Mindset

I’m very grateful to be here at the 3-day MAP Conference in South San Francisco — finally got to meet Malcolm Swan whose lessons I’ve used with my students for many years. I was delighted to see this slide because we did this lesson and it was one of my favorites.

At the end of today's session, we were asked to share questions that we may have for tomorrow's panel of speakers. A teacher asked this question, and it stayed with me. He said something like this:

The students in the video [during Malcolm's talk] are awesome. But my students are not there. They are at zero. Not even zero, they are at negative something...

Negative?? Zero?? It made me sad to hear this. No matter how "low" his students are, no matter how out-of-control they appear, no matter how unmotivated they seem, they cannot be at level zero. That's impossible. We talk a lot about students' mindsets. I worry more about the teacher's mindset. Maybe this teacher didn't mean it the way I'd heard it; but I've heard teachers say directly to me, "My kids can't do that." How do we know that unless we give them a chance.

A Lesson Salvaged

The intended activity from MAP did not go well last week.

I gave these instructions:

1. Pair up. One person is the Describer, the other the Drawer.

2. The Describer is going to look at a Roman mosaic and describe it to the Drawer to draw it.

3. Both people may talk to each other, but no hands or any other bodily gestures.

4. The Describer may not look at the Drawer's paper as he/she works on the drawing.

I gave each Drawer a blank sheet of paper. I gave each student a ruler and a compass. And I gave each Describer a picture of this.

I also told the Describers to get their Drawers to get the size just right — thus the ruler. I encouraged the Describers to use words like rotate, reflect, symmetry. After a while, I walked around looking at the papers and thought, Holy Cow, if-only-you-could-see-what-your-drawer-is-drawing.

I called for the Drawers' papers after about 30 minutes. The results:

What the...? Oh, let's not forget No. 7. Sketches 4 and 7 took up most of the 21.5 cm x 28 cm paper; the actual mosaic was 8 centimeters in diameter.

Then, I thought, Let me try being the Describer!

The results

Sketch D was very close, considering we were all hurrying through as the period was ending. Still, this was not my assignment and not a fair comparison when I had a lot more time to look at the shape. I took the stack home and let it mingle with the other piles of papers on my desk.

Late last night I looked again at the sketches on my desk and thought, I should try to construct this shape in Geometer's Sketchpad (GSP).

It was not an easy task!! I had to really think about each step and kept wondering during my construction if there was a better or more efficient way to do this. I felt great when I was done because it was challenging. No reason to keep this experience to myself, so I asked my geometry kids this morning to construct the Roman mosaic in GSP!

I reminded them that their constructions must pass the "drag test," meaning their Roman mosaic must not collapse when any vertex got dragged about.

Five minutes into the construction, Bobby said, "This makes me crazy!" Yes!

Some works in progress:

Karie was one of the first ones to finish; she talked about her construction:

Alex talked about his construction. You could hear the dismissal bell while he was talking, but no one got up to leave or put away the laptops. I had to tell them!

It was cool that the five students who had finished all had different ways of constructing the mosaic. Theirs were much more elegant than mine. More importantly, my construction did NOT even pass the drag test when I tried it this morning, but I intentionally forgot to tell them this.

A lesson salvaged by GSP. A teacher schooled by her 8th graders.