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  1. Johannah Nikula
  2. https://www.edc.org/staff/johannah-nikula
  3. Senior Project Director
  4. Presenter’s NSFRESOURCECENTERS
  5. Education Development Center
  1. Jill Neumayer DePiper
  2. https://www.edc.org/staff/jill-neumayer-depiper
  3. Research Scientist
  4. Presenter’s NSFRESOURCECENTERS
  5. Education Development Center

Analyzing Diagrams: Supports for English Learners

R305A170297

2021 (see original presentation & discussion)

Grades 6-8

This video highlights how features including diagrams and supports for language access and language production can be built into middle grades mathematics lessons to strengthen the learning experience for emergent multilingual learners (i.e., students identified as English learners by their schools). We developed and studied Grade 6 fraction division lessons that incorporate these features (see http://go.edc.org/adsel) in collaboration with over 30 teachers. This video shares key implications for supporting student participation and learning in mathematics class, and includes the perspectives of some of the teachers who collaborated in this work on how these features supported their students.

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Discussion from the 2021 STEM For All Video Showcase (21 posts)
  • Icon for: Johannah Nikula

    Johannah Nikula

    Lead Presenter
    Senior Project Director
    May 10, 2021 | 09:21 p.m.

    Hello and thank you for visiting our Middle Grades Mathematics Lessons for Multilingual Learners video based on our IES-funded Analyzing Diagrams: A Support for English Learners project. For this project, we developed and studied middle grades mathematics lessons with built-in supports for students who are emergent multilingual in collaboration with over 30 teachers. This video highlights instructional strategies from the lessons that help students get started, promote student problem solving, and encourage mathematical communication on 6th grade fraction content. 

    We would love to hear from teachers about your experiences using any of the strategies from this video in your own mathematics classrooms at any grade level, and what else you are doing to highlight multilingual students’ strengths and set them up for success in the mathematics classroom.

    We also welcome ideas and questions about what resources teachers may need to enact these strategies in the classroom as well as ideas about questions for further research. 

     
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    Ateng' Ogwel
    Kimberly Elliott
  • Icon for: Ateng' Ogwel

    Ateng' Ogwel

    Researcher
    May 13, 2021 | 11:14 a.m.

    Johannah,

    Thanks for this insightful presentation and the project on deepening mathematics learning among multilingual learners.

    Duagrams are at the core of problem solving and and design, and the kind of work you’ve shared elicits learners higher level cognitive abilities. It is also true that communication is richer when we develop tluency in using text, verbal, diagrammatic and non-verbal approaches. The task of translating word problems into diagrams is quite demanding and I appreciate your project’s intervention from middle school.

    i had an experience some years back with secondary students in Kenya, where ability to work out problems on relative motion using diagrams was much lower compared to use of the computational method, interestedly even among top achievers. The other experience is when I was pursuing my studies in Japan, my limited language was supplemented by use of diagrams with limited English text, gestures and use of basic verbs in Japanese. 

    I guess you’ve seen the Presentation by Eric Hamilton in the current showcase where there are similarities is enhancement of multiple intelligences in diverse cultures

     

     

     
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    Kimberly Elliott
  • Icon for: Johannah Nikula

    Johannah Nikula

    Lead Presenter
    Senior Project Director
    May 13, 2021 | 01:55 p.m.

    Thanks for visiting and sharing your experiences, Ateng' Ogwel. We agree that being able to communicate through multiple modalities, including using diagrams, strengthens communication, and it sounds like you had some first-hand experience with this during your studies in Japan.

    And yes, learning to use diagrams in problem solving can take time and scaffolding for students. We had success in these lessons with scaffolding diagramming by using partial diagrams for students to complete and by providing worked examples showing diagramming approaches for students to analyze. Teachers and students found these strategies helped get students started on using diagrams. We will check out Eric Hamilton's presentation--thanks for the suggestion.

     
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    Kimberly Elliott
    Ateng' Ogwel
  • Icon for: Luiz Oliveira

    Luiz Oliveira

    Researcher
    May 11, 2021 | 08:30 a.m.

    Hello Johannah and team! Although I am fluent today, I am actually an English learner myself! (Native language is Portuguese). Growing up in an English speaking school system, I remember certain difficulties in interpreting math word problems, especially when they were not accompanied by a diagram or supporting visual. 

    As a result, I can also attest to the importance of using non-verbal methods of communicating math problems to students! Great job on promoting these methods that facilitate the learning of math for English learners. 

    Throughout this project, did you work with any students besides ones that spoke Spanish? If so, how did your experience differ? Thank you, and fantastic job!

     

     
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    Kimberly Elliott
  • Icon for: Jill Neumayer DePiper

    Jill Neumayer DePiper

    Co-Presenter
    Research Scientist
    May 11, 2021 | 08:53 a.m.

    Thanks for sharing your experiences, Luiz. We have found that diagrams helped students both get started when thinking through the mathematics in a task as well as helped them share their thinking with others.  

    In this project, we had students who spoke over 15 different languages. We interviewed students after their participation to ask about what strategies they found helpful and what they learned, but we did not collect data on how students' experiences differed based on their home language. That would be an interesting avenue to pursue!  As we knew that we'd be working across schools and districts that had many different languages-- in about 6 of the districts that we worked in, the districts report that there are over more than 40 languages spoken by their multilingual students!-- we specifically designed the materials for mathematics teachers to use in classrooms that had multiple languages and as such may not have the resources to adjust their materials for a specific language. We are interested, however, in thinking through about how to meet students' specific language strengths and needs in mathematics and how to support students in sharing their ideas and empowering students in the mathematics classroom. We also know that there are ways to bring students' cultural and linguistic knowledge into the mathematics classrooms, and we are hoping to design materials that have opportunities for teachers to bring students' knowledge into instruction through questions, activities, and prompts for sharing, even when there are multiple languages spoken in one classroom.

    Thanks so much for watching-- I'm going to head to your video now!

    -Jill

     
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    Ateng' Ogwel
    Kimberly Elliott
  • Icon for: Laura Larkin

    Laura Larkin

    Facilitator
    Albert Einstein Distinguished Educator Fellow
    May 11, 2021 | 03:53 p.m.

    Hello Johannah, Jill, and team-

    As a high school math teacher, I have used 3 reads and sentence starters.  While it appears to be most helpful for my students with learning differences and EL students, it is useful for all.  Diagramming is so important to understanding and the scaffolded structure you provide ensures everyone is successful.  These lessons would be very useful in my 9th and 10th grade algebra support classes.

    I appreciate that these lessons demystify perhaps the most misunderstood concept in mathematics - fraction division.  I have a few questions:  Are you anticipating designing some other lessons and if so, around which math topics?

    Can you suggest some additional strategies to encourage oral communication?  Do you have any protocols that seem to work, especially for reluctant speakers?

     
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    Ateng' Ogwel
    Kimberly Elliott
  • Icon for: Johannah Nikula

    Johannah Nikula

    Lead Presenter
    Senior Project Director
    May 11, 2021 | 05:23 p.m.

    Thanks for sharing, Laura. Sounds like you’re doing great work in your algebra support classes and we’re so glad to hear you’ve found these types of strategies and lessons useful there.

    We definitely agree about the importance/challenge of fraction division! We chose it as a focal point for this study and these lessons knowing that understanding of fraction operations is so important to students’ mathematics mathematical learning (in 6th grade and beyond), that diagrams are important tools in this content, and that this is very challenging content to teach and learn so resources could have an impact.

    We are exploring next steps related to this work. We don’t have immediate plans to develop lessons in other content areas, but would be interested in hearing what you and others would find most useful. Through other work we are also thinking about professional learning resources about the kinds of strategies that were embedded in these lessons. (See for example resources at http://go.edc.org/vam.) If you teach algebra support classes, a curriculum you might be interested in from some of our colleagues at EDC is Transition to Algebra. It was not designed specifically for multilingual learners, but it does rely heavily on various visual representations of mathematics.

    To your question about promoting oral communication in mathematics class, including for reluctant speakers: one way we do that in these lessons is through structured pairs work integrating use of sentence starter cards. In each lesson, after students start drawing their own diagrams for a problem, they then meet with a partner to use sentence starters such as “In this diagram, I see…” and “In this diagram, I don’t see…” to talk about each other’s diagrams. During partner work, everyone in the classroom has the chance to talk about the mathematics rather than just one or a few students at a time, and it is a low pressure opportunity to engage in mathematical talk because it is in front of just one other student. Providing every student with a set of sentence starter cards on a ring (e.g., see the handout provided as a resource with this video) also allows students to structure their discussion about the diagrams, and the teacher and/or student volunteers can model how to use the sentence starter cards to talk about a diagram when introducing the cards. We’d love to hear other ideas about how you all promote and support oral communication!

     
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    Ateng' Ogwel
    Annie Wilhelm
    Kimberly Elliott
  • May 12, 2021 | 10:06 a.m.

    Hi Jill and Johannah,

    Always interesting to learn more about your work, and it was great to hear from some of the partnering teachers about their powerful experiences in the classroom! 

    Taking on fraction division is bold, but we know work with rational numbers is so important in the middle grades. I'd like to hear more about the kinds of diagrams that seem especially helpful for teachers and students in addressing this topic. 

     

     
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    Kimberly Elliott
  • Icon for: Jill Neumayer DePiper

    Jill Neumayer DePiper

    Co-Presenter
    Research Scientist
    May 13, 2021 | 09:49 a.m.

    Thanks, Dan! We always appreciate your insights into this work.

    We decided to take on fraction division because we thought that through showing the how and why of fraction division to middle grades’ students may help to build their understandings of and appreciation for fraction operations. Through this project, exploring how diagrams can support students in their understanding and exploration of fraction division has been so interesting. In terms of type of diagram, we included a strong focus on number lines to help emphasize fractions as numbers with magnitude as recommended through research by Siegler and colleagues, but also supported students to develop various diagrams in their problem solving, including area models, to facilitate their own sense-making and attention to relationships in fraction division contexts.

    To promote and scaffold diagram use, we incorporated strategies such as providing partial diagrams for students to complete and worked examples that show diagramming approaches for students to analyze and discuss. During our initial analyses of interviews and written reflections, we have seen a variety of student diagrams and students have shared how number lines help them to organize their thinking and begin solving fraction division tasks.  Teachers also shared that they have found that integrating diagrams into their instruction has helped to them explain more about the relationships in fraction division and focus on what the whole unit is in each case; for example, in a diagram, teachers shared that they could emphasize a third of what or a fourth of a different quantity more easily than when just a calculation or algorithm was used.  The partial diagrams and worked examples were also scaffolds that teachers found useful for getting students started with creating diagrams.

     
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    Kimberly Elliott
    Ateng' Ogwel
  • Icon for: Jonee Wilson

    Jonee Wilson

    Assistant Professor
    May 12, 2021 | 10:35 p.m.

    Nice work! I love the idea of the three-reads as a way to support students in focusing on different aspects of complex tasks. The practice of acting out task context reminds me of the 3-Act Task lessons. Have you heard of this? I think Dan Meyer has some interesting materials that are available that may be very useful for teachers who want to implement this practice in their classrooms. Also strategies like sentence starters and diagrams are relatively simple things that teachers can incorporate into their classrooms that could make a big difference for students.

     
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    Kimberly Elliott
    Ateng' Ogwel
  • Icon for: Jill Neumayer DePiper

    Jill Neumayer DePiper

    Co-Presenter
    Research Scientist
    May 13, 2021 | 09:53 a.m.

    Thanks, Jonee and yes, we also love the 3-Act Task lessons. We have found them really helpful for presenting the mathematics and in particular, videos can provide visual access that reading a task does not. We have used different ones when considering other topics such as mixing paint.

    We have also found that sentence starters support student talk and discussion, and particularly, when teachers craft them to be content-specific, the mathematical talk in the classroom can become really rich. Sentence starters can also be varied for students who have different language strengths and needs and can help students get started in sharing their ideas.  We certainly agree-- these strategies can set up students for success.

     
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    Kimberly Elliott
  • Icon for: Bridina Lemmer

    Bridina Lemmer

    Facilitator
    Technical Assistance Consultant
    May 12, 2021 | 11:01 p.m.

    I have worked with so many teachers that will benefit and be interested in this work.

    Can you say a little more about the cross-section of  teachers and districts you worked with? Were they primarily urban, or some rural?

     
    1
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    Kimberly Elliott
  • Icon for: Jill Neumayer DePiper

    Jill Neumayer DePiper

    Co-Presenter
    Research Scientist
    May 13, 2021 | 09:57 a.m.

    Thanks, Bridina. We worked with teachers across urban, rural, small town, and suburban school districts, and we sought to have a variety of classroom sizes as well, while seeking to have at least three or four emergent multilingual students in each classroom. We were trying to develop and test strategies that could be used by mathematics teachers who have a range of language strength and needs on their classrooms. Many mathematics teachers have a wealth of content expertise but may not know how to best integrate language supports into their instruction, while keeping the mathematical content and rigor at grade level.  We found that setting both language and math objectives for lessons and planning ahead for using language strategies facilitated teachers in taking up new instructional strategies.

     
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    Kimberly Elliott
    Ateng' Ogwel
  • Icon for: Israel Ramirez

    Israel Ramirez

    K-12 Teacher
    May 14, 2021 | 11:37 a.m.

    Thank you for sharing great teaching strategies to teach multilingual learners to enhance understanding in mathematics. As a second language English (Native in Spanish) learner, I know that all these teaching techniques will continue helping lots of students in these urban, rural, and small towns. Keep up the good work!

     
    2
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    Kimberly Elliott
    Ateng' Ogwel
  • Icon for: Johannah Nikula

    Johannah Nikula

    Lead Presenter
    Senior Project Director
    May 14, 2021 | 12:50 p.m.

    Thanks so much! We're glad to hear you find these teaching techniques helpful.

     
    1
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    Kimberly Elliott
  • Icon for: David Barnes

    David Barnes

    Facilitator
    Associate Executive Director, NCTM
    May 14, 2021 | 08:36 p.m.

    Johannah and Jill, I really like this project!  I have seen this work in action – three reads and sentence starters and it really does allow students to engage.   And I really like the use of representations as a third aspect of the work.  Do you have any plans for also providing support materials that would help teachers apply these techniques to their existing curriculum?  Just a thought.

     
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    Kimberly Elliott
  • Icon for: Johannah Nikula

    Johannah Nikula

    Lead Presenter
    Senior Project Director
    May 15, 2021 | 01:35 p.m.

    Thanks, David! We love seeing students dive into problem solving and talking about the mathematics using strategies like the three reads, sentence starters, and visual representations. And yes--in a related work (see go.edc.org/vam) we have been developing and studying professional learning to support teachers in integrating strategies with their own curriculum. We are also always thinking about how to do more of that. I'd be interested to hear ideas you or others have about resources or tools that might be most helpful to teachers.

  • Icon for: David Barnes

    David Barnes

    Facilitator
    Associate Executive Director, NCTM
    May 16, 2021 | 02:33 p.m.

    Wonderful!  I'll have a look!

  • Icon for: Jill Neumayer DePiper

    Jill Neumayer DePiper

    Co-Presenter
    Research Scientist
    May 17, 2021 | 09:46 a.m.

    Thanks, David, and I also wanted to note that we put in the sentence starter cards that we use during partner work in the sidebar. These prompt student to talk about their diagrams with their partner, but could be used to prompt for other conversations as well; instead of, "In this diagram, I see," it could modified to be about graphs drawn or a problem solving approach. We have found that specifically focusing mathematical talk facilitates student talk more than sentence starters such as, "I agree... " or "I disagree..."

  • Icon for: Kimberly Elliott

    Kimberly Elliott

    May 15, 2021 | 11:52 a.m.

    Hi, Johannah and Jill! As a fan of your work, I want to share two brief, related blog posts that you've written that include links to additional resources and support materials for teachers. I know you've shared this--and related--work in books and articles for teachers, but thought these would be handy and fast for interested viewers to check out. "Promoting Problem-Solving for Emergent Multilingual Students" and "Supporting Students Who Are Emergent Multilingual in Mathematics Class."

  • Icon for: Johannah Nikula

    Johannah Nikula

    Lead Presenter
    Senior Project Director
    May 15, 2021 | 01:36 p.m.

    Thanks for pointing out these resources, Kim!

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