AMATYC Keynote Notes: Interaction and Impasse

Nov 19, 2016 by

Thursday I had the honor of providing the opening keynote for the AMATYC Conference in Denver, “Learning Math is Not a Spectator Sport.” I expect the video of the talk will be available to share next week, and rather than provide the slides (124 mostly stick-figure drawings), I’ll point you to some resources that will likely give you the information you’re looking for between now and when the full presentation becomes available.

Selfie with room full of participants in the background

Keynote Selfie

We covered three main themes:

  1. Interaction & Impasse (this post)
  2. Challenge & Curiosity
  3. Durable Learning

I’ll provide resources for each of these categories, starting with Interaction and Impasse, in this post.

Interaction and Impasse


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What if you don’t have enough whiteboards?

Feb 2, 2012 by

Just a quick post to share this video from Betty Love (University of Nebraska – Omaha). Betty attended our MCC Math & Technology Workshop in 2011 and really wanted to try paired boardwork with her students during class. The problem? Not enough whiteboards/chalkboards. The solution? Well, just watch!

If you’ve got pictures or video you’d like to share of your Math ELITE Classroom redesign, or how you’ve incorporated the principles into your teaching, please do!

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What does the classroom say?

Nov 12, 2011 by

Yesterday I had a short talk in the ITLC Themed Session called “Change the Classroom, Change the Learning” about the necessity of math classroom redesign.

Without changing the classrooms, it is unlikely that we will see much change in the instructors or students.

Here is the video from the talk, called “What does the Classroom Say?” and the slides from the presentation.

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Math ELITEs (Classrooms for Active Mathematics)

Feb 24, 2010 by

Thanks to Diane, Gary, and Tom … who also contributed ideas to this classroom redesign project idea.

Objective: Create classroom spaces specifically for a) actively learning mathematics and b) using technology to demonstrate, teach, and learn mathematics.


A Mathematics ELITE is an Engaged Learning Interactive Technology Environment and consists of:

1. Multiple Whiteboards

There should be enough whiteboards in the room so that 24-30 students can work in pairs at the boards. One set of boards should be lowered so that shorter students or a student in a wheelchair could participate more easily (another modification could be to use a portable whiteboard for disabled students).


Students rarely learn mathematics from copying the instructor’s work. When students work on the whiteboards in class, it is relatively easy for the instructor to monitor the work of all student pairs at once, stepping in to answer questions, give hints, and correct notation. Students take turns being the writer and the helper, talking over the mathematics as they learn to solve new types of problems. With an interactive board in the room, one pair of students can record their work on the interactive board, creating a record (PDF file) of all the problems worked in class that day.


2. Document cameradoc_camera4

Can be used for displaying documents (i.e. worksheets, going over a test key, etc.). In a classroom with math manipulatives (i.e. fraction strips, base‐10 blocks, etc.) , these can also be displayed to the class via the document camera.  Scientific and graphing calculator demonstrations can also be shown using a document camera.  It can be helpful to have a mini whiteboard to use with the document camera.

3. Computer station, laptop connection, and ceiling projector

Many simulations and interactive demonstrations (e.g. NLVM, Wolfram Demonstrations) are now emerging on the Web as a way to demonstrate mathematics. A fixed computer station eliminates the problem of tripping over the cord and solves the problem of obstructed student views of the board. Through a laptop connection, instructors can connect their own laptop or tablet.

4. Ceiling speakers

Connecting math to real‐world applications can require extensive knowledge of other disciplines. However, the use of short video clips from the Internet can mitigate this (i.e. TED, Science Friday Videos, etc.).

5. Interactive Whiteboard

Math demonstrations can be shown by the instructor on a traditional computer. Using an interactive whiteboard (e.g. SMART board), students will be able to participate in the demonstrations up at the screen. Interactive whiteboards can be used to record the student board work (see #1). Lessons written on an interactive board can be recorded as video or as documents (PDF files). Many of our future elementary teachers will eventually be teaching in classroom spaces with interactive whiteboard technology, and it’s important that they begin to see how to use these tools effectively.


6. Math manipulatives and storage space

For many math classes (in particular, Developmental Math, Algebra, Math for Elementary Teachers, Excursions in Mathematics, College Algebra with Applications, and Statistics), the students’ understanding of mathematics can be enhanced by playing with math manipulatives. Manipulatives help students make connections between the physical world and abstract concepts. Some math manipulatives must be purchased and some can be assembled using everyday materials, but it is important to have some storage space for these close to the learning space.

7. Half‐round tableskidney-shaped-activity-table

Student seating in clusters instead of rows makes it easier to facilitate group work. Students must be able to view lessons on either the interactive whiteboard or the white board (placed on an adjacent wall), so half‐round tables are used. These tables are also nice because they provide the instructor a space to “drop in” on the group and check their progress by simply walking down the main aisles in the room.

8. Wireless Internet

Anticipating the likely possibility that most students will have a laptop, netbook, or smartphone capable of Internet access in the near future, wireless Internet is a good option for bringing computing power to the hands of students in the classroom.

9. Recording Equipment

The room should also contain some kind of easy way to record classroom activities (for later posting to the web or to help students with recording digital projects).  An easy and relatively inexpensive way to do this is with a Flip Video Camcorder and a tripod.

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