PMENA – November, 2015


I’m excited to participate in PMENA this weekend – very conveniently held at my school, Michigan State University. I have helped out the Local Organizing Committee, but mainly I have enjoyed watching the “behind the scenes” action. Led by Drs. Tonya Bartell and Kristen Bieda, we have worked hard for about a year and a half. I’m excited to see the end result!

I will be participating as a presenter on a brief research report and three posters:

  • Friday, November 6, 9:20 AM – 10:00 AM (Kellogg: Conference 62)  Assessing Teacher Knowledge and Practice
    • Mathematical Knowledge for Teachers: Opportunities to Learn to Teach Algebra in Teacher Education Programs
      Presenters: Eryn M. Stehr, Jeffrey Craig, Hyunyi Jung, Leonardo Medel, Alexia Mintos, Jill Newton
  • Friday, November 6, 4:00 PM – 5:30 PM (Kellogg: Lincoln)  First Poster Session
    • Digital Resources in Mathematics: Teachers’ Conceptions and Noticing
      Presenter: Eryn M. Stehr
    • Building Algebra Connections in Teacher Education 
      Presenters: Hyunyi Jung, Jill Newton, Eryn M. Stehr, Sharon Senk
  • Saturday, November 7, 10:30 AM – 12:00 PM (Kellogg: Lincoln) Second Poster Session
    • Secondary Preservice Teachers’ Opportunities to Learn About Modeling in Algebra
      Presenters: Hyunyi Jung, Eryn M. Stehr, Sharon Senk, Jia He, Leonardo Medel

Fraction Multiplication and Division Using Virtual Measurement Models

Session Presented at the National Council of Supervisors of Mathematics (NCSM) annual conference in April, 2015, in Boston, MA. Because it was NCSM, our participants were professional development facilitators and other teacher educators. We presented a similar session in February, 2015 at regional practitioner conference – we deliberately changed very little between the two sessions, so that we could talk to the teacher educators about what we had seen in the teachers’ interaction with manipulatives in the session

In this session we explored various web-based applets created to support conceptual understanding of fraction, multiplication, and division using spatial measurement models (length, area, volume). We also discussed how these applets can be used in professional development or classroom settings with students.  (View Session Site; Download Session Hand-out and Session Slides)

Overview of session:

We hoped to stimulate discussion focused on the complex interactions of:

  • Students’ understanding of mathematical ideas, such as: measurement models, number lines, and fraction operations
  • Relationships between: quantities and numbers / actions and operations
  • Benefits and limitations of instructional models: manipulatives / applets

Exploration of physical manipulatives:

We provided participants with several physical tools, including rubber bands, linking cubes, WikiStix, and graph paper. We asked them to use the tools to make sense of representing fraction multiplication with discrete quantities and with continuous quantities.

Exploration of virtual manipulatives:

We asked the participants to interact with virtual manipulatives ( that we had created in an attempt to explore discrete versus continuous quantities in multiplication and division of fractions.

We created the applets specifically to support thinking about measurement dynamically and continuously because research has shown students see measurement as static and discrete most often, and yet dynamic and continuous experiences can support students develop flexible understandings of multiplication and division that may support them in understanding later covariational relationships.

Final discussion:

We asked participants to talk about: How can focusing on these ideas support students’ and teachers’ thinking about measurement and fractions? When are virtual manipulatives appropriate? When are physical manipulatives appropriate?

Stehr, E.M., Satyam, V.R., Smith, J.P., & Gilbertson, N. (2015, April). Fraction multiplication and division using virtual measurement models. Presentation to the 2015 Annual Meeting of the National Council of Supervisors of Mathematics, Boston, MA.

Strange Rulers and Strange Questions

I presented on this topic with D. Lee Clark for professional development facilitators from around the state. This meeting was a formal meeting sponsored by Strengthening Tomorrow’s Education in Measurement. We talked about teacher questioning in the context of some STEM tasks, using the Boaler and Brodie (2004) framework:

  1. Gathering information
  2. Inserting terminology
  3. Exploring mathematical meaning and relationships
  4. Probing; getting students to explain their thinking
  5. Generating discussion
  6. Linking and applying
  7. Extending thinking
  8. Orienting and focusing
  9. Establishing context

Measurement Tasks

Jagged Paths

Strange Rulers

Why do we use frameworks for questioning?

  • Direct your thinking/focus
  • Gives us a way to communicate with each other
  • Provides us with a starting point to direct our focus.
  • Goal is not to code all questions identically, but if everyone coded differently then it would be an opportunity to think about the usefulness of that particular framework.

Boaler and Brodie framework

This is only one possible framework of many.  Generated from practice – these are the types of things that teachers from actual classrooms are asking.  Categories are detailed enough without being overwhelming. Nice framework to use for people that are either just beginning to think about their questions or are in the stages between using good questions and trying to get good discussions going in the classrooms.

  • How can you (as facilitators) use intentional questioning in your PD sessions?
  • How might you use this framework (or others) with your teacher-participants?
  • What questioning types are the previous questions? (Is the number important?)

Teacher-participants – How might you want to do this with your teachers?

Very important to have your teachers have time to do a task with questioning in the session – this is a valuable use of time. They will have time to take notes, think about it – gives them the feeling that you value their time and feel this important.

Could be videos of themselves or a video from the Annenberg website