1. Jennifer Knudsen
  2. https://www.sri.com/about/people/jennifer-knudsen
  3. Senior Mathematics Educator
  4. Mathematical Argumentation in Urban Middle-school Classrooms
  5. https://www.sri.com/work/projects/bridging-professional-development
  6. SRI International
  1. Ken Rafanan
  2. https://www.sri.com/about/people/ken-rafanan
  3. Research Social Scientist
  4. Mathematical Argumentation in Urban Middle-school Classrooms
  5. https://www.sri.com/work/projects/bridging-professional-development
  6. SRI International
Public Discussion
  • Icon for: Gerald Kulm

    Gerald Kulm

    Facilitator
    May 16, 2016 | 10:22 a.m.

    Hi. Please expand a little on the Improv technique, perhaps with a specific example. Can you describe the link between the technique and argumentation; that is just how does the activity help teachers to facilitate argumentation ideas in their classrooms?

  • Icon for: Jennifer Knudsen

    Jennifer Knudsen

    Presenter
    May 17, 2016 | 09:32 a.m.

    To help students develop a new view of mathematics as well as learn to engage in argumentation improvisationally, we promote the use of warm up games that are based on improv games. These are the same games that improv actors use to learn their craft. Warm up games have simple rules of interaction to follow that foster spontaneity and strong collaboration among participants. They also encourage playfulness, which leads to the joy in argumentation. The games can be used at the beginning of selected class periods to introduce productive norms for argumentation. We have found that introducing the norms in the sometimes non-mathematical context of games can be important for students who may have never before participated in group discussions about the truth of mathematics.

  • Icon for: Gerald Kulm

    Gerald Kulm

    Facilitator
    May 18, 2016 | 12:09 p.m.

    Not being an actor, I still am not sure of exactly what an improv game or warm up game is. Can you be a little more specific. And again, how would this differ, for example, from a teacher simply encouraging and modeling free and open discussion about math ideas?

  • Icon for: Jennifer Knudsen

    Jennifer Knudsen

    Presenter
    May 18, 2016 | 12:44 p.m.

    Sure! here is an example game called Gift Giving:
    • Partners stand facing each other with an imaginary closet of unlimited gifts behind them.
    • One partner offers the other a gift from the closet, by handing him/her a “wrapped box”. This gift can be of any dimension, and the offerer gives an idea of the size, weight, and/or shape.
    • The receiver then opens the gift and names it by thanking the giver (e.g., “Thank you for this grapefruit”) as he/she picks up and handles the gift.
    • The giver then responds with how he/she selected the gift and why he/she knew the receiver would enjoy it. The roles are then switched.

    Then the teacher leads a discussion in which students can make connections between announcing the gift and conjecturing, and justifying as explaining why the gift was given. The game can encourage bold conjecturing, which we consider particularly important. The game also promotes basic norms important for any classroom discussion such as listening to each other and building off of each other’s ideas.

  • Icon for: Veronica Blackham

    Veronica Blackham

    Research Assistant
    May 17, 2016 | 03:41 p.m.

    In the video, you mention that you have curricular units and software specially designed for teachers to build argumentation in their classroom. I would love to learn more about these tools. Is the curriculum and software something your Bridging team has developed? Or have you identified current curriculum and software that seems to align with what you are trying to teach the teachers?
    Nice video by the way, your project seems very interesting, and I agree that argumentation needs to be further developed in the classroom!

  • Icon for: Jennifer Knudsen

    Jennifer Knudsen

    Presenter
    May 18, 2016 | 07:28 a.m.

    We designed these materials ourselves, to afford plenty of opportunity for teachers to develop math knowledge for teaching in the workshop and to support their teaching argumentation in the classroom.

    Each has a technology tool to help students generate cases from which to argue.
    Grade 6—coordinate geometry and variable. You can find a link to a GeoGebra activity for the unit on our website bridging.sri.com
    Grade 7—proportionality, with simulations of motion
    Grade 8—linear functions, also with simulations of motion.
    Teachers also learn to design their own lessons.
    Thanks, about the video!

  • Icon for: May Jadallah

    May Jadallah

    Associate Professor
    May 17, 2016 | 06:54 p.m.

    This is fascinating! What impact does the PD have on students’ mathematical understanding? Have this been documented?

  • Icon for: Jennifer Knudsen

    Jennifer Knudsen

    Presenter
    May 18, 2016 | 07:26 a.m.

    we are currently collecting pre-post data on the amount and kind of argumentation that occurs in each class as well as doing pre-post interviews with a subset of students to understand their ability to make arguments and what new content they have learned. In prior work, we have found that teachers in the program support significantly more argumentation than teachers in a control group.

  • Icon for: Michelle Perry

    Michelle Perry

    Facilitator
    May 18, 2016 | 05:37 p.m.

    How many teachers participated in the project? Can you explain a bit more how the PD was structured (how often, follow-up supports, etc.)?

  • Icon for: Jennifer Knudsen

    Jennifer Knudsen

    Presenter
    May 18, 2016 | 06:00 p.m.

    we currently have about 30 teachers in one district, though the model can handle more. PD timing: 4 days in the summer, then 4 hrs every school month. The PD is arranged as successive approximations of practice, building up from experiences with targeted teaching moves (we call them teaching games) to improvisational performances of 10 minutes or so of whole class argumentation

  • Icon for: Jennifer Knudsen

    Jennifer Knudsen

    Presenter
    May 18, 2016 | 06:27 p.m.

    you can read more about our model at
    www.sri.com/blog/professional-development-progr...

  • Icon for: Jorge Solis

    Jorge Solis

    Assistant professor
    May 19, 2016 | 05:28 p.m.

    Thank you Jennifer for sharing your work! Im wondering how you perhaps had to deal with the tensions that we often have in the classroom between providing explicit instructions (around argumentation) and allowing students/teachers to grapple with new practices if any?

  • Icon for: Jennifer Knudsen

    Jennifer Knudsen

    Presenter
    May 20, 2016 | 02:40 p.m.

    Teachers do experience this tension. We advise that giving advice about argumentation—like what a conjecture is—is a good idea. Then we help teachers develop and practice specific teaching moves that they can use to support students’ argumentation, in a more open ended way.

  • Further posting is closed as the showcase has ended.