Series: Content Conversations: Strategies for ELLs

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

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?
5 Comments

I was really inspired by the sentence stems to facilitate discussion as well as for the different positions (facilitator, teacher, etc.) in the group.  As a high school teacher, I am often reminded of all of the good scaffolding that help facilitate productive discussion when observing ES classes!  

Next year, I am going to be co--teaching an Algebra 1 class (with Angie!). One of the things we have been discussing is what kinds of ways we can split the classes for discussion/exploration.  I also liked how this class split into different groups and each group was working on the problem both individually and as a group, but all productively.  This is also something that I want to try next year.

But thing that I liked the most was Ms. LaCour's final closing with the students.  "I will try new ideas... because math is fun!"

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Lessons like the one in this video are importnat for showing students how to have discussions and try new strategies in math classes. Monique created a learning space for her students where they felt comfortable sharing their ideas and strategies with their peers and with the class as a whole. She was receptive to students who were struggling, but did not immediately provide them with an answer, she had them work through the problem. This kind of learning environment promotes students trying new ideas and then being able to explain whether or not their ideas worked. For ELLs this is very important as it gives the a space where they can feel comforable practicing both their English and their math skills. 

The reflection the teacher had students do on their strategies was a good thing to see as many students see math as an either it worked or it didn't kind of thing. Getting them to explore why something worked or didn't is important for having students get a deeper understanding of how they learn and use math.

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I enjoyed watching how well your students discussed their mathematics.  I particularly liked how you used sentence prompts to teach students how to engage in the mathematics appropriately.  Academic language is difficult for students to learn and this is something that really can help students know how to use it correctly to engage in discussion about their thinking.  Thank you for sharing.

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This strategy reminds me of the AVID (Advancement Via Independent Determination) tutoring sessions. In the AVID tutoring sessions, a student presents a problem from a homework that he/she has, and then the rest of the group tries to help that student find the solution by asking him/her guiding questions, but not giving him/her the solution. The idea is that the student finds his/her own "aha" moment. Here, all the students are trying to solve the same problem, and they do not necessarily ask questions: they actually share their strategies and try to find the solution together.

I was wondering, though, do the students have to provide feedback, reflections and suggestions every time after they complete a math talk? It seems to me that, after having completed a few math talks, the students might see themselves repeating the same comments and suggestions. In other words, I would think that step is only necessary when students are learning the process; but, once they are comfortable with the process, that step could be ommitted or, perhaps, have the students write an evaluation of the group's performance, but not share it with the class. Any ideas on that?

Overall, I liked the strategy, and I already saved it to my workspace. Thank you.

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“Engaging in Productive Struggle: Number Talks” is very appropriate as Monique gave learners the opportunity engage in academic conversations while exploring important mathematics. Struggling through problem solving is a great impetus for acquiring new knowledge; and I totally agree with Monique for resisting the temptation to give away answers in her interactions with the groups. The engaging hook at the beginning of the lesson was excellent and what a great place to inculcate the discipline of respecting others views; whether they agree or disagree. Hoping the video was an abridged version – otherwise I expected to see more students sharing their strategies with the class.

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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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    Tch
    Teaching Channel

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School Details

Acorn Woodland Elementary School
1025 81st Avenue
Oakland CA 94621
Population: 296

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