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 dusty Joined: Nov 2007 Posts: 547 Senior Member
dusty

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explain thinking during math
03-11-2017, 07:25 AM
 #1

The math standards expect first graders to not just solve math problems or number stories but to also be able to explain their thinking. How much should I be expecting from my first graders when wanting them to explain their thinking?
Ex; for a comparison # story "he has 2 dogs and 8 cats. How many more cats than dogs?", should i be expecting them to just show their thinking by either drawing a picture of 2 dogs/8 cats and circling the 6 extra cats or writing the subtraction sentence: 8 - 2 = 6? Should i be expecting much more, such as writing sentences explaining their steps: "First I drew 8 cats. Next I drew 2 dogs. Then I crossed out the same amounts and circled the extra cats" or is that expecting way too much for some first graders? Should I be differentiating my expectations depending on the student? We do this aloud by orally sharing different ways we could find the same answer but I'm not sure if they should be writing sentences explaining their actual steps but that takes some of my first graders way too long.

Thanks for any guidance

 Keltikmom Joined: Mar 2013 Posts: 6,293 Senior Member
Keltikmom

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Showing thinking
03-11-2017, 09:54 AM
 #2

We use "the big three": either the algorithm (just numbers), a drawing, or words. As long as you can track how they attempted to solve the problem, it is acceptable.

 Sbkangas5 Joined: Aug 2012 Posts: 5,596 Senior Member
Sbkangas5

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03-11-2017, 03:35 PM
 #3

I have my kindergartners explain their thinking when we solve word problems. Here are some examples of things I often hear.

I used the number line. I started on 8 and then went backwards four because the problem said they started with 8 and then four went away.

I used my fingers. (I then ask how they used their fingers, and hope for an explanation!).

I used the tens frame. First I put 8 on the tens frame, and then I took four off because it said four went away.

And my very favorite - I used my brain.

My high kids can give a very detailed explanation of their thinking. My grade level kids can tell me what they did, but can't always tell me why without some prompting.

My low kids can't even solve the problem.

I think I'd have pretty high expectations that a first grader could orally explain their answer. Writing it is a whole different ballgame.

 dusty Joined: Nov 2007 Posts: 547 Senior Member
dusty

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03-11-2017, 04:05 PM
 #4

Thank you Keltikmom Sbkangas5. Both of your responses were very helpful. Sbkangas5 -- those examples were very helpful. I laughed at "My low kids can't even solve the problem." because I can definitely relate to that. So maybe I should have high expectations for my first graders to explain their thinking but not necessarily expect them to write sentences explaining their thinking. That makes a lot of sense, I'm just trying to figure out what most 1st grade teachers expect for this standard: explain their thinking orally/pictures and maybe the higher kids explain by writing OR expect all of my first graders to explain their thinking by writing sentences.
thanks again, would love to hear anymore thoughts especially on the first grade place value standard that includes "…relate the strategy to a written method and explain the reasoning use." I'm trying to understand what they mean by that statement (relate strategy to a WRITTEN method).

Last edited by dusty; 03-11-2017 at 04:41 PM..

 irises Joined: Jul 2008 Posts: 2,675 Senior Member
irises

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Dusty
03-12-2017, 06:39 PM
 #5

my first grade team mate and I have often talked about this very thing. We both have our students draw a picture and we work up to writing the subtraction equation using the phrase "finding the difference." At first we accept addition equations (counting up) but then show them why it is subtraction.
As others have said, many though not all explain their strategies orally. While oral expression may be hard for some, expecting a
written explanation would be harder. After all, we are evaluating their math knowledge/strategies not their ability to explain in writing...the encoding alone would bog many down.

 fran123 Guest
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explaining
03-13-2017, 04:13 PM
 #6

I agree with PP's! Just wanted to add, for your example, I would accept the simplest, most accurate answer, "e.g. 8 is 6 more than 2." or "I started at 2 and counted up to 8 and I got 6." I do NOT expect them to write a "How-To" procedural text for solving a math problem.

Doing Number Talks is the BEST thing for having kids explain their math strategies! Before they write it, they must be able to say it!

 k28 Joined: Jul 2014 Posts: 548 Senior Member
k28

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03-16-2017, 04:19 AM
 #7

I went to a training this summer about number talks. In theory, it is a great idea. It takes time and training. That is reality and we don't often have time.

You can use sentence starters to help too.

 fran123 Guest
fran123

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number talks
03-16-2017, 03:25 PM
 #8

i respectfully disagree re: number talks! they only take us about 6 minutes a day and give you so much bang for your buck. i've never had any formal training...just watched a couple youtube videos! lol

 gardener5 Joined: Sep 2008 Posts: 1,352 Senior Member
gardener5

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love number talks
03-19-2017, 08:44 AM
 #9

Very worthwhile and let's children work at their level of understanding

 Munchkins Joined: Nov 2010 Posts: 15,467 Senior Member
Munchkins

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Number talks
03-19-2017, 10:27 AM
 #10

Is this a program you purchase, or can I find examples online? We use GoMath, which includes a "Write Math" problem each day. But we could always use more math talk! Thanks!

 fran123 Guest
fran123

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number talks
03-19-2017, 02:54 PM
 #11

It's not a curriculum, but a math routine that you can incorporate into your math block, or outside it (we do ours during Morning Meeting). If you google it, you will find SO much information. There is also an official "Number Talks" books that you can find on Amazon, but it is expensive.

 Eliza Joined: Jun 2008 Posts: 132 Full Member
Eliza

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Number Talks
03-19-2017, 04:38 PM
 #12

I agree that using number talks is hugely beneficial for all students. In the beginning your struggling students may not be able to answer the question, but they'll be listening and learning and trying some of the strategies their peers are using. It's the most powerful 5-10 minutes of my math day.

You can look online and find some, but for a complete overview, here's a link to the book.

Number Talks

 Munchkins Joined: Nov 2010 Posts: 15,467 Senior Member
Munchkins

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03-19-2017, 05:30 PM
 #13

Thank you!

 linda2671 Joined: Jul 2006 Posts: 23,024 Senior Member
linda2671

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I'm late getting in on this conversation, but
04-02-2017, 01:15 PM
 #14

we talk about it to each other and then share. When we are talking about a problem, I tell them to discuss it with their elbow buddies. I give them a minute or two to discuss it, and then I call on a few kids to tell what they discussed. Then, we write an acceptable answer on the board and the kids write it and draw a picture to go with it if applicable.

 seenthelight Joined: Feb 2014 Posts: 619 Senior Member
seenthelight

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04-02-2017, 01:43 PM
 #15

He has 6 more cats than dogs because 8-2=6. Is how we teach it,

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