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
7 MIN
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?

142 Comments

  • Private message to Ashley M

This was such a great lesson. I think it is incredible to see these second grade ELLs working so hard together in groups and independently to discover so many unique solving methods and ideas.  They clearly have done an exercise like this before since they seemed so comfortable working on the boards and communicating with each other in their groups. This is also a clear indication of the work the teacher put into creating a safe learning environment for all to feel comfortable to try new things, take risks and make mistakes.  Ms. LaCour took time in the lesson to encourage mistakes, reminding students that mistakes show that we are trying something new, which is such an important message for students to hear within the classroom.

This Number Talk lesson is clearly an excellent way to meet all ELLs where they are, while also incorporating all academic language modalities.  Students were seen collaborating to discover new methods to solve the challenging subtraction problem.  When a method was found, the student gave directions to another student to write on the board, then the other students in the group critiqued and helped make any necessary corrections to the work.  I really liked this portion of the lesson, and feel that it benefits all students, but especially ELLs in developing their academic language.  This learning method could be used in all levels of math, even in my high school Algebra course. 

Recommended (0)
  • Private message to Joseph Cendrowski

This was a fantastic lesson and a great video to watch. I really enjoyed everything she did with her teaching, starting with an overview of what the students should expect throughout the class and the goals of the lesson, allowing all the students to be prepared for what is to come and what a successful class will look like.

I also like the “number talks.” I feel like so many people do not know how to give or receive constructive feedback without being hurtful as it gives them the framework for a conversation or a polite debate. In addition, they also need to defend their procedures which means they are taking an active role in their learning, resulting in better retention of the material. I’m also a big fan of productive struggle. In life, the answers will not always be given, and students need to learn to work through those difficult moments to make progress towards a goal.

My favorite part was the reflection at the end, and how the students can improve upon this for next time. This can be beneficial in so many ways, from the teacher being able to see the students’ needs and making the lesson better to the students being aware of where they could have improved (like participating more). It let’s students know that there is always room to improve.

Overall, it seemed like it was a very engaging experience for the students, and they genuinely enjoyed that style and one that I am going to try to replicate in my classes.

Recommended (0)
  • Private message to Brian Hayes

I really enjoyed the “Engaging in Productive Struggle: Number Talks” video lesson.  The flow of the lesson was tremendous.  The “launch,” the group work, and the “post-it” conclusion exercise all tied in so nicely together.  The kids were engaged.  I love, love, love how instead of having the student explain and show their work, the teacher had one student talk out their strategy while a second student wrote it out on the whiteboard.  As far as language demands that group activity hit on ALL FIVE listening, speaking, writing, reading, and Representing.  This setup also allowed all group members to agree, disagree, clarify, add-on, and/or connect to another strategy.  I really loved it!  

 

I thought the summarizing activity at the end was also excellent.  The use of post-its was great.  It made the students REFLECT on their mathematical thinking and group execution (it is clear that the class spends a lot of time on their Math Talk initiative).  And this reflection hit on ALL FIVE language demands - reading, writing, speaking, listening, and representing.  


 

My final takeaway was the the great classroom culture Ms. LaCour has created in her classroom. The kids were so willing to share even if they were unsure of whether their strategy was correct or not.  I think how Ms. LaCour started class with the reading of the Math Talks “rules” and established some great expectations for the class.  Also, at the end class, the students repeat together that they will drive a new strategy next class.  All great practice!!

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  • Private message to Nicole Takac

I found this video very interesting! I liked how she allowed the students to experiment both independently and in groups. The emphasis on students genuinely having an opportunity to stuggle productively in a safe enviornment gave them an opportunity to create their own learning. I think the reflection at the end is also beneficial for the students to demonstrate their learning from the experience and what new ideas to try the next time around. Ackowledging that mistakes are a part of the learning process allows for a higher sense of security and exploration within the students. 

This lesson seemed engaging for the students. At all times they were working towards a solution exploring new methods. She allowed for all types of practice with English, including writing, speaking, reading, and listening. Working with other students allowed students to engage in both group and independent work while practicing these skills. They were able to help each other as needed and provided a student-centered enviornment. This seemed to be a great lesson for the students and I would like to see where the students progress with future lessons!

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  • Private message to Jenny Moline

It was really interesting to watch this video while completing the LDML activity. This teacher did a great job including each of the modes of language. It was great to see the students talking to each other, and leading their own small groups. I think the teacher did a really effective job at establishing the expectations of the groups ahead of time, so the students could be successful while they were working. It was also neat to watch the productive struggle take place. Especially when the student regrouped incorrectly, and realized he did it wrong, and his classmates helped explain to him what his mistake was. The teacher was able to act as a facilitator and allow the students to do the thinking, which is how they will ultimately make the strongest connections. 

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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!
    GFX:
    Tch
    Teaching Channel

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School Details

Acorn Woodland Elementary School
1025 81st Avenue
Oakland CA 94621
Population: 286

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Teachers

Monique LaCour