Series Content Conversations: Strategies for ELLs: Engaging in Productive Struggle: Number Talks

Math.Practice.MP1

Common core State Standards

  • Math:  Math
  • Practice:  Mathematical Practice Standards
  • MP1:  Make sense of problems and persevere in solving them.

    Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, \"Does this make sense?\" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Download Common Core State Standards (PDF 1.2 MB)

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Math.Practice.MP3

Common core State Standards

  • Math:  Math
  • Practice:  Mathematical Practice Standards
  • MP3:  Construct viable arguments and critique the reasoning of others.

    Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Download Common Core State Standards (PDF 1.2 MB)

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Math.2.NBT.B.5

Common core State Standards

  • Math:  Math
  • 2:  Grade 2
  • NBT:  Number & Operations in Base Ten
  • B:  Use place value understanding and properties of operations to add and subtract
  • 5: 
    Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Download Common Core State Standards (PDF 1.2 MB)

Engaging in Productive Struggle: Number Talks

Lesson Objective: Explore subtraction strategies through student-led number talks
Grade 2 / Math / ELL
Math.Practice.MP1 | Math.Practice.MP3 | Math.2.NBT.B.5

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Discussion and Supporting Materials

Thought starters

  1. What tools does Ms. LaCour use to support her ELL students?
  2. What are the benefits of having students lead the number talk?
  3. How do number talks encourage students to try new math strategies?

118 Comments

  • Private message to Felise DeCastro

What a fabulous learning community!  I appreciate how Ms. LaCour has built in so many routines for the students to learn from each other and engage in the productive struggle.  This piece around strengthening students' ability to take risks, make bloopers, and grow is critical.  The self-reflection at the end of the lesson also supports students becoming more self-aware of themselves as learners (I wish I had this type of instruction in elementary school).  Shout out to Acorn Woodland - what an amazing community of teachers and learners!  I was lucky enough to do my student teaching there many moons ago. 

Recommended (0)
  • Private message to Adam Orenstein

The math lesson looks great.  The teacher engages her students to solve a subtraction problem.  Instead of showing one method through lecture as if that method is the only way to subtract, she has students work in groups and try different strategies.  Then the students work together in their groups and evaluate each strategy.  What the teacher is doing is what I was trying to do in a new course at my school tried called quantitative reasoning developed by Carnegie Math Pathways.  That course involved a lot of group work and one of its goals is to teach the idea of productive struggle.  Namely students must struggle and work hard to solve a problem, as the teacher in the video was showing.  I really like how the teacher taught that it is also okay to make mistakes.  Mistakes are a part of productive struggle.  I wish somebody taught me that when I was younger.  This kind of encouragement is what I want to put towards my students when I teach.  I want my students to not give up and work hard.  I especially like how the teacher said she even makes mistakes.  This helps relate her to the students.         

Teaching to work together is important with the world as it is.  It is very easy to collaborate thanks to advances in technology.  Learning from each other and with each other is very engaging.

What also really stood out to me was the feedback with the sticky notes.  Students give each other feedback, even themselves if they want to, and what the class can do to make the lesson better on the sticky notes.  This will help students see how important feedback is and will help students learn how to give and receive constructive criticism.  We all can improve in many ways.  Feedback is how we learn to improve and fix what we did wrong.

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  • Private message to Sara Davis

I really liked that these students were told that they could solve the problem any way they wanted. For these students to use all the strategies they have been shown gives them power over their learning. Many times I have talked with teachers and their students can only do a problem one way to get the answer correct. This is limiting these students and they need to feel like they can do it however they feel comfortable. I also like the idea of a math talk. I have always thought that it is important for students to learn from each other and this is the perfect way to do that. It would work well for any level of student as well which is great.

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  • Private message to Daniel Riseman

Ms. LaCour is an inspirational teacher. I love how she empowers her students, allowing them to experiment with new strategies in small groups. Instead of forcing one way of calculating a subtraction problem, Ms. LaCour carefully watches as her students engage in a productive struggle to think of new ways to solve the problem. Ms. LaCour recognizes the vast potential of her students. As she says, "Students are going to learn a million times more from one another than just from a teacher providing input." By focusing on collaboration and teamwork, Ms. LaCour has created a compassionate and caring classroom. Students engage in academic conversations and debate; they never attack each other on a personal level. Rather, they support each other's thinking. Students recognize that they are all valued members of the learning community, "building [their] understanding together." 

It is wonderful that Ms. LaCour views student mistakes in a positive manner. According to Ms. LaCour, "Mistakes help us to learn." As a result, she has built a classroom in which students are willing to take intellectual risks and push themselves because they know that their teacher will always support them. Students are highly valued members of the classroom community, and following lessons, Ms. LaCour provides students the opportunity to provide feedback on how the lesson went. Through such self-reflection and constructive criticism, students view themselves as equals in the classroom. By truly valuing every student, Ms. LaCour has built an incredible learning community in which students communicate clearly and effectively with each other.

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  • Private message to Clare Sorokes

I loved that the students were encouraged to use as many strategies as possible. Often I find myself only teaching one method to solve problems when I should be celebrating different methods. I liked that sentence frames were provided and that students had pre-assigned roles in the discussions to keep everyone involved. I have been wanting to use post-it notes for exit tickets in my classroom and this was a great example of how I could incoporate them!

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Transcripts

  • Engaging in Productive Struggle: Number Talks Transcript

    +++ 00:00:00 +++
    GFX:
    Tch
    Teaching Channel
    Card:
    Engaging Students in
    Productive Struggle with

    Engaging in Productive Struggle: Number Talks Transcript

    +++ 00:00:00 +++
    GFX:
    Tch
    Teaching Channel
    Card:
    Engaging Students in
    Productive Struggle with
    Number Talks
    Lower Third:
    2nd Grade Math
    Monique LaCour: One, two, three, eyes on me.
    Class: One, two, eyes on you!
    Lower Third:
    Monique LaCour
    Acorn Woodland Elementary, Oakland, CA
    66 percent of students are ELLs
    Monique LaCour: My name is Monique LaCour, I teach second grade at Acorn Woodland Elementary in Oakland, California.
    Monique LaCour: Today, we're getting ready to have another Number Talk.

    +++ 00:00:29 +++
    Monique LaCour: So today's lesson was about building experiences for students around academic conversation, and exploring how to regroup in two places in a tricky subtraction problem.
    Monique LaCour: Go back to the Number Talk sentence frame, and we're going to read through those.
    Monique LaCour: Number Talks, they're a district-wide strategy that we're encouraged to use in support of Common Core.
    Class: I disagree with you, "blank," because "blank."
    Monique LaCour: It supports risk-taking, it supports creating a classroom culture in which students are striving to find many ways to solve a problem. The learning goals for the lesson we built together from the posters in our Introductory Time.
    Monique LaCour: So these are some things I want you to think about with math today. Okay? So number one--
    Class: Try new strategies.
    Monique LaCour: We were looking at academic conversation goals, and we were looking at mathematical process goals.
    Monique LaCour: This is just a quick reminder, when you do many strategies, it helps you to check your answer.
    Monique LaCour: The problem is 123 minus 65. There is a correct answer. However, within that problem--
    Card:
    Common Core State Standard
    Use strategies to subtract within 100
    Monique LaCour: -- it's like a rainbow, an array of ways that you can get there.
    Monique LaCour: We're going to take about three minutes to try to solve it as many ways as you can on your whiteboard. And then we're going to share out for the Number Talk. Okay, you guys, get started.

    +++ 00:01:56 +++
    Monique LaCour: I wanted them to be thinking about, "How many strategies can I use, and how can I support myself to grow as a mathematician?"
    Monique LaCour: All right, students, we are going to begin the Number Talk. As I walk around, and you're working in your Number Talk group, I'm going to be looking for people to be doing their jobs, okay? So the facilitator will be teaching and leading the talk.
    Monique LaCour: I let the students know that they would be going into their small groups, which we'd been practicing in.
    Student: Who would like to defend the answer?

    +++ 00:02:29 +++
    Monique LaCour: In walking around the groups, I could see very different qualities of work and struggles.
    Monique LaCour: Yeah, which strategy are you using, Jaida [ph?]?
    Jaida: Regrouping.
    Monique LaCour: You're going to do some regrouping, but I notice you're doing the equal signs next to them, and that's a different strategy that might use regrouping.
    Student: Well, that's another way to solve for this.
    Student: You put 123 on top.
    Student: Then put a line.
    Student: I know!
    Monique LaCour: Students are going to learn a million times more from one another, than just from a teacher providing input.

    +++ 00:03:01 +++
    Student: And then I crossed out the three, and made it to a 13, and then 13 minus 5 equals 8. So I got the answer, 58.
    Student: On top of the three, put 13.
    Monique LaCour: The gradual release of responsibility is, I think, a really important model for our classrooms today.
    Student: Two or three?
    Student: Three.
    Monique LaCour: The result is that you're building a culture in which students, no matter what the challenge, they're gonna believe that they can take it on, and they're gonna get what they need to sort through it.

    +++ 00:03:34 +++
    Student: How is it gonna be that if it's bigger numbers?
    Student: Because I'm not really understanding you.
    Student: You cross out 320, and 100 and 3.
    Student: And the 3 turns into a 13, and the 20 turns into 10.
    Student: And the 10 turns into 100?
    Student: Yeah. The 100 turns into a 90.

    +++ 00:04:02 +++
    Monique LaCour: As a teacher, I kind of wanted to step in and be like, "Okay, do this." But that robs them of the experience of working as a team, collaborating and figuring it out together.
    Student: You don't turn it into 90. You take away the whole a hundred, not ten, the whole thing.
    Student: The whole thing?
    Monique LaCour: If you put them on top of each other and did hundreds, tens and ones, we call that--
    Student: Place value.
    Monique LaCour: Place value!
    Student: Two plus five equals--

    +++ 00:04:33 +++
    Student: Seven.
    Student: Seven.
    Student: Seven. Wait, I did it wrong. It's supposed to be two and then--
    Student: Six.
    Student: Yeah, I made a mistake.
    Monique LaCour: That's okay! It happens to me all the time where I get confused in the middle, and I make mistakes. Mistakes help us to learn. So that's a great thing, if you're making mistakes, that means you're trying new things.

    +++ 00:04:56 +++
    Monique LaCour: We want to keep all the lines of communication open. We want to keep students trying to find the right answer. And saying, "Wow! I've got some great thinking in there. What could I try that's different that will get me closer?"
    Student: And then you got to count the line.
    Student: What do you mean?
    Student: Count the ten.

    +++ 00:05:16 +++
    Monique LaCour: Was the lesson a success? My priority for them is really around productive struggle and giving them the tools to engage in difficult content and not give up and to learn from each other. So for me, it was a successful lesson, because there was that grit of, "There's not an easy answer. What do we do? How do we work as a team to find new ground?"
    Monique LaCour: Students, I want you to turn to your partner and show them a new strategy that you learned about.

    +++ 00:05:43 +++
    Monique LaCour: So after the groups, we came back to the carpet and students were sharing out feedback, a chance to say, "This worked. This didn't work." And we can start to brainstorm around how to make things work in a more smooth way.
    Monique LaCour: I would like you guys right now on your whiteboard, you're going to put a sticky note. I want you to think about any feedback you have for anyone or yourself. Or an idea about something we should try next time to make our Number Talk stronger.
    Monique LaCour: I find that post-it notes are really, really helpful, especially for second graders.
    Student: I'll try not to interrupt.

    +++ 00:06:18 +++
    Student: We could try to get the group to listen.
    Student: What if a student is quiet and the reader can't share his answer?
    Monique LaCour: It really sort of helps to sort of crystalize their thinking.
    Student: People can learn by telling how they got their answer.
    Student: I should try to speak more.

    +++ 00:06:37 +++
    Monique LaCour: As they come forward reflecting, I'm already really excited, because I feel like that's meeting the criteria that I've set of students being self-aware and being aware of how the academic conversation is unfolding. So we're in the conversation together on how do we learn math? And how do we talk about math? And how do we create a world where it's safe to wonder? And to build our understanding together?

    +++ 00:07:05 +++
    Monique LaCour: Tomorrow?
    Class: Tomorrow.
    Monique LaCour: I will try and use strategy.
    Class: I will try and use strategy.
    Monique LaCour: I will try some new ideas!
    Class: I will try some new ideas.
    Monique LaCour: Because math is fun!
    Class: Because math is fun!
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Acorn Woodland Elementary School
1025 81st Avenue
Oakland CA 94621
Population: 292

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