Recently I was reminded of an activity that I used with students that I called The Traffic Jam Activity. View the URLs below if you’re interested in more of the details. There were several ideas that I was working on, but this morning I’m thinking again about concrete (in this case, the little plastic people) manipulatives vs. the virtual (in this case, the Java applet by Mike Morton) manipulatives.

I’m convinced after working for several years with students in a lab environment that using both is better than using one over another. I remember that when I first tried it using both helped me extend the students’ problem solving experience. My students didn’t complain that we were “still” working on a problem or that we were doing a problem “again” if the second time they were trying it with virtual manipulatives. I’m not sure if they considered it to be a different problem or if they liked working on the computer so much they didn’t want to complain or maybe a little of both?

I often observed that for many of my students we had to really work for them to connect the concrete and the virtual experiences. And, in fact, it reminded me of how much we had to work to go from a manipulative environment to a more symbolic environment.

Do you use both kinds of manipulatives when you’re working on a problem? Do you have students have concrete Activity Pattern Blocks (for example) as your students have that applet in front of them? or Tangrams? or Algebra Tiles? or Dice?

I wonder if the conversations that you might have with students as they make connections between the concrete and the virtual might be a starting point for the conversations that you might have with them about going from the concrete to the abstract?

What are your thoughts?

**Some “Traffic Jam” links** in case you are interested:

- ON-Math Fall 2002, Volume 1, Number 1: Developing Algebraic Thinking
- Suzanne’s Lessons: Traffic Jam Activity
- Teaching Math with Technology by Ihor Charischak with Suzanne Alejandre
- Technology Problems of the Week (tPoWs): Traffic Jam