Friday, January 9, 2015

The Numbers Don't Lie

Rewind back a few weeks to just before winter break. We were at the end of our science project and in the throes of confronting our misconceptions about the James River. Remember back to our previous field trip, when we followed our creek to its end where it joined the waters of The Mighty James. While we had been there, the children were trying to determine what the water in the river was doing. Was it moving? Which way was it going?

To our left, we could see water flowing over a dam. The waterfall was flowing our direction. And yet, at the same moment, the wind was blowing back across the river diagonally back up steam causing ripples that were flowing in the opposite direction. To help them sort out what was happening the children had thrown sticks-- lots of them-- into the river to see which direction the water would carry them. Every single stick traveled downstream to our right, matching the flow we could see up river at the dam and yet everyone could see the ripples on the surface of the river further out. We couldn't throw sticks far enough out into the water of the river to test the current clear out there!

As we headed home from our creek-chasing-adventure the children developed a theory. The majority of the class decided that they believed that the river behaved differently from our creek. They began to hypothesize that the water was traveling different directions depending on which side of the river one was on, much like the flow of traffic on a road.

An example of the many diagrams we saw
the children draw to show their thinking

Over time, Mauren and I tried EVERYTHING we could think of to help the children confront their idea. We had our Force Battles, we had conversations, we posed questioned, brought up shared experienced that contradicted the new theory, built a model of mountain ranges and made it rain so that we could observe the water flowing one direction. And yet the idea that the water in the James was traveling both directions simultaneously persisted. Eventually, as our collaborative teams met to discuss the work, we decided that they needed to figure this out with the river itself.

To make a long story short, we planned a field trip to play a giant game of Pooh Sticks (a game played by Winnie the Pooh and his friends where they drop sticks into the stream and watch them flow with the water's current). We knew the perfect place-- a pedestrian bridge that spanned the majority of the width of the river. We knew certain things would have to happen for this experience to be convincing enough for the children.

  • We needed to be able to throw sticks from various places across the bridge in order to test the current all the way across.
  • We needed to throw A LOT of sticks to be sure the results were consistent over time.
  • We hopped the wind would blow against the current so that the sticks movement would have to be attributed to the current rather than the wind.
  • We wondered if one bridge would be convincing enough or if we would have to go to several in order to really feel certain about the water's behavior.
We built a model before we went to discuss what we thought we might see.
What would it mean if the sticks traveled this way?
What would it mean if we threw them of this side and then they traveled that direction?

And so we headed out to the bridge armed with piles and piles of sticks. As it turns out, just being over the water we could tell which direction it was moving and we could see how swiftly it was moving. We could see debris and foam. We could see ripples. We could see the water parting to move around rocks and pillars. And then we started throwing our sticks into the river. All the way across the bridge and all the way back, the children hurled sticks off the bridge and into the rushing water. They threw them off both sides of the bridge and watched closely to see the journey of each stick.

Back at school we sat down to discuss what we had observed. At first, as I questioned the children, it became obvious that some of them STILL wanted to hang on to their idea that the river water traveled multiple directions at the same time. They focused in on the few sticks that were outliers, the ones that got stuck in eddies or had some other pause before heading down stream. I decided that the only hope I had of letting this experience help them release those ideas would be to look at the data. And so, we each gave an account of the ten sticks we had thrown into the river, putting a tally to represent which direction the sticks had traveled. As children stopped to give detailed accounted of those exceptions they had seen, I pushed further with, "And what did that stick eventually do?" Each time they relayed that the stick had eventually traveled down stream like all of the rest.

Eventually we had the results:
148 to 0. One hundred and forty eight floated downstream. Zero floated up stream.

Dillon: Well zero can’t win against 148. Because 148 is 148 more than zero, so how could zero win? It means that the current has to be going that way. The current could be going this way if it’s windy enough, but….

Sydney: I wouldn’t be that convinced because if only one goes this way how do we know that the other way couldn’t….If 148 go this way, to zero over here, which way is most likely?

Tom: Yes, because there’s nothing for it to go against. It’s like a wrestler going against nobody, they won the match. Cause there’s nobody for them to go against.

The numbers eventually did the convincing because the numbers can't lie.