I've always found that the secret to change manips from toys to tools was to change my language w/ students. #
mathchat
12:02 am
mathchat
:
Improving teaching by using manips:
http://bit.ly/cEXobB
#
mathchat
12:03 am
ccampbel14
:
Or do you not asses the use of manips? Let them use what they need and assess the process & result? #
mathchat
12:03 am
mathheadinc
:
@
ccampbel14
What if they write a report on what patterns they found? #
mathchat
12:03 am
ColinTGraham
:
@
ccampbel14
How does concretely apply to abstract concepts? What areas of the curriculum are difficult to assess this way? #
mathchat
12:03 am
MariaDroujkova
:
Finger multiplication 610
http://www.youtube.com/watch?v=_eFnzNw10Qc
#
mathchat
12:04 am
ccampbel14
:
Is there a difference between a student who shows how they do something with manips versus paper & pencil? #
mathchat
12:04 am
jrsteach
:
@
Saskateach
I talk about the diff between tools & toys and manps we call math tools in my kdg room #
mathchat
12:04 am
mathchat
:
Learning Mathematics with virtual manipulatives:
http://bit.ly/1gcyd1
#
mathchat
12:04 am
mathheadinc
:
@
ccampbel14
I only remember using manips in kindergarten. Would have been useful throughout school. #
mathchat
12:05 am
MariaDroujkova
:
Binary system counting on fingers
http://www.youtube.com/watch?v=yLBCL0qW908
#
mathchat
12:05 am
Saskateach
:
Can we assess efficient use? RT @
ccampbel14
:Or do u not asses use of manips? Let them use what they need & assess process & result?#
mathchat
12:05 am
bosoxfan9819
:
RT @
ghewgley
: Playing with manips is actually learning. Nothing wrong with playing  up to a point... #
mathchat
12:06 am
ccampbel14
:
@
ColinTGraham
Most of my curriculum includes concrete but it isn't always possible. Will have to think about this. #
mathchat
12:06 am
msseessm
:
RT @
MariaDroujkova
: Finger multiplication 610
http://www.youtube.com/watch?v=_eFnzNw10Qc
#
mathchat
12:06 am
ColinTGraham
:
In case anyone is unfamiliar with the term chisanbop is a South Korean finger math for doing abacuslike arithmetic! #
mathchat
12:06 am
mthman
:
@
Saskateach
Best way to assess is through f2f interaction/observation.... #
mathchat
12:06 am
mathheadinc
:
@
ccampbel14
Yeahm that! #
mathchat
12:06 am
jrsteach
:
@
ccampbel14
it would be neat to read the research findings on manips to paper/pencil & standardized tests #
mathchat
12:06 am
ccampbel14
:
@
Saskateach
Perhaps we can't assess efficient use but correct use? #
mathchat
12:07 am
grade1
:
@
ccampbel14
No, that's why I always have a camera ready. Explaining thinking & showing with manipulatives can be captured easily. #
mathchat
12:07 am
ghewgley
:
@
ccampbel14
"How do you assess the use of manips?" Answer (maybe) is: Are they getting the concepts down? #
mathchat
12:07 am
ColinTGraham
:
@
ccampbel14
Last night's Math 2.0 on calculus provided many fine examples of concrete being applied or extensible to the abstract #
mathchat
12:07 am
ccampbel14
:
Do you all assess the use of manips? Is it a requirement for your curriculum? #
mathchat
12:08 am
mthman
:
@
Saskateach
You could also pose problems that show the manipulatives and ask students to translate it #
mathchat
12:08 am
mathheadinc
:
@
ccampbel14
I tell them they are mathematical scientists and they must write all their results! They like that. #
mathchat
12:08 am
ColinTGraham
:
Mathematical tools such as rulers and protractors need to be assessed, but do others manips? #
mathchat
12:08 am
MariaDroujkova
:
Manipulatives can be used for construction tasks, art, and problemsolving. All can be assessed with rubrics #
mathchat
12:09 am
Saskateach
:
@
jrsteach
called them tools in my K3 classrms too. They understand tools 4 construction these r tools to construct understanding #
mathchat
12:09 am
grade1
:
@
ghewgley
That's why I always have a camera ready. Let them explain thinking (video) & take pictures. #
mathchat
12:09 am
ccampbel14
:
@
mathheadinc
Mathematical scientists  great! I have used the term math private investigators  Math P.I.s #
mathchat
12:09 am
mthman
:
@
ccampbel14
Not a requirement...I tell students manipulatives are crutches until you've taught yourself to think abstractly. #
mathchat
12:09 am
mathheadinc
:
@
ccampbel14
Manips are a means to an end: helping kids visualize and understand math patterns. #
mathchat
12:10 am
ccampbel14
:
@
mthman
Do you think there are some people that can't move to the abstract & must always rely on manips? #
mathchat
12:10 am
MariaDroujkova
:
In Soviet Union all assessments were either essays (for problemsolving) or oral exams (for theory) #
mathchat
12:10 am
mathheadinc
:
@
ccampbel14
Oh, Math P.I., I like that very much. Solving mysteries is a very sticky method. Must borrow htat :D #
mathchat
12:10 am
mthman
:
@
ccampbel14
Absolutely...and that is okay so long as they don't give up or give in to a negative stigma... #
mathchat
12:11 am
ColinTGraham
:
I have had insights about other things while 'playing', doing origami for example... manips don't have to be tied in directly #
mathchat
12:11 am
Saskateach
:
@
ccampbel14
but one can be correct and not efficient. If they are using manips in a way that is inefficient wld u model a diff way?#
mathchat
12:11 am
ccampbel14
:
@
MariaDroujkova
Essays or oral exams, wow! Did all students learn how to perform well for these tests? #
mathchat
12:11 am
MariaDroujkova
:
@
ccampbel14
People who can't move to the abstract would not be able to acquire speech, since it's metaphorbased #
mathchat
12:11 am
Saskateach
:
Good idea RT @
mthman
: @
Saskateach
You could also pose problems that show the manipulatives and ask students to translate it #
mathchat
12:12 am
ghewgley
:
@
MariaDroujkova
I've learned to use whatever it takes to get the students to learn. Learning is the goal, not the process. #
mathchat
12:12 am
ccampbel14
:
@
Saskateach
I would ask all students to share their methods & hopefully they would see another way that would be more efficient. #
mathchat
12:12 am
ColinTGraham
:
I think it is possible for many to grasp a mathematical concept but not to verbalize or explain it. Manips can help show understdg #
mathchat
12:12 am
padgets
:
#
mathchat
@
ccampbel14
that was one thing for me I have problems with spatial relations, so abstract was one of my worst subjects
12:13 am
mthman
:
@
Saskateach
That is one way I teach twostep & multistep equations... #
mathchat
12:13 am
ccampbel14
:
@
MariaDroujkova
Never heard that before about speech. Then why is it so hard for some people to move to the abstract in math? #
mathchat
12:13 am
ccampbel14
:
Can anyone think of how to use manips with order of operations? #
mathchat
12:14 am
ColinTGraham
:
The blog post @
mthman
mentioned earlier about showing working:
http://bit.ly/b1e3PK
#
mathchat
12:14 am
mthman
:
@
MariaDroujkova
@
ccampbel14
You are so right! They must acquire the language first...make them use the terminology. #
mathchat
12:14 am
ghewgley
:
Speech and abstract thinking use different parts of the brain. #
mathchat
12:14 am
mathheadinc
:
@
ccampbel14
Yes, need more than 140. #
mathchat
12:14 am
ccampbel14
:
I find that the use of manips is quite natural in younger grades and becomes more challenging through junior high & high school. #
mathchat
12:14 am
mthman
:
@
ccampbel14
Have you tried developing a flowchart for order of ops (OOO)? #
mathchat
12:15 am
ColinTGraham
:
Using language, for me, must come after a demonstration of understanding/application, otherwise it is meaningless #
mathchat
12:15 am
mthman
:
RT @
ColinTGraham
: The blog post @
mthman
mentioned earlier about showing working:
http://bit.ly/b1e3PK
#
mathchat
12:15 am
Saskateach
:
Agree RT @
ColinTGraham
: I think it's possible 4 many 2 grasp math concept but not verbalize/explain it. Manips can show understdg #
mathchat
12:15 am
ccampbel14
:
I guess I have used a flowchart for OOO. Is that a manipulative? Or could we make a simple machine to represent it? #
mathchat
12:16 am
ghewgley
:
Manipulatives change as you get older, but necessarily the use of manipulatives  just different toys! #
mathchat
12:16 am
mathheadinc
:
@
ColinTGraham
Don and I tell kids to explain the best way they can. We help them find the words. #
mathchat
12:16 am
mthman
:
@
ccampbel14
Good question...that's why I asked about a definition. I think a flowchart (virtual, paper, or simple machine) is! #
mathchat
12:16 am
ccampbel14
:
Quite often, if a student can't explain their thinking, I ask them what they 'did' & they can show me & it seems much easier. #
mathchat
12:17 am
ColinTGraham
:
@
ccampbel14
Lego or cuisenaire rods to show additive/commutative/distributive. #
mathchat
12:17 am
ccampbel14
:
RT @
ColinTGraham
: Think it's possible 4 many 2 grasp math concept but not verbal/explain it. Manips can show understdg #
mathchat
12:18 am
ColinTGraham
:
Yes, kids like to know the 'big' words! RT @
mathheadinc
: Don & I tell kids to explain the best way they can. We help find words. #
mathchat
12:19 am
ColinTGraham
:
@
ccampbel14
I always had a stack of origami paper (squares), Lego big red bucket and at least 3 boxes of cuisenaire rods... #
mathchat
12:19 am
jrsteach
:
@
mthman
math language is like a foreign language to kids #
mathchat
12:20 am
Saskateach
:
@
ccampbel14
Manip lists per grade wld depend on grade students and teacher #
mathchat
. We have lists in our curric as a guide.
12:20 am
ghewgley
:
The important part of all this is scaffolding and modeling. #
mathchat
12:20 am
ColinTGraham
:
@
mathheadinc
Yes, for example once kids spot 3x5 = 5x3 you can label it... #
mathchat
12:21 am
mathheadinc
:
@
joelsopp
When you can't show how you did it then you must have been cheating. #
mathchat
12:21 am
mthman
:
@
jrsteach
True...but if you learn to adapt it to their language...instead of cancelling, we used "Angela's Rule" last year! #
mathchat
12:21 am
ghewgley
:
@
jrsteach
Math is a language. 2 + 2 = 4 is a sentence. Numbers are symbols, letters are symbols. #
mathchat
12:21 am
ccampbel14
:
Some of my favourite professional produced manips are: cuisenaire rods, different types of cubes, pattern blocks & geoboards. #
mathchat
12:22 am
Saskateach
:
@
joelsopp
do you think u had a real understanding when u could get answer but not explain how? #
mathchat
12:22 am
mathheadinc
:
@
ccampbel14
Keep track by how much sense it sense. #
mathchat
12:22 am
mathchat
:
Chisanbop for addition:
http://www.ehow.com/how_4861020_finger
mathbasicadditioncounting.html #
mathchat
12:22 am
mthman
:
@
jrsteach
Then when a student doesn't remember "Angela's Rule" someone in the class explains. It takes time, but they OWN it. #
mathchat
12:23 am
mthman
:
Any middle school teachers (math or science)? Excellent resource:
http://www.msteacher2.org/
#
mathchat
12:23 am
math2go
:
RT @
ccampbel14
: Some of my favourite professional produced manips are: cuisenaire rods, different types of cubes, pattern blocks & geoboards. #
mathchat
12:23 am
ColinTGraham
:
I was able to explain placeholder systems and work with bases when I was around 8, but never called it that till I was much older! #
mathchat
12:23 am
mathheadinc
:
@
ccampbel14
I mean keep track by how much sense the reasoning makes. #
mathchat
12:23 am
ccampbel14
:
I love beginning with a story, using manips and then asking students for questions they might ask. This leads to great PS. #
mathchat
12:24 am
mathheadinc
:
@
ColinTGraham
Yeah, but I make THEM label it after I show them how :) #
mathchat
12:25 am
math2go
:
@
ghewgley
: math is the 'language' of science. However, it is not a language in the sense of other languages. #
mathchat
12:25 am
ColinTGraham
:
So, in the last five minutes or so, what activity with manips do you always use because of its effectiveness? #
mathchat
12:25 am
mthman
:
@
msseessm
We developed "Angela's Rule" when working w/Alg Tiles. The 1st step, "canceling on both sides" became "Angela's Rule" #
mathchat
12:26 am
ccampbel14
:
I forgot, I love algebra tiles. Students can learn many things on their own with my guidance right up into high school. #
mathchat
12:26 am
POWERORGmath
:
#
mathchat
Video clips & livescribe.com Smartpens are good 4 our higher ed studs
12:26 am
ColinTGraham
:
However, it is not a language in the sense of other languages @
math2go
Oh big disagree with that! You haven't read my blog post! #
mathchat
12:26 am
mthman
:
@
ColinTGraham
Algebra Tiles for solving equations! #
mathchat
12:27 am
ghewgley
:
@
math2go
We're just arguing semantics here. Both, in written form, are symbol based communication. #
mathchat
12:27 am
padgets
:
@
mthman
can I ask you to share the whole rule? #
mathchat
love to learn it :)
12:27 am
mathheadinc
:
@
math2go
Uhh, it has nouns, verbs, adjectives. Not a language in what sense? #
mathchat
12:27 am
mthman
:
Algebra Tiles allow for great abstract work w/area & perimeter, factoring, & problem solving! #
mathchat
12:27 am
ccampbel14
:
A big lesson I've learned about manips is the order they are presented. I tried manips after solving equations symbol  disaster! #
mathchat
12:27 am
joelsopp
:
Not true. Some can do it. @
Saskateach
RT @
mathheadinc
: @
joelsopp
When you can't show how you did it then you must be cheating. #
mathchat
12:27 am
ccampbel14
:
Have to remember concretely, pictorially and then symbolically/abstractly #
mathchat
12:28 am
ColinTGraham
:
Tangrams for area, congruence, shape names, triangles, similarity, area, rotations, symmetry... fun! #
mathchat
12:28 am
mthman
:
@
padgets
Absolutely...let me think about the best way to demo it, then I'll tweet it out. #
mathchat
12:28 am
ghewgley
:
@
joelsopp
Some, but not many. #
mathchat
12:28 am
ccampbel14
:
Geoaboards are great for perimeter, area, Pythagoriean, square #
s
, If it has 100 squares  percents, decimals, etc. too #
mathchat
12:29 am
ColinTGraham
:
Also, if you accept Piaget/Vygotsky, then moving to the abstract before 11 or so may be a waste of time... #
mathchat
12:29 am
POWERORGmath
:
Just waving at #
mathchat
& #
mbachat
12:29 am
ccampbel14
:
I love the feel of wooden pattern blocks. Great for shape & space  polygons, angles, sides, patterns, etc. #
mathchat
12:29 am
mthman
:
@
ccampbel14
Oooh...I forgot about geoboards! Love it! How about symmetry? #
mathchat
12:29 am
mathheadinc
:
@
joelsopp
I know. I was being facetious! Teachers want to know how you get ans bc you can still get right answers w/wrong methods. #
mathchat
12:29 am
coreman2200
:
RT @
ghewgley
: Math is a language. 2 + 2 = 4 is a sentence. Numbers are symbols, letters are symbols. #
mathchat
12:30 am
joelsopp
:
@
Saskateach
Yes, I truly feel that way. Some people can just figure things out without showing the pathway. #
mathchat
12:30 am
ccampbel14
:
Geoboards are also good for transformations  translations, reflections & rotations #
mathchat
12:30 am
ColinTGraham
:
OK, 140 characters and the time as usual are not enough! The archive of today's chat will be online in about 30 mins. #
mathchat
12:30 am
ccampbel14
:
@
mthman
Yes, I just added a tweet about transformations #
mathchat
12:30 am
Saskateach
:
So true it's a continuum RT @
ccampbel14
: Have to remember concretely, pictorially and then symbolically/abstractly #
mathchat
12:30 am
mathheadinc
:
@
joelsopp
And the higher the education goes the more one must be able to show how or no credit. #
mathchat
12:31 am
ghewgley
:
@
ColinTGraham
Piaget's time frames are "averages" and in no way specific times. Some students move faster, some not at all. #
mathchat
12:31 am
ccampbel14
:
Does any1 use base 10 materials? I've been told that they simply represent our base 10 system but don't help kids think about it. #
mathchat
12:31 am
ColinTGraham
:
If you want to revisit the topic, then we will be chatting again on Monday 19:30 GMT #
mathchat
12:31 am
MariaDroujkova
:
@
ccampbel14
Did everybody learn to perform well? We wish, lol! But people had harder time with multiple choice when that started #
mathchat
12:32 am
joelsopp
:
@
ghewgley
True. #
mathchat
12:32 am
ColinTGraham
:
@
ghewgley
Yes, I know. But basically the abstract is only going to work once the concrete is there... No concrete, no foundation! #
mathchat
12:33 am
ColinTGraham
:
Thank you again everyone or another stimulating #
mathchat
12:33 am
math2go
:
@
ColinTGraham
well send it to me if you will, but I still don't see grammar, tense, etc. #
mathchat
12:33 am
joelsopp
:
My bad...lol RT @
mathheadinc
: @
joelsopp
I know. I was being facetious! #
mathchat
12:33 am
math2go
:
RT @
mthman
: @
ColinTGraham
Algebra Tiles for solving equations! #
mathchat
<definitely aglebra tiles  the area model!
12:33 am
ghewgley
:
@
joelsopp
That's why I try to figure out how the student is thinking (or I ask him/her) to avoid this. #
mathchat
12:33 am
math2go
:
RT @
ghewgley
: @
math2go
We're just arguing semantics here. Both, in written form, are symbol based communication. #
mathchat
<probably so!
12:34 am
padgets
:
#
mathchat
thanks everybody for letting a science geek join the conversation, always learn something from you folks!
12:34 am
ColinTGraham
:
@
math2go
as a quick example of grammar, how about order of operations? #
mathchat
12:34 am
Saskateach
:
@
ccampbel14
I agree about base 10 blocks they are cumbersome for larger numbers. Students tend to prefer quick drawings over them #
mathchat
12:35 am
ColinTGraham
:
Feel free to keep chatting everyone! #
mathchat
12:35 am
mathheadinc
:
@
joelsopp
Cool. The other problem is, kids who only write answers do poorly in the long run. #
mathchat
12:35 am
mthman
:
Thanks for great convo tweeps! @
ccampbel14
@
padgets
@
jrsteach
@
Saskateach
@
ColinTGraham
@
msseessm
@
mathheadinc
@
ghewgley
#
mathchat
12:35 am
math2go
:
@
mathheadinc
I see it as building on the language that we already use, along with a hefty dose of latin & greek #
mathchat
12:35 am
ghewgley
:
@
math2go
Language is a form of communication. Math sentences communicate something. #
mathchat
12:35 am
ccampbel14
:
@
ColinTGraham
Abstract after the concrete  an e.g. would be basic facts. Until they understand they won't speed up (timed tests) #
mathchat
12:36 am
mathheadinc
:
@
joelsopp
We tell students, "The more work you show. the faster your grades will get better, the sooner you get rid of the tutor." #
mathchat
12:36 am
Saskateach
:
@
ColinTGraham
Thanks for the great discussion. My Internet is down so using my phone. Feels so much slower. #
mathchat
12:36 am
ccampbel14
:
Great convo tweeps! @
mthman
@
ccampbel14
@
padgets
@
jrsteach
@
Saskateach
@
ColinTGraham
@
msseessm
@
mathheadinc
@
ghewgley
#
mathchat
12:37 am
math2go
:
I love chips for adding & subtracting integers using zero pairs too #
mathchat
12:37 am
ColinTGraham
:
@
ccampbel14
Yes, I tend to work using the revised Bloom's taxonomy for both ESL and maths and IT and... #
mathchat
12:37 am
ccampbel14
:
@
ColinTGraham
Not that I agree with timed tests...many people ask me about that. They also ask about practice sheets & flashcards #
mathchat
12:38 am
ColinTGraham
:
@
Saskateach
It gives you more time to think Jen, unless you're shopping too! #
mathchat
12:38 am
ghewgley
:
@
mathheadinc
I think the lack of "showing work" greatly limits feedback in math. Some students don't need it, but most need lots. #
mathchat
12:38 am
Saskateach
:
Thanks 4 the great conversation everyone. Always a pleasure:) #
mathchat
12:39 am
mathheadinc
:
@
math2go
I can see that. #
mathchat
12:39 am
ColinTGraham
:
OK I am off to archive. Catch you later everyone! #
mathchat
12:39 am
mathheadinc
:
RT @
mthman
: TY for great convo tweeps! @
ccampbel14
@
padgets
@
jrsteach
@
Saskateach
@
ColinTGraham
@
msseessm
@
mathheadinc
@
ghewgley
#
mathchat
12:39 am
ccampbel14
:
My husband just asked if my mathchat is finished. Guess he wants help with the kids. See you all next time! #
mathchat
12:40 am
ghewgley
:
Timed tests test the wrong thing. They test how fast you work, not necessarily if you can answer the questions. #
mathchat
12:40 am
mathheadinc
:
@
ghewgley
Feedback from teachers? #
mathchat
12:40 am
ghewgley
:
Thanks everyone. I love the sharing of your ideas! #
mathchat
12:40 am
ccampbel14
:
@
math2go
I also use the small unit pieces from algebra tiles for integers. Nice square shapes for mult & div #
mathchat
12:40 am
math2go
:
@
ColinTGraham
not surprisingly someone in #
edchat
convinced me that it was not a complete language maybe it's a dialect! :) #
mathchat
12:41 am
ghewgley
:
@
mathheadinc
Feedback from teachers, checking your own work (self), feedback from peers, etc. #
mathchat
12:42 am
ColinTGraham
:
@
math2go
I always ask the doubters why Chomsky had to use mathematical symbology to notate Universal Grammar... ;) #
mathchat
12:42 am
mathheadinc
:
@
math2go
Chips as in fries or pokers chips or...?#
mathchat
12:43 am
ghewgley
:
@
math2go
I would maybe go with "it's not a complete language" but are computer languages languages? #
mathchat
12:43 am
ccampbel14
:
Okay, I am really going now...hard to tear myself away. I love talking math! #
mathchat
12:43 am
ColinTGraham
:
Or potato crisps? RT @
mathheadinc
: @
math2go
Chips as in fries or pokers chips or...?#
mathchat
12:43 am
mathheadinc
:
@
ghewgley
YES! I want my students to remember what they did. Answers aren't enough for that unless memory is photographic. #
mathchat
12:44 am
JustKDean
:
@
BLAKOBEN
didn't know about #
mathchat
gonna hafta peep it out
12:44 am
mathheadinc
:
THOSE, TOO! RT @
ColinTGraham
: Or potato crisps? RT @
mathheadinc
: @
math2go
Chips as in fries or pokers chips or...?#
mathchat
12:45 am
ghewgley
:
@
mathheadinc
So it's the process that's important? #
mathchat
12:45 am
math2go
:
@
mathheadinc
lol , not fries! twocolor poker chips. one side positive, one side negative #
mathchat
12:46 am
mathheadinc
:
@
math2go
Just wonderin'! I thought that's what you meant. #
mathchat
12:47 am
mathheadinc
:
@
ghewgley
Now you have it. The process gets A's. Answers change, processes don't. #
mathchat
12:47 am
math2go
:
@
ghewgley
or is cat talk or dog talk a language? I guess it's pretty hard to define. #
mathchat
12:49 am
ghewgley
:
@
mathheadinc
That's why showing your work is showing the process you went through. #
mathchat
12:49 am
Caro_lann
:
Sorry I'm late. I use string. Make curves of equations line, quad, cubic and move to change coefficients. All on floor.#
mathchat
12:50 am
mathheadinc
:
CORRECT! RT @
ghewgley
: @
mathheadinc
That's why showing your work is showing the process you went through. #
mathchat
12:50 am
ghewgley
:
@
math2go
I tell my students that math is a language, and like language it has to make sense (answers and process). #
mathchat
12:51 am
math2go
:
I also like unit cubes so students can see sides to draw nets #
mathchat
many cannot visualize in three dimensions
12:51 am
mathheadinc
:
@
math2go
I had a cat once and I knew when he was saying, "I want to eat that bird." #
mathchat
12:52 am
math2go
:
@
ghewgley
I like that. It is kid language! #
mathchat
12:52 am
ghewgley
:
@
mathheadinc
Manipulatives can help the students through the process(es). #
mathchat
12:54 am
ghewgley
:
@
math2go
Yes. It's a form of communication  in this case communicating math concepts. #
mathchat
12:56 am
math2go
:
@
ghewgley
well if communication=language then I would agree... math is certainly communication! #
mathchat
12:56 am
justwonderinY
:
@
ccampbel14
: Have to remember concretely, pictorially and then symbolically/abstractly #
mathchat
< wasn't at mathchat, but love this
12:57 am
ghewgley
:
Thanks again #
mathchat
people  great discussion!
12:59 am
math2go
:
RT @
ghewgley
: Thanks again #
mathchat
people  great discussion! < even coming in late, it was thoughtprovoking! thanks!
1:07 am
ghewgley
:
I love my PLN  especially #
elemchat
#
ellchat
, and now #
mathchat
. Thanks to you all!
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As it happened on Thursday, 5th August 23:30  00:30 GMT