Icon for: William Zahner

WILLIAM ZAHNER

San Diego State University
Public Discussion
  • Icon for: William Zahner

    William Zahner

    Lead Presenter
    May 12, 2019 | 11:07 p.m.

    Thank you for watching our video! We are working hard to build more equitable high school mathematics learning environments where English learners can participate in robust classroom discussions. We are in year 3 of 5 of this project, and we are currently deep into our second design cycle. The video shows some of our work from the pilot phase and the first cycle. I'd like to invite you to join our thinking about some of the questions we have encountered in our design work.

    First, recently our group has been re-considering what we mean by "participation." Often we (teachers and researchers) have a tendency to only notice verbal participation in the whole-class setting. However, by watching video recorded lessons with a camera focused on a small group of students, we are seeing evidence that other forms of participation (either in the small group discussion, or forms of non-verbal participation) may also be important. This leads to one question:

    • What are some of the non-verbal ways students, especially English Learners, might participate in a classroom discussion? How could we measure these forms of participation? How can we document the effects of such forms of participation on student learning?

    A second strand of our work is sharing our findings in teacher professional development. We have found that scaling this work is a challenge because the process of developing lessons together is very powerful.  

    • What models have you seen as effective for scaling up or disseminating this kind of intensive professional development?

     

     
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    Fatai Bakare
  • Icon for: Kathy Perkins

    Kathy Perkins

    Researcher
    May 13, 2019 | 01:37 a.m.

    It's great to hear about your work with English Learners - so important! What has been the most powerful piece of the work for the teachers? That is, what trainings or strategies do you think has resulted in the most significant pedagogical shifts in the classroom? 

    Also, your video mentioned integrating more active ways to learn mathematics, and that made me wondering if there might be an opportunity for a collaboration between our two projects. We have been developing and studying interactive simulations for middle school mathematics teaching, and see these tools being used by teachers to create more student-centered learning environments compared to their normal instruction. While we haven't (yet) conducted research around how these tools may benefit English Learners specifically, they provide new ways to access and communicate about mathematics. Interaction with these tools might provide access to interesting non-verbal forms of participation - e.g. showing a peer something through interaction with the sim. 

    Also, I was wondering if you have taken a look at or tried using the EQUIP tool for documenting participation with its focus on equitable teaching in mathematics (One of its creators, Daniel Reinholz, is at SDSU): https://www.equip.ninja/

  • Icon for: William Zahner

    William Zahner

    Lead Presenter
    May 13, 2019 | 10:57 a.m.

    Hello Kathy, 

    Thanks for your comment. I will check out your project--it sounds like we have similar foci and could have mutually beneficial discussions. I think for the teachers the sustained collaboration around a single problem of practice has been powerful. At this stage I would be hesitant to name a single component of what we do as the main lever for development, but that is a great question for us to consider. 

    Connecting to your work, we have used forms of simulation, but at the level of depth you have developed. In a collaboration earlier in my career we looked at student participation in classrooms using SimCalc, and dynamic technology is dear to my heart. In our current design work we have used both digital math simulation technologies (e.g., we created dynamic distance-rate-time sims in Desmos taking advantage of the computational layer capabilities) and we have incorporated simulations of student reasoning (e.g., worked examples or argumentation prompts). Both of these have been very powerful for transforming classroom norms and forms of participation.

    I am familiar with EQUIP (Dan's office is down the hall from mine :). We have run some of our data through the EQUIP-style analyses (outside of the app, though) and that has been a valuable source of discussion for us. On the SDSU connection front, I was happy to see Ian in your video too!

  • May 13, 2019 | 08:49 a.m.

     I was just watching the Visual Access to Mathematics video at https://stemforall2019.videohall.com/presentations/1452 and wonder what your projects have in common, beyond the most obvious (supporting mathematics learning for students who are English learners via professional development of teachers). 

  • Icon for: William Zahner

    William Zahner

    Lead Presenter
    May 13, 2019 | 12:21 p.m.

    Hi Catherine-

    Thanks for your question! I think there are many similarities between my project and Visual Access to Mathematics (VAM--In full disclosure, I am on the advisory board for VAM). From the VAM project we have adopted their principles for thinking about language demand, identifying language to access the task, and language to discuss and solidify understanding. The VAM team has also created amazing teacher professional development materials that influence what we do with teachers.

    The biggest difference between the projects is the grade level / content focus and our goal of developing principles for the design of learning environments at the high school level. A secondary distinction is our desire to examine the effects of our designs within the classroom, as seen in patterns of participation. 

  • Icon for: Peter Tierney-Fife

    Peter Tierney-Fife

    Curriculum/Instructional Design Associate
    May 13, 2019 | 04:40 p.m.

    I am excited to learn more about your project. I wonder if you have additional information you can share at this point about your work on principles for the design of high school learning environments, including how these principles are specific to high school.

    I appreciate your questions about non-verbal ways students might participate in whole-class discussions, and these are closely connected to our work in VAM. Although we don't focus explicitly on strategies to include non-verbal participation by students who are English learners in whole-class discussions, we do model some strategies that can be used without students speaking and that educators have reported (in general terms) to be useful in their classrooms. For example, a student might share a visual representation (without speaking or explaining), and the teacher may call on a different student to verbally describe or indicate with gestures something about that representation; the sharing student may then be able to respond in some way (either verbally or non-verbally). I also very interested in what Kathy was writing above about looking at student interactions with simulation tools or apps. We have apps in our course that teachers use and can choose to use with students, and we also haven't yet examined their use by students who are English learners.

    I'm also interested in related questions, such as: What can educators do to foster a classroom culture in which students expect and feel confident about non-verbal participation as part of whole-class discussions? What strategies (or combinations of strategies) seem particularly helpful to support students as they shift from non-verbal participation in whole-class math discussions to some verbal participation?

     

  • Icon for: William Zahner

    William Zahner

    Lead Presenter
    May 14, 2019 | 12:05 p.m.

    Thanks for your great questions, Peter!

    We have not published our design principles yet. As a preview, we think of our design at multiple levels simultaneously. The levels might be described as (1) task level, (2) module or unit level, and (3) learning environment level.  I'll give a brief illustration of a principle from each level and relate it to the video.

    1) Task level: At the task level our goal is to remove unnecessary linguistic complexity, and to be intentional about when and how linguistic complexity is introduced in problems. In the video we see the use of "2x6" to describe a board as an example of unnecessary linguistic complexity. In our designs we do not  want to remove applied problems that create additional complexity, but rather we want to be able to anticipate this complexity and have a plan for using it productively. Language access strategies like 3 Reads can be valuable as a tool to address this task-level complexity. A paper on our analysis of linguistic complexity is here: https://doi.org/10.1016/j.jmathb.2018.04.003.&n...

    2)  Unit level: At the unit level we have looked carefully at the development of mathematical concepts and how these concepts are sequenced. We are especially interested in the use of metaphors or "real life" applications of a mathematical concept. Here we built on the work that has examined how students develop a deep understanding of the slope of a linear function as describing the rate of change. When we examined the existing curriculum we found 3 different meanings for slope that were introduced in close proximity: rate of change, measure of steepness, and constant slope as a defining property of linear equations. In our revision we decided to build a unit focused on rate of change first and delay introducing the other two meanings. 

     3) Learning Environment: Here we examined overall environment with an eye toward understanding what factors might promote or inhibit participation by emergent bilingual students. At this level we incorporated explicit discourse supports such as structured group interactions, and mathematics language routines. We also considered questions of language use and grouping strategies. Finally, we strategically incorporated technology and simulations (mostly using the teacher features of Desmos) to both give students access to dynamic technology and to create shared co-constructed artifacts that students could use to communicate using gestures, actions and so on.

    Last, when thinking across all three levels, we also considered ideas around cultural relevance and building on students assets & interests. 

  • May 14, 2019 | 10:19 a.m.

    Inspiring video -- so great to see teachers excited about getting students talking in high school math. Can you give some examples of the kinds of changes in their classrooms that teachers are making? 

  • Icon for: William Zahner

    William Zahner

    Lead Presenter
    May 14, 2019 | 12:10 p.m.

    Hi Jeremy-

    I think I may have answered your question in my response to Peter. Some of the changes are at the task level--becoming much more intentional about when and how linguistic demand is introduced and how EB students are supported. We have also thought deeply about the unit level development of mathematical ideas, with a goal of focus and coherence. Relating to your work, we are also using networked dynamic technology (created on Desmos for this project) to create spaces where students can create, see, comment on, and revise their mathematical communication using multiple modes of communication.

    Last, the teachers are re-structuring their overall classroom learning environment through the intentional and supported use of students' peer discussions, providing appropriate structure to ensure that EB students can join in.

  • Icon for: Perla Myers

    Perla Myers

    Higher Ed Faculty
    May 14, 2019 | 11:25 a.m.

    This is such important work! Thank you for sharing! I am also interested in the question that Peter asks above about students feeling confident in their non-verbal participation in whole class discussions and their transition to verbal participation.

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    William Zahner

    Lead Presenter
    May 14, 2019 | 12:52 p.m.

    Thanks, Perla. This is a great question. One interesting thing we see is a big contrast in how students (especially emergent bilingual students) engage in peer-peer discussions and how they engage in whole class discussions. In general, during traditional recitation style classes, student contributions to the whole class must be verbal. However, in small group discussions it may be easier to create tasks that allow multiple modes of participation (e.g. physically manipulating a shared representational space, or drawing a representation). So, we are trying to take these ideas back to the whole group discussion. 

  • Icon for: Abby Funabiki

    Abby Funabiki

    Facilitator
    May 14, 2019 | 12:09 p.m.

    I am inspired by the premise of your work! And also by your willingness to learn and iterate your process. The two questions posed by William Zehner in the Public Discussion show how willing you are to rework and challenge your own perceptions. I'm very excited to see this work continue! 

  • Icon for: Abby Funabiki

    Abby Funabiki

    Facilitator
    May 14, 2019 | 12:14 p.m.

    Does teaching a concept in a way that encourages robust classroom discussion take longer? Do high school math teachers have the autonomy to adjust the actual content of their class to encourage this? Or are they still responsible for teaching the same content? In which case is their goal to teach the same content it in a way (and in the same amount of time) that's most conducive to these discussions? Thanks so much for any info! 

  • Icon for: William Zahner

    William Zahner

    Lead Presenter
    May 14, 2019 | 12:57 p.m.

    Hello Abby. Teaching a concept through discussion does take time. One way to create time for this is to focus on the most important concepts that will have the highest yield. This is why, for example, we focused on the slope of a linear function as a rate of change, and de-emphasized some of the alternative meanings or uses of slope (e.g. steepness, pitch). This is a tradeoff, but we think worth the investment.

    Another important thing we have going in our current work is the schools where we work have a block schedule that gives extra time to math classes. This forgiving schedule gives us more space to learn in our development process, though our goal is to design lessons that may fit in a traditional 50 minute class.

     

  • Icon for: Cathy Carroll

    Cathy Carroll

    Researcher
    May 14, 2019 | 01:04 p.m.

    Thanks for sharing your video, Bill. It's great to hear about what you are working on. The lesson development process sounds great, with potential for getting better with each iteration and learning a lot along the way. Like you, I wonder about participation beyond simply verbal participation. We need to figure out better ways to notice, elicit, and learn from various participation styles.

  • Icon for: William Zahner

    William Zahner

    Lead Presenter
    May 14, 2019 | 11:11 p.m.

    Hi Cathy- thank you for your kind words! Our shared interest sounds like an opportunity for more thinking together and (multimodal) conversations in the future!

  • May 14, 2019 | 01:28 p.m.

    I enjoyed watching the video. Looks like a very interesting project. What are some of your design principles of your professional development?

  • Icon for: William Zahner

    William Zahner

    Lead Presenter
    May 14, 2019 | 11:20 p.m.

    Hello Teruni-

    At present our professional development is embedded in the design research. We are focused  on co-designing around a problem of practice. Thinking of the principles that guide our work, we have incorporated sustained engagement around mathematics, the interaction of mathematics and language, and teaching with that interaction in mind guiding principles. Since this project is rooted in design research, we did not start as a PD project. But, looking ahead, I can see that the next step (assuming our design efforts continue to be fruitful) will be to think about how to share this work with larger audiences. I know you have done large scale PD across the state of Nevada. I would love to hear your insights from directing such a project and lessons learned!  

  • Icon for: Quinn Burke

    Quinn Burke

    Facilitator
    May 14, 2019 | 06:24 p.m.

    William (and team) - thanks for sharing this video!  Yes, talking and reading math matters, and I appreciate the point made here on this thread that it is not simply linguistic complexity on the task level but the conceptual clarity on the unit level. Thanks for grounding this in the actual example of conceptualizing slope. 

    I realize the work is ongoing, but at some point is the goal to develop a guide/ manual on the 9th grade level for math teachers to review their lesson plans accordingly, analyzing their content across task/ unit/ learning environment?

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    William Zahner

    Lead Presenter
    May 14, 2019 | 11:23 p.m.

    Hello Quinn- In short, yes, one of our goals is to share the design principles that we are developing through this work. In theory these principles could then be used by other teams to engage in design around the dozens of related topics in school mathematics. Looking at the point Lisa raises below, and connecting to Sebastian Ulloa's statement near the end of the video, I am wondering whether the process is as important as the product. I suppose that is a researchable question for another project :)

     
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    Quinn Burke
  • Icon for: Lisa Miller

    Lisa Miller

    Facilitator
    May 14, 2019 | 09:54 p.m.

    Thank you for sharing your video on the important work you are doing!  In the initial post by William, he stated:

    "A second strand of our work is sharing our findings in teacher professional development. We have found that scaling this work is a challenge because the process of developing lessons together is very powerful. "

    Could you say a little more about the challenges you are having with sharing and scaling your work and, if possible, some of the ideas/approaches you are trying? 

  • Icon for: William Zahner

    William Zahner

    Lead Presenter
    May 14, 2019 | 11:28 p.m.

    Thanks for your question, Lisa.  At present we have not made a move to scale our efforts since we are still in the design phase. However, I asked that question because I am anticipating that in the next 16 months we will be sharing this work. We will start by sharing with local teachers (at schools where we have existing relationships), and then I anticipate we will be asking ourselves how we can share this more widely. For that work I am not sure how to sustainably scale a model that involves sustained and intensive collaboration. If you have seen models that we should be looking at, I would be happy to learn more!

     
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    Lisa Miller
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    Jim Malamut

    Informal Educator
    May 15, 2019 | 12:15 p.m.

    I loved this video and am excited to learn more about how you are creating these professional learning experiences with teachers!

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    William Zahner

    Lead Presenter
    May 15, 2019 | 11:08 p.m.

    Thanks, Jim. You would be happy to know that in our design work we are using the wonderful paper on Math Language Routines that you wrote with Jeff Zwiers, Jack Dieckmann, Sara Rutherford-Quach, Vinci Daro, Renae Skarin, and Steven Weiss. Thanks for making that great resource available! 

  • Icon for: Amy Hackenberg

    Amy Hackenberg

    Higher Ed Faculty
    May 15, 2019 | 02:32 p.m.

    I enjoyed learning about your project. Thanks for the video!

  • Icon for: William Zahner

    William Zahner

    Lead Presenter
    May 15, 2019 | 11:28 p.m.

    Thanks, Amy.  I also enjoyed learning about your work by watching your video! I am already thinking about potential points of overlap in how you are thinking of differentiation and our efforts to create classroom learning environments where linguistically diverse groups of students can learn important mathematical concepts.

  • May 20, 2019 | 07:01 p.m.

    This is an amazing project! I am in San Diego and have a research interest in improving ELLs' mathematical learning experience. So it is great to know that this important work is happening in our neighborhood. Thanks for sharing the video and would love to learn more and connect in the future. 

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