#TCMchat Archive | Participate

MissLori_B Sep 14 @ 9:00 PM EDT

#tcmchat

Zakchamp Sep 14 @ 9:00 PM EDT

Let's do this! #TCMchat

TCM_at_NCTM - Moderator Sep 14 @ 9:01 PM EDT

Here are a few tips to help you get the most out of this #TCMchat https://t.co/yCtVkGPHST

TCM_at_NCTM - Moderator Sep 14 @ 9:01 PM EDT

Please welcome TCM author Kimberly Morrow-Leong @kmorrowleong #TCMchat https://t.co/L1Y1I8FUfI

NCTM - Moderator Sep 14 @ 9:01 PM EDT

We hope that you can all join the #TCMchat tonight! We're looking forward to a great discussion! https://t.co/YTScpgYkVY

TCM_at_NCTM - Moderator Sep 14 @ 8:55 PM EDT

Tonight's discussion article is a sneak peek at the Oct Focus Issue on assessment https://t.co/HAACIqz0bz #TCMchat https://t.co/HMzHBkUOLG

Zakchamp Sep 14 @ 9:01 PM EDT

Thanks for joining us @kmorrowleong and for your awesome manuscript! #TCMChat

MFAnnie Sep 14 @ 9:02 PM EDT

Hi @BethNctm! I'm ready for #TCMchat for sure.

kmorrowleong Sep 14 @ 9:02 PM EDT

Thanks, Zac! #TCMchat

davidwees Sep 14 @ 9:03 PM EDT

I'm going to try to jump into #TCMchat tonight too if I can.

BethNctm Sep 14 @ 9:03 PM EDT

Welcome to #TCMchat @kmorrowleong Thanks for a great article and helping us preview the 2016 Focus Issue on Assessment

kmorrowleong Sep 14 @ 9:03 PM EDT

@BethNctm Hi, everyone! I am happy to join you! #TCMchat

MFAnnie Sep 14 @ 9:03 PM EDT

@Zakchamp @kmorrowleong Yea, welcome to #TCMchat, and thanks for addressing such an important topic.

Zakchamp Sep 14 @ 9:03 PM EDT

@the_dp The Turner Classic movies folks sometimes try and take over our #TCMChat - but this is straight Teaching Children Mathematics (TCM)

JaneMWilburne Sep 14 @ 9:04 PM EDT

Hi all. Excited for tonite' chat #TCMchat

BethNctm Sep 14 @ 9:04 PM EDT

@MFAnnie I'm glad you are with the #TCMchat tonight (and not driving for a change) tee hee

Dina0Brien Sep 14 @ 9:04 PM EDT

Dina from Edison NJ. Math specialist and coach for K-5 #TCMchat

jamiedunc3 Sep 14 @ 9:04 PM EDT

Jamie Duncan here from California. :) #tcmchat

MFAnnie Sep 14 @ 9:04 PM EDT

Well @davidwees, you ARE mentioned in the article, so I would expect nothing less! #TCMchat

MarkChubb3 Sep 14 @ 9:04 PM EDT

Hi everyone! I'm going to try to be here tonight... Kids aren't quite sleeping yet though. #tcmchat

danie11e1 Sep 14 @ 9:04 PM EDT

Danielle 4th grade teacher from MA stopping in tonight #TCMchat

Zakchamp Sep 14 @ 9:04 PM EDT

@MFAnnie @davidwees That's right! You gotta join. :) #TCMChat

pearse_margie Sep 14 @ 9:05 PM EDT

#TCMchat Hi Margie from PA. My Internet is as slow as molasses tonight! Darn, I was SO much looking forward to this hour.

TCM_at_NCTM - Moderator Sep 14 @ 9:05 PM EDT

Q1 As you introduce yourself, answer: Have you tried to sort student work by strategy? What did you find?#TCMchat https://t.co/p3cY7KJjjR

zack_hill Sep 14 @ 9:05 PM EDT

Hi Everyone! Zack Here from Florida. Excited to talk about this article. #TCMchat

BethNctm Sep 14 @ 9:05 PM EDT

@MarkChubb3 We will try to keep our voices down so we don't disturb the kiddos, #TCMchat

Elementarist Sep 14 @ 9:05 PM EDT

Hello all, 4th grade Math T in KY. Moving to our STEAM lab on Tuesday. #TCMchat

AdamBrownEDU Sep 14 @ 9:06 PM EDT

Hi! Adam from VA. K - 12 Principal #TCMchat

davidwees Sep 14 @ 9:06 PM EDT

@Zakchamp @MFAnnie On a bus headed home from an interesting talk so expect some intermittent participation! :) #TCMchat

MissLori_B Sep 14 @ 9:06 PM EDT

Hi all! Lori from MO here- elem math specialist and interventionist #TCMChat

Elementarist Sep 14 @ 9:06 PM EDT

A1 I have tried sorting work by strategy. Sometimes strategy showed developmentl level. Sometimes not #TCMchat

TCM_at_NCTM - Moderator Sep 14 @ 9:06 PM EDT

It looks like we've got a nice size crows tonight for #TCMchat. Welcome all! We are so glad that you are here.

TCM_at_NCTM - Moderator Sep 14 @ 9:07 PM EDT

It looks like we've got a nice size crowd tonight for #TCMchat. Welcome all! We are so glad that you are here.

Zakchamp Sep 14 @ 9:07 PM EDT

A1: Zak Champagne here, researcher from Fl. & Pres. of @FCTMath. Sorting student work by strategy is tough, but very rewarding #TCMChat

drkchilds Sep 14 @ 9:07 PM EDT

A1: Kris (Texas). Yes, I found I was able to better scaffold how solution strategies were shared opposed to arbitrarily picking Ss #TCMchat

davidwees Sep 14 @ 9:08 PM EDT

A1: I wrote tools for 20 different pre-unit "preview the math" tasks across our curriculum, so yeah very! #tcmchat https://t.co/bcW2ek7OEK

TCM_at_NCTM - Moderator Sep 14 @ 9:05 PM EDT

Q1 As you introduce yourself, answer: Have you tried to sort student work by strategy? What did you find?#TCMchat https://t.co/p3cY7KJjjR

jamiedunc3 Sep 14 @ 9:08 PM EDT

A1: I have sorted work by concrete models, representational and abstract #TCMchat

kmorrowleong Sep 14 @ 9:08 PM EDT

@MFAnnie @davidwees I had to address his blog post! It fit so well with what I was thinking! #TCMchat

Zakchamp Sep 14 @ 9:08 PM EDT

Dr. Childs starting us off strong! Big fan of this. #TCMChat https://t.co/4U25hg5ILg

drkchilds Sep 14 @ 9:07 PM EDT

A1: Kris (Texas). Yes, I found I was able to better scaffold how solution strategies were shared opposed to arbitrarily picking Ss #TCMchat

MarkChubb3 Sep 14 @ 9:08 PM EDT

A1 Mark Instructional Coach from Niagara I have noticed many strategies overlap. Noticed I have a lot to learn about development #tcmchat

MFAnnie Sep 14 @ 9:08 PM EDT

Annie from @themathforum near Philly. I've done lots of Looking at S Work with Ts, often using #NoticeWonder (surprise). #TCMchat

BethNctm Sep 14 @ 9:08 PM EDT

A1 I'm Beth your TCM Editor. I've never used this type of sorting assessment #TCMchat

MrsL_DHS Sep 14 @ 9:08 PM EDT

Hi All! Dawn here from DE, teaching 9th Alg and 12th PreCalc this year. #TCMchat

poly_math_ Sep 14 @ 9:08 PM EDT

Hi. I'm the chair of @MTMS_at_NCTM. Here to support TCM. #TCMChat

tcesarski Sep 14 @ 9:08 PM EDT

Hi I'm Taylor and I'm a preservice secondary math teacher from NC! #tcmchat

Zakchamp Sep 14 @ 9:09 PM EDT

@jamiedunc3 Do find some pieces of work difficult to fit in exactly one category? #TCMChat

zack_hill Sep 14 @ 9:09 PM EDT

A1 Forgot to mention I'm a K-5 Math Coach. Sorting S's work I always find myself wanting them there to ask clarifying questions. #TCMchat

BethNctm Sep 14 @ 9:09 PM EDT

@poly_math_ I'm glad you are here for the #TCMchat

MFAnnie Sep 14 @ 9:09 PM EDT

@kmorrowleong @davidwees Exactly! And both article and his post mirror much Looking at S Work (LaSW?) we've done @themathforum. #TCMchat

AdamBrownEDU Sep 14 @ 9:10 PM EDT

A1. I tried to implement a tiered system of differentiation. Attempted to include mix-ability Ss to work with on common assignment #TCMchat

TCM_at_NCTM - Moderator Sep 14 @ 9:10 PM EDT

Q2 Let’s do some math! #TCMchat https://t.co/AnDKsKyalE

jamiedunc3 Sep 14 @ 9:10 PM EDT

@Zakchamp Yes, so then I rely on my interactions with them on similar tasks using #TCMchat

Zakchamp Sep 14 @ 9:10 PM EDT

@MarkChubb3 This is what I want to talk about tonight. The overlap. And what it means instruction wise- if anything? #TCMChat

MrBinfield Sep 14 @ 9:10 PM EDT

Hi everyone. Nehlan from niagara here #TCMchat

MFAnnie Sep 14 @ 9:10 PM EDT

@zack_hill Exactly why we like to use #NoticeWonder. What do U notice about the work? What do U wonder? What Q do you want to ask? #TCMchat

MarkChubb3 Sep 14 @ 9:10 PM EDT

@zack_hill That's the great part about formative assessments... you CAN ask your Ss what they meant... #TCMchat

Zakchamp Sep 14 @ 9:11 PM EDT

It's worth noting that @zack_hill wrote a brilliant series of blog posts related to this topic! #TCMChat https://t.co/3u73GBTAZ2

Elementarist Sep 14 @ 9:12 PM EDT

A1 teaching Ss how to show their thinking makes this much easier if you aren't observing them working. #TCMchat sometimes biggest obstacle

jamiedunc3 Sep 14 @ 9:12 PM EDT

A2. I picture it on a number line. #TCMchat

Zakchamp Sep 14 @ 9:12 PM EDT

YES!!!!!! Best part of twitter chats - doing math. #TCMChat https://t.co/WCPktmnHHQ

TCM_at_NCTM - Moderator Sep 14 @ 9:10 PM EDT

Q2 Let’s do some math! #TCMchat https://t.co/AnDKsKyalE

MFAnnie Sep 14 @ 9:12 PM EDT

Q2: For 1st I used decimal equivalents since I know my eighths, and second I simplified. #TCMchat

MrBinfield Sep 14 @ 9:13 PM EDT

A1 when selecting and sequencing S thinking I try to weave a common thread in strategies to connect ideas #TCMchat

BethNctm Sep 14 @ 9:13 PM EDT

How did that work for you @AdamBrownEDU #TCMchat https://t.co/KTlcclaIFp

AdamBrownEDU Sep 14 @ 9:10 PM EDT

A1. I tried to implement a tiered system of differentiation. Attempted to include mix-ability Ss to work with on common assignment #TCMchat

Dina0Brien Sep 14 @ 9:13 PM EDT

A2 I thought about benchmarks of 0, 1/2, and 1 #TCMchat

danie11e1 Sep 14 @ 9:13 PM EDT

A2: I would look at distance from 1/2 #TCMchat

jamiedunc3 Sep 14 @ 9:13 PM EDT

@Zakchamp @MarkChubb3 I wonder if Ss use one representation to double check another that they're not totally confident with yet #tcmchat

MarkChubb3 Sep 14 @ 9:13 PM EDT

A student might compare each fraction to 1/2 5/8 and 6/10 are both 1 piece larger than 1/2 8ths are larger than 10ths #tcmchat

MFAnnie Sep 14 @ 9:13 PM EDT

@jamiedunc3 @themathforum At least we are consistent! #TCMchat

AdamBrownEDU Sep 14 @ 9:14 PM EDT

A2. When I was in the classroom, I had basketball-crazed Ss. Fractions represented free throw shots. Ss used that as a platform #TCMchat

MFAnnie Sep 14 @ 9:14 PM EDT

@jamiedunc3 @themathforum But honestly, #NoticeWonder allows better focus on evidence, not judging based on speculation. #TCMchat

kmorrowleong Sep 14 @ 9:14 PM EDT

@MrBinfield I'm interested! Could you give us an example?#TCMchat

BethNctm Sep 14 @ 9:14 PM EDT

Thanks for sharing the link @Zakchamp I agree @zack_hill wrote a set of must read blog posts #TCMchat https://t.co/22ofBIPiuS

Zakchamp Sep 14 @ 9:11 PM EDT

It's worth noting that @zack_hill wrote a brilliant series of blog posts related to this topic! #TCMChat https://t.co/3u73GBTAZ2

zack_hill Sep 14 @ 9:14 PM EDT

A2 The first thing I thought of with the first set is that they're both close to one half. #TCMchat

Zakchamp Sep 14 @ 9:14 PM EDT

A2: 5/8 is 1/8 more than a half but 6/10 is only 1/10 more than a half. So 5/8 is greater. #TCMChat

drkchilds Sep 14 @ 9:14 PM EDT

A2: for 5/8 and 6/10 possibly using a benchmark of 1/2; both are 1 away (then think in terms of pizza & use dem to discuss sizes) #TCMchat

tcesarski Sep 14 @ 9:14 PM EDT

A2: I would simplify both and find a common denominator in 1st, but Ss might find a common denominator in both bc always works #tcmchat

MarkChubb3 Sep 14 @ 9:15 PM EDT

A student might want to look for friendlier fractions 8/12 is 2/3 10/15 is 2/3 #tcmchat

AdamBrownEDU Sep 14 @ 9:15 PM EDT

@BethNctm Mixed results. Some pretty unique lessons and some not so much. I left the classroom for admin role before perfecting it. #tcmchat

Zakchamp Sep 14 @ 9:15 PM EDT

@drkchilds Same page pal! #TCMChat

drkchilds Sep 14 @ 9:15 PM EDT

A2: the key is ensuring Ss compare fractions & not converting to decimals as the goal is for them to make sense of fractions #TCMchat

Elementarist Sep 14 @ 9:15 PM EDT

A2 i made denominators equivalent. Had a hard time visualizing on a number line #TCMchat

TCM_at_NCTM - Moderator Sep 14 @ 9:16 PM EDT

Diggin all of the mathematical thinking around Q2/A2 being shared tonight #TCMchat

kmorrowleong Sep 14 @ 9:16 PM EDT

@Zakchamp @TCM_at_NCTM A2 One student used 180 as a common denominator. Many others used 120! Correct, but oh so inefficient #TCMchat

jamiedunc3 Sep 14 @ 9:16 PM EDT

@MFAnnie @themathforum @JSchwartz10a recommended responding to student work with #noticewonder I think it encourages deeper refl. #tcmchat

Zakchamp Sep 14 @ 9:17 PM EDT

@kmorrowleong @TCM_at_NCTM Ouch! That's a lot of work. Interesting work - but A LOT. #TCMChat

MrBinfield Sep 14 @ 9:17 PM EDT

If Ss are asked a prob that centres around multiplication, I look for sol’ns that use repeated add’n, ->grouping->regrouping groups #TCMchat

MarkChubb3 Sep 14 @ 9:17 PM EDT

Developing Fractional reasoning is important! Converting to decimals is avoiding this development! #TCMchat https://t.co/VhYEDQsilG

drkchilds Sep 14 @ 9:15 PM EDT

A2: the key is ensuring Ss compare fractions & not converting to decimals as the goal is for them to make sense of fractions #TCMchat

MFAnnie Sep 14 @ 9:17 PM EDT

@drkchilds On other hand, I chose to convert to decimals because I "know" what they both are w/o calculating, so very efficient. #TCMchat

PiffQ Sep 14 @ 9:18 PM EDT

Larry here from MD #TCMchat

zack_hill Sep 14 @ 9:18 PM EDT

@kmorrowleong @Zakchamp @TCM_at_NCTM Yes, loved the focus on fluency, specifically being flexible with strategies. #TCMchat

MrBinfield Sep 14 @ 9:18 PM EDT

Look for evidence of distributive or commutative properties. Then help Ss connect these ideas as they talk #TCMchat

Zakchamp Sep 14 @ 9:18 PM EDT

@MarkChubb3 @drkchilds - Assuming kids develop a solid understanding of fractions, when does converting to decimals become helpful? #TCMChat

jamiedunc3 Sep 14 @ 9:18 PM EDT

@MarkChubb3 Hhahaha When I was a kid I would totally convert to decimals! #tcmchat

MFAnnie Sep 14 @ 9:19 PM EDT

@jamiedunc3 @themathforum More evidence that @JSchwartz10a is very wise. #TCMchat

janetdnuzzie Sep 14 @ 9:19 PM EDT

A1: Hello, Math Colleagues! I'm Janet from Pasadena ISD in TX. I serve as an Instructional Specialist for K-4 Mathematics. #TCMchat

Zakchamp Sep 14 @ 9:19 PM EDT

@zack_hill @kmorrowleong @TCM_at_NCTM Hang tight - can't wait to talk fluency tonight! #TCMChat

MarkChubb3 Sep 14 @ 9:19 PM EDT

@jamiedunc3 @Zakchamp Having multiple methods allows us to choose best for the numbers given. Also to double check our reasoning! #TCMchat

MFAnnie Sep 14 @ 9:19 PM EDT

@kmorrowleong @Zakchamp @TCM_at_NCTM And Ss LOVE to use strats they know will work, however inefficient. One thing to watch for. #TCMchat

TCM_at_NCTM - Moderator Sep 14 @ 9:20 PM EDT

Q3 What similarities and/or differences do you see between strategies & representations? #TCMchat https://t.co/Ph1Pvr2Q9g

TCM_at_NCTM - Moderator Sep 14 @ 9:20 PM EDT

Strategy vs Representation #TCMchat https://t.co/tpVWGmm5TV

drkchilds Sep 14 @ 9:20 PM EDT

@MFAnnie however from a student perspective does it allow for them to make sense of fractions? #tcmchat

Zakchamp Sep 14 @ 9:20 PM EDT

@MFAnnie @kmorrowleong @TCM_at_NCTM And efficiency is in the eye of the beholder. #TCMChat

MarkChubb3 Sep 14 @ 9:21 PM EDT

@Zakchamp @drkchilds This IS an important piece! Making the connections between this is key. But don't rush for it!!! #TCMchat

janetdnuzzie Sep 14 @ 9:22 PM EDT

A1: We've mostly been focusing on analyzing student work with the 4 Critical PLC Questions. No sorting by strategy - yet! #TCMChat

kmorrowleong Sep 14 @ 9:22 PM EDT

@zack_hill @Zakchamp @TCM_at_NCTM I read S work sooo many times because I knew SOMETHING wasn't quite right, despite 92% overall. #TCMchat

MrBinfield Sep 14 @ 9:22 PM EDT

A2 I looked at the size of the pieces, to compare how many of each size piece. #TCMchat

MFAnnie Sep 14 @ 9:23 PM EDT

A3 Really liked the description of the difference. Makes you dig beyond "drew a picture" to "what thinking are they really doing? #TCMchat

tcesarski Sep 14 @ 9:23 PM EDT

One similarity between strategies & representations is that there are many diff poss strategies and reps for a single problem #tcmchat

BethNctm Sep 14 @ 9:23 PM EDT

A3 #TCMchat I'm wondering if strategy is the teacher's interpretation of student thinking or more of something in the student tool kit

janetdnuzzie Sep 14 @ 9:23 PM EDT

A1: We've been focusing on analyzing student work with the 4 PLC Questions. No sorting by strategy - yet! #TCMChat https://t.co/JIZYNxB3tT

TCM_at_NCTM - Moderator Sep 14 @ 9:05 PM EDT

Q1 As you introduce yourself, answer: Have you tried to sort student work by strategy? What did you find?#TCMchat https://t.co/p3cY7KJjjR

Zakchamp Sep 14 @ 9:23 PM EDT

@drkchilds @MarkChubb3 Like sports? 92 hits per 300 at bats vs. 95 hits per 302 at bats? #TCMChat

MarkChubb3 Sep 14 @ 9:24 PM EDT

A3 We've been learning about Fosnot's work last 5-6 years here. Direct connections between strategies, representations & big ideas #tcmchat

AdamBrownEDU Sep 14 @ 9:24 PM EDT

A3. Representation is a S demonstrating a deeper understanding of content. A S being able to teach the content to others is one way #tcmchat

tcesarski Sep 14 @ 9:24 PM EDT

A3: One similarity between strategies & representations is that there are many diff poss strategies and reps for a single prob! #TCMchat

zack_hill Sep 14 @ 9:25 PM EDT

A3 I noticed that the samples with visual representations were bar models or circular models. Wonder if this was a trend... #TCMchat

Zakchamp Sep 14 @ 9:25 PM EDT

@tcesarski Nice point Taylor! #TCMChat

celinerc Sep 14 @ 9:25 PM EDT

Q1 Hi from Ottawa. Here is a sorting of strategies for multiplication from 3 grade four classes #TCMchat https://t.co/U3ga5jFJcq

jamiedunc3 Sep 14 @ 9:26 PM EDT

A3: I'm not sure. I thought strategies helped Ss find a way to solve a prob and a representation is more displaying their thinking #tcmchat

MarkChubb3 Sep 14 @ 9:26 PM EDT

Here are fraction representations and strategies you would see. Lower are earlier examples https://t.co/Fj3JfxA74J #tcmchat

kmorrowleong Sep 14 @ 9:26 PM EDT

@MarkChubb3 That work is a big inspiration. Think: models OF learning and models FOR learning! #TCMchat

MFAnnie Sep 14 @ 9:26 PM EDT

@drkchilds Depends how they came to understand decimal equivalents, among other things. Could already be "beyond" the task even. #TCMchat

janetdnuzzie Sep 14 @ 9:26 PM EDT

A2: My strategy: visual benchmarks ... but those first two fractions would be challenging! #TCMChat https://t.co/5DHuNxlW2G

TCM_at_NCTM - Moderator Sep 14 @ 9:10 PM EDT

Q2 Let’s do some math! #TCMchat https://t.co/AnDKsKyalE

Zakchamp Sep 14 @ 9:27 PM EDT

@jamiedunc3 I struggle here too - is the representation just for us as teachers? #TCMChat

MrBinfield Sep 14 @ 9:27 PM EDT

A3 a strategy is the steps a S takes to solve a problem. The representation is the chosen visual to communicate key understandings #TCMchat

janetdnuzzie Sep 14 @ 9:28 PM EDT

Annie: You're adding to my toolbox! Decimals didn't enter my mind! #TCMChat https://t.co/BOoXE6p5fO

MFAnnie Sep 14 @ 9:12 PM EDT

Q2: For 1st I used decimal equivalents since I know my eighths, and second I simplified. #TCMchat

jamiedunc3 Sep 14 @ 9:28 PM EDT

@Zakchamp Sometimes I think Ss are beyond needing a strategy or tool, but they create a rep. because they think they have to #tcmchat

drkchilds Sep 14 @ 9:28 PM EDT

@MFAnnie they could be beyond the task, however typically this is not the case; even some Ts have trouble making sense of fractions #tcmchat

Zakchamp Sep 14 @ 9:28 PM EDT

@kmorrowleong @MarkChubb3 Another clever use of the "prepositional permutation" #TCMChat https://t.co/zjmtCmOLvn

kmorrowleong Sep 14 @ 9:29 PM EDT

@zack_hill This surprised the teacher as well. I don't think these exercises lent themselves to visual justifications. #TCMchat

MFAnnie Sep 14 @ 9:29 PM EDT

A3 cont: As in, they drew this picture in order to do WHAT work? #TCMchat

MarkChubb3 Sep 14 @ 9:29 PM EDT

Ideally, the contexts we provide will help make the representations make sense. The strategy though will depend on Ss understanding #tcmchat

zack_hill Sep 14 @ 9:29 PM EDT

@jamiedunc3 @Zakchamp I think there are times too where a representation can act as a support as S's work through a strategy. #TCMchat

jamiedunc3 Sep 14 @ 9:29 PM EDT

@zack_hill @Zakchamp Yes! #tcmchat

Zakchamp Sep 14 @ 9:30 PM EDT

@jamiedunc3 Yep! And who is that really helping? Us or them? #TCMChat

janetdnuzzie Sep 14 @ 9:30 PM EDT

Love this! Wouldn't it be awesome if all of our #mathematics students reasoned like this! #TCMChat #PISDMathChat https://t.co/IeagREjZN5

Zakchamp Sep 14 @ 9:14 PM EDT

A2: 5/8 is 1/8 more than a half but 6/10 is only 1/10 more than a half. So 5/8 is greater. #TCMChat

jamiedunc3 Sep 14 @ 9:30 PM EDT

@Zakchamp Makes me think that my task needs work. The ceiling wasn't high enough. #tcmchat

TCM_at_NCTM - Moderator Sep 14 @ 9:30 PM EDT

Q4 What insights do you have into Michael’s mathematical thinking? #TCMchat https://t.co/IUnXYJzozj

kmorrowleong Sep 14 @ 9:30 PM EDT

@zack_hill @jamiedunc3 @Zakchamp Yes!! Like a placeholder while they think!! #TCMchat

MFAnnie Sep 14 @ 9:30 PM EDT

@drkchilds Oh, I know that for sure (we can all tell stories, I'm sure). That's why we all end up wanting to ask the Ss Qs. #TCMchat

drkchilds Sep 14 @ 9:31 PM EDT

@Zakchamp that was my strategy too #tcmchat

zack_hill Sep 14 @ 9:31 PM EDT

@kmorrowleong Yeah, some of them seemed really challenging to tackle visually due to the need for such precision. #TCMchat

MarkChubb3 Sep 14 @ 9:32 PM EDT

@janetdnuzzie If we provided more opportunities for our Ss to reason through number lines, this could easily be a reality!!! #TCMchat

Zakchamp Sep 14 @ 9:32 PM EDT

We could talk about this all night! #TCMChat https://t.co/q1xKZlChP3

TCM_at_NCTM - Moderator Sep 14 @ 9:30 PM EDT

Q4 What insights do you have into Michael’s mathematical thinking? #TCMchat https://t.co/IUnXYJzozj

drkchilds Sep 14 @ 9:32 PM EDT

A4: he was attempting to model 5/8 & 6/10; he does not realize the picture is not draw to scale; see if he can show me a diff way #TCMchat

BethNctm Sep 14 @ 9:33 PM EDT

So let's talk @Zakchamp We've got nothing but time #TCMchat https://t.co/pBXP3Oiq79

Zakchamp Sep 14 @ 9:32 PM EDT
We could talk about this all night! #TCMChat https://t.co/q1xKZlChP3
- TCM_at_NCTM - Moderator Sep 14 @ 9:30 PM EDT
  
  Q4 What insights do you have into Michael’s mathematical thinking? #TCMchat https://t.co/IUnXYJzozj

celinerc Sep 14 @ 9:33 PM EDT

A2 #TCMchat Student explaining his strategy - some explanation using description of a representation (in french) https://t.co/AkpePSDrOx

Zakchamp Sep 14 @ 9:33 PM EDT

@BethNctm hehehehe! #TCMChat

drkchilds Sep 14 @ 9:33 PM EDT

A4: In addition, I would have him verbally explain his thinking; this could tell me alot in regards to his thought pattern #TCMChat

MFAnnie Sep 14 @ 9:33 PM EDT

A4: I notice wholes are same size, each is split into right num of chunks, right num shaded, chunks aren't same size. #TCMchat

PiffQ Sep 14 @ 9:33 PM EDT

Same whole, 8ths bigger than 10ths, meaning of num and den #TCMchat

kmorrowleong Sep 14 @ 9:34 PM EDT

@Zakchamp @jamiedunc3 I think a representation is tailored for the "audience", to borrow from ELA. That should help with choices. #TCMchat

janetdnuzzie Sep 14 @ 9:34 PM EDT

A3: Strategy = verb ... Representation = noun #TCMChat https://t.co/3c4fqJbX59

TCM_at_NCTM - Moderator Sep 14 @ 9:20 PM EDT

Q3 What similarities and/or differences do you see between strategies & representations? #TCMchat https://t.co/Ph1Pvr2Q9g

mathcoachrivera Sep 14 @ 9:35 PM EDT

If the problem was a in context he is familiar with I think it could help. #TCMchat

MrBinfield Sep 14 @ 9:35 PM EDT

@TCM_at_NCTM he knows size of the whole matters. Equipartitioning is mostly there. #TCMchat

BethNctm Sep 14 @ 9:35 PM EDT

Ahh, nice observation #TCMchat https://t.co/ymRz07Xq6F

janetdnuzzie Sep 14 @ 9:34 PM EDT
A3: Strategy = verb ... Representation = noun #TCMChat https://t.co/3c4fqJbX59
- TCM_at_NCTM - Moderator Sep 14 @ 9:20 PM EDT
  
  Q3 What similarities and/or differences do you see between strategies & representations? #TCMchat https://t.co/Ph1Pvr2Q9g

MFAnnie Sep 14 @ 9:35 PM EDT

A4: I wonder if he knows pieces need to be same size. Would ask Qs about that. #TCMchat

MarkChubb3 Sep 14 @ 9:35 PM EDT

A4 Michael seems to recognize bars need to be equal in length He knows how many pieces in total & how many shaded #tcmchat

tcesarski Sep 14 @ 9:35 PM EDT

A4: He understands that fractions are parts of a whole but is comparing unequal denominators Ask him about the size of each section #tcmchat

janetdnuzzie Sep 14 @ 9:35 PM EDT

Oh my gosh ... students having fraction sense like this would take me to a #mathematical heaven! #TCMChat https://t.co/SHiWTiFEwz

MarkChubb3 Sep 14 @ 9:32 PM EDT

@janetdnuzzie If we provided more opportunities for our Ss to reason through number lines, this could easily be a reality!!! #TCMchat

Zakchamp Sep 14 @ 9:35 PM EDT

A4: Lots about this is "right" But I wonder if his representation really proves it. #TCMChat

MarkChubb3 Sep 14 @ 9:36 PM EDT

I am not sure if he understands pieces need to be equal within each shape, but different between the 2 bars #tcmchat

Zakchamp Sep 14 @ 9:36 PM EDT

@kmorrowleong @jamiedunc3 I think I agree here. So would you agree that representations are NOT always necessary for kids? #TCMChat

MarkChubb3 Sep 14 @ 9:37 PM EDT

I wish I could have watched him draw. Where did he "cut" the bar first? Randomly or at the halfway point??? #tcmchat

Zakchamp Sep 14 @ 9:37 PM EDT

Love this phrasing from @kmorrowleong "a representation is tailored for the audience" #TCMChat https://t.co/swCFu861hH

kmorrowleong Sep 14 @ 9:34 PM EDT

@Zakchamp @jamiedunc3 I think a representation is tailored for the "audience", to borrow from ELA. That should help with choices. #TCMchat

BethNctm Sep 14 @ 9:38 PM EDT

At this age how important is precision in rep? Should we allow for drawing ability, manual dexterity ex #TCMchat https://t.co/nwZR0iPLg4

Zakchamp Sep 14 @ 9:35 PM EDT

A4: Lots about this is "right" But I wonder if his representation really proves it. #TCMChat

drkchilds Sep 14 @ 9:38 PM EDT

A4: in the Ss defense how many times do we as Ts say “Draw a Picture?” Something to think about #TCMchat

kmorrowleong Sep 14 @ 9:38 PM EDT

@MarkChubb3 I wondered if it was a dexterity issue or a conceptual issue. #TCMchat

MarkChubb3 Sep 14 @ 9:39 PM EDT

I really like that we are thinking about what he IS doing... not just what is wrong. ASSET THINKING is best way to assess! #tcmchat

janetdnuzzie Sep 14 @ 9:39 PM EDT

A4: Ask, "How does the model show your thinking?" #TCMChat https://t.co/qMshVVKUH4

TCM_at_NCTM - Moderator Sep 14 @ 9:30 PM EDT

Q4 What insights do you have into Michael’s mathematical thinking? #TCMchat https://t.co/IUnXYJzozj

Zakchamp Sep 14 @ 9:39 PM EDT

@MarkChubb3 Focusing on what students DO know is so much more helpful than focusing on what they do not. #TCMChat

mathcoachrivera Sep 14 @ 9:40 PM EDT

I think students struggle partitioning a number line as much as they struggle partitioning a shape into equal parts #TCMchat

TCM_at_NCTM - Moderator Sep 14 @ 9:40 PM EDT

Q5 In what other ways do you use your student’s work to assess their fluency and understandings? #TCMchat https://t.co/YpoVK67ai6

TCM_at_NCTM - Moderator Sep 14 @ 9:40 PM EDT

Properties of fluency #TCMchat https://t.co/dnIEWrS6AB https://t.co/J1qQYe2zyQ

kmorrowleong Sep 14 @ 9:41 PM EDT

@MarkChubb3 Me too! #TCMchat

MathMileMarkers Sep 14 @ 9:41 PM EDT

Yes! Building flexibility with numbers and approaches helps Ss learn to think and connect ideas. #tcmchat https://t.co/b7O9iIlR3m

MarkChubb3 Sep 14 @ 9:19 PM EDT

@jamiedunc3 @Zakchamp Having multiple methods allows us to choose best for the numbers given. Also to double check our reasoning! #TCMchat

jamiedunc3 Sep 14 @ 9:41 PM EDT

@Zakchamp @kmorrowleong it depends on the purpose of what they're doing. Are you student representations as the fuel for discourse #tcmchat

MrBinfield Sep 14 @ 9:41 PM EDT

Interesting how we tell Ss that a math drawing is not detailed like art, at the same time effective representation is very precise #TCMchat

MarkChubb3 Sep 14 @ 9:41 PM EDT

@mathcoachrivera Yes, but with more practice, number lines are easier because you can make your line exactly the length you want! #TCMchat

kmorrowleong Sep 14 @ 9:42 PM EDT

@MarkChubb3 Oooooh, asset thinking. I like. #TCMchat

davidwees Sep 14 @ 9:42 PM EDT

A5: I use student work to inform my future plans with students. Not "What's wrong?" but "What's next?" #TCMchat https://t.co/1My3WAe9Iw

TCM_at_NCTM - Moderator Sep 14 @ 9:40 PM EDT

Q5 In what other ways do you use your student’s work to assess their fluency and understandings? #TCMchat https://t.co/YpoVK67ai6

Zakchamp Sep 14 @ 9:43 PM EDT

@kmorrowleong @jamiedunc3 Yeah my tweet was unintentionally trying to trap you for sure. :) #TCMChat

MFAnnie Sep 14 @ 9:43 PM EDT

@MarkChubb3 And that is a big shift for some teachers. We find using #NoticeWonder to LaSW helps focus more on evidence. #TCMchat

MissLori_B Sep 14 @ 9:43 PM EDT

Q4 I like that the end of the bars are aligned on the left side to help make accurate comparisons #TCMChat

jamiedunc3 Sep 14 @ 9:43 PM EDT

@Zakchamp @kmorrowleong even an equation is an abstract rep of the work which can be connected to other student work #tcmchat

Zakchamp Sep 14 @ 9:43 PM EDT

This is beautiful - Just beautiful. #TCMChat https://t.co/WoibdQshfH

davidwees Sep 14 @ 9:42 PM EDT
A5: I use student work to inform my future plans with students. Not "What's wrong?" but "What's next?" #TCMchat https://t.co/1My3WAe9Iw
- TCM_at_NCTM - Moderator Sep 14 @ 9:40 PM EDT
  
  Q5 In what other ways do you use your student’s work to assess their fluency and understandings? #TCMchat https://t.co/YpoVK67ai6

MarkChubb3 Sep 14 @ 9:44 PM EDT

@MFAnnie That is an easy way of transitioning! #TCMchat

janetdnuzzie Sep 14 @ 9:44 PM EDT

A4: Next? Maybe provide a set of partitioned # lines and prompt the student to justify w/ another tool #TCMChat https://t.co/qMshVVKUH4

TCM_at_NCTM - Moderator Sep 14 @ 9:30 PM EDT

Q4 What insights do you have into Michael’s mathematical thinking? #TCMchat https://t.co/IUnXYJzozj

Zakchamp Sep 14 @ 9:44 PM EDT

I hope we all become @davidwees when we grow up. #TCMChat

MarkChubb3 Sep 14 @ 9:45 PM EDT

The best assessments come from me listening... me observing... me questioning having conversations... In-the-moment stuff!!! #tcmchat

mathcoachrivera Sep 14 @ 9:45 PM EDT

@davidwees @TCM_at_NCTM Yes, tells me which models kids use to build mathematical understandins and shows common misconceptions #TCMchat

PiffQ Sep 14 @ 9:45 PM EDT

A5. Depends on the concept, but generally things like decomposing numbers, applying place value or properties flexibly #TCMchat

janetdnuzzie Sep 14 @ 9:45 PM EDT

How does this definition of fluency impact work w/fact fluency? #PISDMathChat #ElemMathChat #TCMChat https://t.co/TDGItPSkos

TCM_at_NCTM - Moderator Sep 14 @ 9:40 PM EDT

Properties of fluency #TCMchat https://t.co/dnIEWrS6AB https://t.co/J1qQYe2zyQ

MFAnnie Sep 14 @ 9:45 PM EDT

@MarkChubb3 Yes. Wonder esp gives new language to what were judgements. "She rushed" becomes "I wonder if she rushed". Big diff. #TCMchat

zack_hill Sep 14 @ 9:46 PM EDT

A5 I think level of efficiency is often evident in students work, but not always. Still need to carve out the time to talk to S's. #TCMchat

Zakchamp Sep 14 @ 9:46 PM EDT

Talk to kids, find out what they know, & adjust your instruction based on that info. That's teaching. #TCMChat https://t.co/GNzIDkyhoH

MarkChubb3 Sep 14 @ 9:45 PM EDT

The best assessments come from me listening... me observing... me questioning having conversations... In-the-moment stuff!!! #tcmchat

zack_hill Sep 14 @ 9:46 PM EDT

A5 I think level of efficiency is often evident in students work, but not always. Still need to carve out the time to talk to S's. #TCMchat

kmorrowleong Sep 14 @ 9:46 PM EDT

@Zakchamp @jamiedunc3 But to get philosophical, mathematics does not really exist without any representations. #TCMchat

MFAnnie Sep 14 @ 9:47 PM EDT

@MarkChubb3 No doubt you are listening TO the students, not listening FOR specific things. Makes assessment way more useful. #TCMchat

MarkChubb3 Sep 14 @ 9:47 PM EDT

@Zakchamp After... if you have time... I'd love some feedback on my thoughts: https://t.co/MBcZVAyeao #TCMchat

Zakchamp Sep 14 @ 9:47 PM EDT

@kmorrowleong @jamiedunc3 Trap coming...I agree, but when kids are solving a problem on their own, do they "need" a representation? #TCMChat

Zakchamp Sep 14 @ 9:48 PM EDT

@MarkChubb3 Will do pal. #TCMChat

MarkChubb3 Sep 14 @ 9:49 PM EDT

@MFAnnie Big difference here! We can learn a lot when we listen interpretively, not evaluatively!!! #TCMchat

TCM_at_NCTM - Moderator Sep 14 @ 9:50 PM EDT

Q6 As teachers we have to make choices. #TCMchat https://t.co/oUUa9LpFY5

kmorrowleong Sep 14 @ 9:50 PM EDT

@Zakchamp @jamiedunc3 There IS a representation. What you mean is, does T need to see it? #TCMchat

MFAnnie Sep 14 @ 9:51 PM EDT

@Zakchamp @kmorrowleong @jamiedunc3 It's like writing. Do we need to write in math? Sometimes helps you learn. Another tool. #TCMchat

Zakchamp Sep 14 @ 9:52 PM EDT

@kmorrowleong @jamiedunc3 YES!!! And I'd add, does the representation need to be clear to me (the teacher) or to the student. #TCMChat

janetdnuzzie Sep 14 @ 9:52 PM EDT

A5: We compare their work to our answers to #PLC Question 2 "How will we know when they've learned it?" #TCMChat https://t.co/s8fQuhdxY5

TCM_at_NCTM - Moderator Sep 14 @ 9:40 PM EDT

Q5 In what other ways do you use your student’s work to assess their fluency and understandings? #TCMchat https://t.co/YpoVK67ai6

drkchilds Sep 14 @ 9:52 PM EDT

A6: I think the key is that assessments are on-going & are a natural part of the teaching/learning process & not a separate “thing” #TCMchat

MFAnnie Sep 14 @ 9:52 PM EDT

@Zakchamp Wish Ts could do more of that and less writing/assembling their own curriculum. #TCMchat

MFAnnie Sep 14 @ 9:53 PM EDT

A6: Need to make time for doing enough of this sort of assessment that Ts get better and more efficient at it. Big pay off. #TCMchat

kmorrowleong Sep 14 @ 9:53 PM EDT

@Zakchamp @jamiedunc3 What does the Twitter audience think? Does the T NEED to see a representation? #TCMchat

Zakchamp Sep 14 @ 9:54 PM EDT

@MFAnnie Me too. It's easy for me (not currently in the classroom) to say that. I get that the reality is sometimes very different #TCMChat

MarkChubb3 Sep 14 @ 9:55 PM EDT

"T's can't always assess in this much detail" Wonder if this comes to time, or our own understanding of the mathematics? MK4T? #tcmchat

janetdnuzzie Sep 14 @ 9:55 PM EDT

A6: Strategically chosen prompts for exit tickets could yield valuable real-time data! #TCMChat https://t.co/FjD2b4mNHI

TCM_at_NCTM - Moderator Sep 14 @ 9:50 PM EDT

Q6 As teachers we have to make choices. #TCMchat https://t.co/oUUa9LpFY5

MFAnnie Sep 14 @ 9:55 PM EDT

@PiffQ @MarkChubb3 For sure. But need to learn to dig into Ss thinking eventually, so make moments where that is the goal. #TCMchat

jamiedunc3 Sep 14 @ 9:56 PM EDT

@Zakchamp @MFAnnie I think using the framework of the #5practices helps immensely with this. #tcmchat

MrBinfield Sep 14 @ 9:56 PM EDT

@kmorrowleong @Zakchamp @jamiedunc3 it depends on who I’m talking to. Some Ss no, some yes. Depends on what they say/do each day #TCMchat

MrTippin Sep 14 @ 9:56 PM EDT

Q6: At the elementary level, interim assessments are the natural fit for rigorous analysis. In class its math convos for insight. #TCMchat

Zakchamp Sep 14 @ 9:57 PM EDT

@MrBinfield @kmorrowleong @jamiedunc3 I think this is an important point. Thanks for sharing! #TCMChat

MarkChubb3 Sep 14 @ 9:57 PM EDT

@PiffQ @MFAnnie How might this differ from what I said? Curious what you mean here? #TCMchat

zack_hill Sep 14 @ 9:57 PM EDT

A6 I think the critical areas pages of the CCSSM could possibly give some direction here. #TCMchat

MathMileMarkers Sep 14 @ 9:58 PM EDT

Ideal approach getting Ss reasoning about numbers and where they live on the number line. #tcmchat https://t.co/MgTVJiuct5

Zakchamp Sep 14 @ 9:14 PM EDT

A2: 5/8 is 1/8 more than a half but 6/10 is only 1/10 more than a half. So 5/8 is greater. #TCMChat

MFAnnie Sep 14 @ 9:58 PM EDT

@Zakchamp And for many, that describes teaching language arts, but not math. They need to look more similar than different. #TCMchat

jamiedunc3 Sep 14 @ 9:59 PM EDT

@zack_hill That's what I was think too #tcmchat

kmorrowleong Sep 14 @ 9:59 PM EDT

@jamiedunc3 @Zakchamp @MFAnnie I agree, Jamie. I work a with teachers on Anticipation. It takes a lot of experience to do it well. #TCMchat