1. Andrew Izsak
  2. Professor
  3. Investigating Proportional Relationships from Two Perspectives
  4. http://temrrg.wix.com/temrrg
  5. University of Georgia
  1. Sybilla Beckmann
  2. https://faculty.franklin.uga.edu/sybilla/
  3. Meigs Distinguished Teaching Professor
  4. Investigating Proportional Relationships from Two Perspectives
  5. http://temrrg.wix.com/temrrg
  6. University of Georgia
  1. laine bradshaw
  2. https://coe.uga.edu/directory/profiles/laineb
  3. Associate Professor
  4. Investigating Proportional Relationships from Two Perspectives
  5. http://temrrg.wix.com/temrrg
  6. University of Georgia
  1. Torrey Kulow
  2. Post Doctoral Researcher
  3. Investigating Proportional Relationships from Two Perspectives
  4. http://temrrg.wix.com/temrrg
  5. University of Georgia
Public Discussion
  • Icon for: E Paul Goldenberg

    E Paul Goldenberg

    Facilitator
    May 16, 2016 | 05:05 p.m.

    Watching a brief video and taking a full course are naturally quite different but I noticed that I had to watch two video segments—the transfer of the gold grams per part to the copper parts (1:55 in your video), and the expanding/contracting parts (2:25)—twice to see what you were doing. What (if any) places in your work do you find teachers needing to “look twice”? Do you see any cases (especially in the first representation) in which teachers seem to get the “method” but not understand the idea? This is, by the way, very intriguing work!

  • Icon for: Andrew Izsak

    Andrew Izsak

    Presenter
    May 17, 2016 | 04:55 p.m.

    Hi Paul,

    Thank you for the question. In our experience working with preservice teachers and talking to mathematics education colleagues, thinking about proportional relationships from the variable parts perspective takes time to develop. We devote several weeks to developing the perspective in courses for future middle and secondary grades teachers. We pose tasks and allow students to reason with strip diagrams and develop methods that make sense to them. We have found that working on proportional relationships helps teachers deepen their understandings of measurement and partitive division.

    Andrew, Sybilla, and Torrey

  • Icon for: E Paul Goldenberg

    E Paul Goldenberg

    Facilitator
    May 17, 2016 | 09:57 p.m.

    Thanks, all. I assume it’s too early to know how this shows up in these preservice teachers’ (future) teaching, but will that at some point be part of this study? I always wish we had more time for longitudinal views!

  • Icon for: Miriam Gates

    Miriam Gates

    Facilitator
    May 17, 2016 | 11:25 a.m.

    I was very interested in this work. I am curious, though, about the use of variable parts. You note in the video that this is the first such application in the US. I’m curious if this method has been used elsewhere and what lessons, if any, you have drawn on in implementing this approach with your teachers.

  • Icon for: Andrew Izsak

    Andrew Izsak

    Presenter
    May 17, 2016 | 04:58 p.m.

    Hi Miriam,

    Our inspiration comes from Japanese and Singapore curricula. That said, we have developed all of our own activities for use in teacher education courses. We continue to experiment with tasks that help future teachers reason with variable parts. Thank you for your interest in our work.

    Andrew, Sybilla, an Torrey

  • Icon for: Miriam Gates

    Miriam Gates

    Facilitator
    May 19, 2016 | 03:59 p.m.

    Thanks for your response. Are some sample tasks available somewhere?

  • Icon for: Sybilla Beckmann

    Sybilla Beckmann

    Co-Presenter
    May 19, 2016 | 10:08 p.m.

    Hi! If you look through some of the slides from our presentations on our website:
    http://temrrg.wix.com/temrrg
    you will find some of the tasks we have used there.

  • Icon for: Courtney Arthur

    Courtney Arthur

    Facilitator
    May 17, 2016 | 05:19 p.m.

    What does your teacher professional development entail? How long and what is the focus (primarily engaging in mathematics, focusing on pedagogy, etc?)

  • Icon for: Andrew Izsak

    Andrew Izsak

    Presenter
    May 18, 2016 | 04:29 p.m.

    Hi Courtney,

    The project is situated in mathematics content courses for teachers. In the middle grades preparation program multiplication, division, and fractions are developed in a fall semester-long course on number and operation. The two perspectives on proportional relationships are developed in the subsequent spring course on algebra. In the secondary grades preparation program, these topics are the backbone of a semester long content course on multiplication. I think we are fairly unusual in requiring a semester long course on multiplication topics for future secondary teachers, but in our experience it is much needed. Pedagogy is covered in separate courses.

    Andrew

  • Small default profile

    Chad Paul

    Guest
    May 21, 2016 | 08:42 p.m.

    I was a little confused by the video. The posed question said the ratio of gold : copper is 7:5 and ask how much gold needed to be mixed with 25 grams of copper but the variable parts diagram seems to reverse this. On the other hand, the direct variation seemed to fit the original ratio, so I thought I would ask.
    That said, I like the way you tie everything back to the meaning of multiplication.

  • Icon for: Sybilla Beckmann

    Sybilla Beckmann

    Co-Presenter
    May 22, 2016 | 09:08 a.m.

    Good catch! There was an error in the statement of the problem. I’m sorry we missed that. In the statement, it should have said that there was 25 grams of gold. The solution that is presented goes along with that.

  • Further posting is closed as the showcase has ended.