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


Virtual Manipulatives and Dynamic Representations in Length and Area Measurement.

Session presented at the Math in Action annual conference at Grand Valley State University in Allendale, MI. We explored measurement concepts using virtual manipulatives and dynamic simulations to encourage reasoning and sense-making that can support robust understanding of measurement.

Download session slides here.

We created three tasks for participants to explore during the session, each considering area: one as a paper and pencil task, one using physical manipulatives, and the third using an online tool from NCTM Illuminations.

Download task sheet here.

Pencil and Paper Task – We asked participants to determine the area of parallelograms and to mark those with the same area.

Physical Manipulatives Task – We asked participants to create a parallelogram with the same base and height as a given rectangle. We asked: How do the areas of the original shape and your new shape compare? Explain.

Virtual Manipulatives Task – We sent participants to the NCTM Illuminations page:  We asked them to find as many parallelograms as they could, all with area of 88 square units. We asked them to discuss patterns they saw.

We ended by asked: What could the learning goal for these three tasks be? How do the three tasks support learning in different ways? How does each block learning in different ways?

Possible benefits of simulations:

Stehr, E.M. & Siebers, K. (2013, February) Fractions as lengths. Paper presented at the Math in Action Conference, Grand Valley State University, Allendale, MI