Elementary math chat is a weekly math chat where participants come to discuss best practices, examine student work, explore routines for reasoning and research that guides and supports pedagogy centered on problem and student based learning.
Welcome to #elemmathchat! We are so glad you joined us tonight as we talk about developing mathematical comprehension. Introduce yourself by telling us your name, where you are from, and a little about your job. Don't forget to use the hashtag #elemmathchat.
Welcome to #elemmathchat! We are so glad you joined us tonight as we talk about developing mathematical comprehension. Introduce yourself by telling us your name, where you are from, and a little about your job. Don't forget to use the hashtag #elemmathchat.
Andrew from Northern Indiana, where the temperature hit 70 for first time since October! I'm an instructional coach for k-5, teaching all subjects #elemmathchat
Q1 Let's start out by doing a little mental math. If you had $1.25 for every time a student missed a problem and you said, "If only they would read!", how much do you estimate you would have earned. Justify your solution. :) #elemmathchat
A1 About $2,500. I estimated that each month of the school year I probably said it at least 9 times, so I rounded 9 x 9 up to 100. I taught for 20 years, so 100 x 20 = 2,000, 2,000 x $1 = $2,000, plus 1/4 of 2,000 is $500. Really thought it would be higher! #elemmathchat
Q1 Let's start out by doing a little mental math. If you had $1.25 for every time a student missed a problem and you said, "If only they would read!", how much do you estimate you would have earned. Justify your solution. :) #elemmathchat
RT Q1 Let's start out by doing a little mental math. If you had $1.25 for every time a student missed a problem and you said, "If only they would read!", how much do you estimate you would have earned. Justify your solution. :) #elemmathchat
I hear many teachers using phrases like this.
But I wonder if the issue is that they can't read, or if they are just too eager to start solving a problem that they jump to a solution strategy before they know what the problem is asking.
They DO before they THINK!
#elemmathchat
a1: If a student response was worth $1.25 I'd estimate I'd have around (25 students respond at least 3 times a day for 180 days multiplied by 10 years =around $17,000) definitely on the low side #elemmathchat
Welcome to #elemmathchat! We are so glad you joined us tonight as we talk about developing mathematical comprehension. Introduce yourself by telling us your name, where you are from, and a little about your job. Don't forget to use the hashtag #elemmathchat.
You're right. They are not reading into the problem/situation. I think it's not a reading issue but one of knowing how to get the info they need from it and knowing how to use it. #elemmathchat
RT Q1 Let's start out by doing a little mental math. If you had $1.25 for every time a student missed a problem and you said, "If only they would read!", how much do you estimate you would have earned. Justify your solution. :) #elemmathchat
A1 1,250
I estimated it to be 1,000 times. First I multiply the 1 whole. Then I did the 0.25 I k ow that 500 times 0.25 is &125. Then I double that up. #elemmathchat
Q1 Let's start out by doing a little mental math. If you had $1.25 for every time a student missed a problem and you said, "If only they would read!", how much do you estimate you would have earned. Justify your solution. :) #elemmathchat
If we keep having the same problem.... and keep telling students to do the same things... and it's still not working.............
Maybe we need to get to the heart of the problem!
#elemmathchat
Q2 What impact do processes such as CUBES or similar "box this, underline that" processes have on mathematical comprehension? (Not familiar with CUBES? Google it...) #elemmathchat
These processes in isolation can strip the mathematical thinking from an activity. I do think there is a way to incorporate these techniques into activities with deep math thinking though. #elemmathchat
Q2 What impact do processes such as CUBES or similar "box this, underline that" processes have on mathematical comprehension? (Not familiar with CUBES? Google it...) #elemmathchat
Q2 As an interventionist working with students from many different classrooms and grade levels, I often saw students just box and circle as the "read". I'd ask them why they underlined the question, and they couldn't tell me. This is NOT understanding! #elemmathchat
RT Q2 What impact do processes such as CUBES or similar "box this, underline that" processes have on mathematical comprehension? (Not familiar with CUBES? Google it...) #elemmathchat
#elemmathchat friends, how many people would it take if they contributed $5 to fully fund this project? What would the impact be on a Ss future? Feel free to share :) Thnx for support Ascending to New Heights https://t.co/jfwByRc6q8
A2: I believe our students dont conceptually understand when we search for key words or phrases. We need more thinking about the problem and more making sense of situation. #elemmathchat
Q2 As an interventionist working with students from many different classrooms and grade levels, I often saw students just box and circle as the "read". I'd ask them why they underlined the question, and they couldn't tell me. This is NOT understanding! #elemmathchat
A1 1,250
I estimated it to be 1,000 times. First I multiply the 1 whole. Then I did the 0.25 I know that 500 times 0.25 is $125. Then I double that up. Thinking again if it is for every year I have taught it must be higher #elemmathchat
Q1 Let's start out by doing a little mental math. If you had $1.25 for every time a student missed a problem and you said, "If only they would read!", how much do you estimate you would have earned. Justify your solution. :) #elemmathchat
A2 Sometimes Ss just circle all numbers in a problem or underlining everything and they aren’t understanding what is the important information to solve the problem #elemmathchat
190 day contract for 11 years equals 2,090 days. Multiply that by 3 times a day that I've said it and that is 6,270 times. 6270 x 1.25 = $7,837.50!! #elemmathchat
RT Q1 Let's start out by doing a little mental math. If you had $1.25 for every time a student missed a problem and you said, "If only they would read!", how much do you estimate you would have earned. Justify your solution. :) #elemmathchat
A2
Ideally, we want kids to SLOW down and think more. Notice/Wonder does this. Boxing stuff/underline things can become another procedure kids are mindlessly doing.
I would always prefer kids thinking more!
#elemmathchat
A2 I think when we ask S's to box this or underline that, we are taking away from them constructing their own meaning. It's a false level of support and when it's taken away and S's are asked to problem solve, they struggle and don't know where to start #elemmathchat
A2: I've always thought that those "strategies" are not very effective if students don't actually know how to find the "important" information. I think we need to let them explore and discover their methods to solve real life problems when introducing new concepts. #elemmathchat
Q2 What impact do processes such as CUBES or similar "box this, underline that" processes have on mathematical comprehension? (Not familiar with CUBES? Google it...) #elemmathchat
Right! Rote process that ss can follow and still get the wrong answer because they didn’t take the time or don’t have the skills to visualize and understand the problem #elemMathchat
A2: It furthers the idea that math is this magical code thing, and if you only decipher it, you'll know what to do. Sense-making plays no part in this whatsoever. #ElemMathChat
A2: I also encourage teachers to write math problems based on stories students are reading so they don't struggle with character names and they have a context. #elemmathchat
Q2 What impact do processes such as CUBES or similar "box this, underline that" processes have on mathematical comprehension? (Not familiar with CUBES? Google it...) #elemmathchat
A2 NONE all we want is student to understand the problem and think I it through. Creating models for their problems is more powerful to help with understanding #elemmathchat
RT Q2 What impact do processes such as CUBES or similar "box this, underline that" processes have on mathematical comprehension? (Not familiar with CUBES? Google it...) #elemmathchat
Q1 Let's start out by doing a little mental math. If you had $1.25 for every time a student missed a problem and you said, "If only they would read!", how much do you estimate you would have earned. Justify your solution. :) #elemmathchat
Oooh @pearse_margie I saw your response coming! I often share your blog post with proponents of CUBES. I’m not always the most popular girl! 😀 our students and their learning are worth it! #elemmathchat
I like the idea of giving kids a calculation and some word problems with the same numbers and having them work out which problem can be solved with the calculation. #elemmathchat
Q3 Literacy folks know there is a strong connection between reading and writing. How could we incorporate writing to help students better comprehend word problems? #elemmathchat
A3: We use the Daily three rotation model in math. We use Math Writing as a way for learners to share their understanding. This happens through writing, poster making, video creation, or they create a animation. #elemmathchat
A3 If a student can write a word problem, they can likely solve them. We need to spend as much time having students write problems as solving them. So easy to differentiate, because you can give different students different equations. #elemmathchat
A2: I think this is a good way for students to get started. As their comprehension grows they will be able to do it without thinking and look at the entire question without getting confused. #elemmathchat
Q1 I’m so over CUBES, RUBIES, etc.. I find it’s the comprehension of the problem not the actually art of reading, circling, underlining, boxing, etc..that best support students making sense of the problem #elemmathchat
RT Q1 Let's start out by doing a little mental math. If you had $1.25 for every time a student missed a problem and you said, "If only they would read!", how much do you estimate you would have earned. Justify your solution. :) #elemmathchat
A3: I think it's essential to ask them to document their thinking, justify their answer. I think somebody just said it here, if they can't represent it, they may have not understood it!! #ElemMathChat
Q3 Literacy folks know there is a strong connection between reading and writing. How could we incorporate writing to help students better comprehend word problems? #elemmathchat
RT Q3 Literacy folks know there is a strong connection between reading and writing. How could we incorporate writing to help students better comprehend word problems? #elemmathchat
Problem:
Kids learn a skill in isolation
Then they are given "problems"
Teachers notice kids not reading the problem
Maybe the problem stems from the fact that kids aren't doing enough thinking AS they are learning the concept in the first place!!
#elemmathchat
Agree! I do think there can be benefit if the strategy is taught well. Just like highlighting when reading text. These are skills to be explicitly taught, not just mentioned without connection #elemMathchat
A3: Here is example of animation our learners have made to show learning. IF they can write and explain their thinking they start to engage with it differently. https://t.co/ilqbDdDDzJ#elemmathchat
A3 I also like to give students problems with lots of information and no question. They get to write their own question and decide what information they need to solve it. https://t.co/2IgEchf3pO#elemmathchat
A3 In writing in Math Ts can see the organization of the S’s thinking, just as they organize their ideas in writing. Having students use writing to explain their thinking allows Ss to also see their steps to a solution #elemMathchat
A3: Problem solving is messy. Ss must test ideas and revise ideas before coming to any conclusions. I encourage my Ss to think of this messiness as their ‘first draft.’ Then, I ask them to organize their thinking more logically so that it can be shared with others. #elemmathchat
A3: We need to consider that writing can be a tool to LEARN mathematics, not just to show your work. Writing and organizing can help with understanding. #ElemMathChat
I could not agree more! I find more and more that my students do so much “math” rotely, without any connection to mathematical reasoning. #elemmathchat
I agree! It is a way for teachers to support the learners. We use our math writing as a check before they get to prove mastery of the standard. #elemmathchat
A3 I do something similar by giving them lists of data and then pose different questions about it each day or let them write their own questions. Pushes them to think about the situation, select data, decide on strategy... #elemmathchat
A3 I also like to give students problems with lots of information and no question. They get to write their own question and decide what information they need to solve it. https://t.co/2IgEchf3pO#elemmathchat
A2: CUBES and other such procedures shortchange student thinking... they also assume all problems fit nearly into that kind of format. Of course, the best problems don’t... more often than not, maths is a bit messy- that’s what makes it cool! #elemmathchat
A3- I have been working on restating the question as a statement. This is so challenging for students! Using the same strategy my ELA partner uses helps. I tell my Ss we are making a math and ELA sandwich! #elemmathchat
A3: Here is a new thing I just came across. It is called the 3-ACT TASKS. This is awesome to get learners thinking differently about math. https://t.co/0NL0U7lZ6j#elemmathchat
Teaching students to write problems without numbers. Passing to classmate who selects acceptable numbers to be used in problem. Third student reads, makes sense, & solves. Passed back to 1st student who shares with group how classmate solved using students thinking #ElemMathChat
A3 - Part 1: I think retelling and summarizing are great skills for students to make sure they are fully comprehending and understanding the problem. #elemmathchat
Q4 What happens when you take the numbers out of a problem? You get the numberless word problem movement! "Some girls entered a school art competition. Fewer boys than girls entered the competition." #numberlesswp@bstockushttps://t.co/MMw724wGWn#elemmathchat
That might not be a bad thing. What if other Ss #NoticeWonder about those stories? Could they pull out some math? Could their wonderings be possible questions? #ElemMathChat
If kids do "problems" after they've learned the skill... they learn to expect that the "problems" involve that skill.
Learn to multiply... then do some word problems that involve multiplication.
This actually teaches kids to ignore the contexts!
#elemmathchat
A3: Ss need to know that mathematical thinking is not done until they’ve adequately communicated their understanding (just as important as getting answer). Writing is not some add-on, but an integral part of communicating mathematical ideas #elemmathchat
A3- Part 2: previously, I’ve taught students to pull out key words, but it makes so much more sense to stress the fact that these are real-world scenarios and our students need to visualize these things actually happening. Also gives Ss purpose for learning skills. #elemmathchat
I just saw a template from Robert Kaplinsky that awards point for every attempt ss used to solve a problem if they reflect on it and what they learned from the attempt. I thought it was cool and promotes productive struggle. #ElemMathChat
A3: By students writing what they notice about a problem & what they wonder about before they start trying to solve is powerful.
Also being able to write your answer or solution helps focus on the what is being asked. #elemmathchat
Including opportunities for students to write problems and reflect on math learning are so important as well! If they can write problems they are more likely to understand the thinking behind problems they are solving. #elemmathchat
RT Q3 Literacy folks know there is a strong connection between reading and writing. How could we incorporate writing to help students better comprehend word problems? #elemmathchat
A3: I have a 4th grade teacher who does 2 Truths and a Lie. The Ss have to write about each answer. They then @Flipgrid their thinking. The final part is for them to create their own, then share. It has dramatically helped conceptual understanding! #elemmathchat
RT Q4 What happens when you take the numbers out of a problem? You get the numberless word problem movement! "Some girls entered a school art competition. Fewer boys than girls entered the competition." #numberlesswp@bstockushttps://t.co/MMw724OhNV#elemmathchat
Yes and this is where publishing companies drive me crazy.
One page of multiplication problems, followed by 3 word problems on, guess what, multiplication. No thinking there
#elemmathchat
If kids do "problems" after they've learned the skill... they learn to expect that the "problems" involve that skill.
Learn to multiply... then do some word problems that involve multiplication.
This actually teaches kids to ignore the contexts!
#elemmathchat
That’s a good start... you put up one of their stories and then have a discussion about what kinds of questions could we ask about this situation? That’s good ELA and math work at the same time! 😊#elemmathchat
#elemmathchat A2: I see a keyword strategy destroy statistics students at university. They see the word "relationship" and think they have to calculate a correlation.
A4: So nice to help kids visualize a story, and the relationships in the story, without them having to focus on what to DO with the numbers. #ElemMathChat
I think we really need to consider WHY we use contexts.
A) to show kids real life times math is used
B) help make math more interesting
C) help students use sense-making strategies
Personally, I think only one of these is an important aspect of contexts!
#elemmathchat
Kinda takes the thinking out of it, right? If the worksheet is titled "Multiplication Problems" what are they chances a problem will require division? #elemmathchat
Q4 What happens when you take the numbers out of a problem? You get the numberless word problem movement! "Some girls entered a school art competition. Fewer boys than girls entered the competition." #numberlesswp@bstockushttps://t.co/MMw724wGWn#elemmathchat
A4- I love doing this bc it forces Ss to slow down and understand the context. It is always amazing what they understand when the quantities are not stated. It exposes a habit of answer getting and allows an opportunity to think before the Do #elemmathchat
Q4 What happens when you take the numbers out of a problem? You get the numberless word problem movement! "Some girls entered a school art competition. Fewer boys than girls entered the competition." #numberlesswp@bstockushttps://t.co/MMw724wGWn#elemmathchat
A4: removing numbers also reinforces the notion that while math may provide insights related to a problem, there may be non-mathematical factors that are relevant #elemmathchat
A4: Love numberless word problems. I definitely need to work them into my instruction more! Force students to focus on the context and THINK. #elemmathchat
Or, throw out a problem before you have taught the skill and see what happens. Many students will figure out a creative solution despite not having the skill formally presented. So cool to see how Ss think when they are given the opportunity. #elemmathchat
Q4 The comprehension is finally addresses versus what to circle, underline, box, cross out.. It’s like Dr. Phil says, “How’s that working for ya!” #elemmathchat
Q4 What happens when you take the numbers out of a problem? You get the numberless word problem movement! "Some girls entered a school art competition. Fewer boys than girls entered the competition." #numberlesswp@bstockushttps://t.co/MMw724wGWn#elemmathchat
And they're SO easy to do - tape over the numbers, or put boxes over them on the smartboard, or whatever works with the "tech" you're using. The conversations change immediately (right after, "Hey, wait! There aren't any numbers!). #ElemMathChat
A4: Talking with some teacher aides over a few beers about this. They were completely blown away by the idea. Completely makes sense for making sense before understanding the purpose of the numbers. #elemmathchat
A5 Drawing pictures or models helps students develop the ability to visualize. When I read "4 baskets with 3 apples in each basket", I automatically form a mental image. Kids need to draw to develop that skill. https://t.co/c2xtNcWDbV#elemmathchat
A4
Numberless word problems can help us think about problem situations more than operations. Best thing about these, is that kids are learning about ANY problem like this one, instead of just filling in an answer and moving on.
#elemmathchat
A3Written expression in math is completely underestimated. I am realizing that more and more with my students.These are S's who struggle with math but then asking them to articulate, reason and justify their thinking opens up their understanding to a whole new level #ElemMathChat
As we start our numberless word problem, we move to “What did you notice?” And “What do you wonder?” It’s amazing to see what happens from here! #elemmathchat
RT Q5 Visualization is another reading comprehension strategy. How do we help students visualize the math a problem is asking them to do? #elemmathchat
A5: Give students manipulatives to "act out" the problem. Write problems that they can actually act out. I know a kindergarten class who had story problem theater. #elemmathchat
A4: This is where the comprehension really sets in! I like students to visualize and make that “movie in your mind” as they work to understand the wordless problem. What does fewer boys than girls look like?#elemmathchat
A5: Can I answer Q5 by saying "see Q4"? Numberless word problems are a great way to encourage Ss to "make a movie in their mind", since they aren't focused on calculations. #ElemMathChat
I am reminded of @MFAnnie experiment- present the story without math context and see what Ss do, then present another time with math context. Is the fact it is math what throws Ss off? #elemmathchat
A5 I taught Ss to do this in multiple reads. Visualize in parts. Draw/plan parts of story problem and what it “looks like” Ex Jack has 8 eggs. Rita has 13 more than Jack. What does each part of that look like? #elemMathchat
The first step is to give them the time to visualize and the opportunity to share what they have visualized and opportunities to revise their thinking. It is a habit that must be formed. #elemmathchat
I walked into a 4th gr classroom & wrote 1/2 + 1/4 on their board then left. I could hear the kids chattering about the different denominators before I made it to the door #elemmathchat
Yes! What I see is students that erase their answer if I ask, "why do you think that?" They assume they are wrong! It's a mindset that I've been trying to change. Working with upper elementary is a little harder b/c they come with those mindsets already. #ElemMathChat
A5- I like to ask Ss to explain what is happening. If this was a YouTube video, what would we see? How could we represent that mathematically? Visualization is so important to comprehension. #elemmathchat
A5
A strategy I've been working with many teachers lately is Visualize, Verbalize, Verify.
We've seen lots of success with this to help students make sense of all kinds of problems!
#elemmathchat
If kids do "problems" after they've learned the skill... they learn to expect that the "problems" involve that skill.
Learn to multiply... then do some word problems that involve multiplication.
This actually teaches kids to ignore the contexts!
#elemmathchat
A5
A strategy I've been working with many teachers lately is Visualize, Verbalize, Verify.
We've seen lots of success with this to help students make sense of all kinds of problems!
#elemmathchat
A5: Draw a picture just to get the comprehension of the problem. It seems so simple but it helps see what students are not understanding about what the problem is all about. #elemmathchat
That experiement is still sort of a thing, except that @NCTM turned of access to our blogs (where I wrote about it). I'll work on making that available somewhere else. And happy to send the problem "set" to anyone who wants to try it. #ElemMathChat
A5: We need to continually ask Ss what they see when they close their eyes. We have Ss tell us they see nothing or they ask us were they supposed to see something. The same is true of ELA. Close your eyes, what do you see when a story is being read. Great connection #elemmathchat
I think that is key, Donna. We take a lot of our mathematical thinking for granted and forget to explicitly teach/model it. Guilty as charged!! #ElemMathChat
A6: I have given the answer to the question and asked Ss to explain how to get the answer or why it is reasonable/logical. I have also given them the equation and asked them to write a story for it. #elemmathchat
A6 I love her to blow my Ss minds by giving them the answer! I tell them I'm not interested in the answer, I'm interested in their strategies and justifications. #elemmathchat
Good news is that that is easy to change. If you ALWAYS ask "How do you know?", they quickly figure out that you will ALWAYS ask, regardless of right or wrong. Ss are pretty adaptable that way. #ElemMathChat
In reply to
@MathCoachCorner, @joellealrce, @LanaSteiner4
A6: help Ss feel accountable for everyone’s learning. We’re not successful unless everyone’s ?s have been resolved. Having that as a goal shifts the nature of the communication #elemmathchat
A6 I focus heavily on using manipulatives and sharing math thinking in our discussions but my biggest task lately has been modeling written thinking. S's can talk all day about their thinking but ask them to justify and reason mathematically in writing. Eye opening #ElemMathChat
You do it enough, and they eventually give the answer, give you a look, and then say, "And I know that because...." They know darn well you're doing to ask, so they just skip the part where they wait for you to say anything! #ElemMathChat
That is awesome. They sometimes get to the right answer by chance, without sound mathematical reasoning. If they know the process/thinking is the most important aspect, they will always try to get that right! #ElemMathChat
@MFAnnie I recently did an assignment for s class I was taking on coding. It was a ‘computational thinking autobiography.’ I used the #noticewonder strategy as a structure for the entire assignment. #elemmathchat
@numbertalks Number Talks by Sherry Parrish has been rewarding this year with multiple K-4 classrooms @WestlakeSchools. I tried to get a student to agree with my wrong answer. She said I'm not going to tell you that you are wrong, I'm going to CONVINCE you. #elemmathchat
A6: I give students the answer. That clearly shifts the focus from "the answer" to other things. @JSchwartz10a gives them two or three answers and asks, "What would the question need to be for the answer to be X? Y? Z?" #ElemMathChat
A6
The best strategy to help your kids "comprehend" more... is to raise the level of cognitive demand (which doesn't mean making harder tasks - but expects kids to think more... make more connections... notice relationships.....)
Stick to the right side of this:
#elemmathchat
A6: Number Talks have definitely helped my students have the vocabulary and confidence to defend their answers. This also helps them when writing about their math thinking. I need to do this more! #elemmathchat
@MathCoachCorner@MFAnnie@robertkaplinsky How common is it for Ss to need time to ‘consolidate’ their learning after being engaged in cognitively demanding problem solving tasks? Do Ss often need time to go back after and review their process to solidify thinking? #elemmathchat
A6 I love for students to share what they are visualizing with their thinking partner. Students conversations tell me so much about their understanding. I use the same strategies for mathematical comprehension as I do for reading. #Elemmathchat
