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?
82 Comments

This video opened my eyes to many effective teaching strategies. I loved that she had students working in groups and reasoning with each other. That collaboration helps them become more comfortable within their classroom, but also encourages them to try new strategies and explain their ideas to their peers. The students are picking up on many beneficial skills by spending their class time this way.  I also liked how she had students reflect on their work after the activity. By reflecting and hearing explicitly what their expectations are, students are reminded of how they can improve for the next time they meet. I loved this video and learned so much by watching! 

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Our district made a push for math talks this year, but in a slightly different way.  The district was looking for the middle and high schools to just get kids talking, even the kids with low skills.  So the idea was to put an image or images on the board and have kids explain how the images were similar or different, something about the images or something else non-threatening to get everyone a chance at success to begin the class.

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I loved watching this video!  Ms. LaCour did a wonderful job of setting her students up to be successful in both math and language experiences.  In the beginning, she was positive as she reviewed what the expectations were of the students, while also giving them the opportunity to read and vocalize the expectations.  She provided scaffolding with the use of sentence frames to enable ALL students at all levels of English proficiency to be able to participate.  Having the students work in small groups, having obviously been taught how to accept and encourage each other was so beneficial to those students that may lack confidence and be afraid to take risks.  The students did a great job of solving their problems and were easily able to share explanations of their thinking.  

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I enjoyed watching this activity. Ms. LaCour promotes learning in different ways, she sets up the learning tone of the lesson before getting started. Ms. LaCour gets sentences frames ready before the talking activity to support ELLs. She states the learning goal and makes sure everyone understands it.

One of the benefits of having students lead the talk is that it promotes language development. Another advantage is that this “in charge” experience gives them the opportunity to see what works. At the end of the activity, students share ways how the activity could be improved the next time, which becomes their own assessed reflection of it.

This is an engagement activity, all students had the opportunity to talk and share their thoughts. The conversation keeps everyone engages and learning, this what makes this a valuable strategy.

 

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I liked this video, which reminded me a little of my own education in the 1970s (at least what I now remember) in an "open classroom" that encouraged discussion and interaction.  Of course, it would have been neat if one of the students had done the subtraction problem 123-65 using place value as follows:  3 minus 5 is -2; 20 minus 60 is -40; 100 minus 0 is 100; 100-40-2 is 58. Voila!  Anyhow, this method is seldom taught.  Something I did notice was that one of the boys had to count on his hands when adding 5 and 2.  You would think that students doing 3-digit subtraction would have already mastered single digit addition, but maybe this young man was just having a bad day.  I like the self reflection, as well as what appeared to be parity between boys and girls when it came to leading discussion in groups.  So often, boys can be allowed to dominate at the expense of the girls.  Glad everyone's getting a chance to show their stuff.  First-rate teaching. 

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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: 296

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