mental maps and real maps

Sparked by a discussion in their classroom about whether you can come back to the same place you start on a walk, the children in the kindergarten are mapping the path they take from a certain tree behind their classroom into the forest and back. Most of the children were representing the path they take as a straight line, on long paper. I wondered if this was the best way to illustrate a loop for children who are about 5 and forming new conceptions of space and circularity.

So, I asked a small group to try showing the path on a round piece of paper. My aim was to see if they would feel the circular representation was more true than the straight line one. 
* this is much the same group that did so much mapping a couple of years ago

Me "I notice that when you draw the path on a long piece of paper you have to draw the starting tree twice -once at the beginning of the map and again at the end. If you use round paper, you could just draw it one time. Would you like to try it?"

Me "So, what do you think about drawing it the circle way?"

Poppy "I think, see on here, because it's a circle, things that you put...see the trailers, they're kind of tipping. And then things will be upside down, things will be sideways. But if it (the map) is a square...

Anna draws landmarks around the outside of Poppy's square

Poppy (notices that things are upside down around the square, and changes her mind)" You know, if its a straight line, nothing is upside down."

Kaiya "Yeah, I'm voting for the straight line way now."

the bumpy square shape

 Isabel "I like (drawing it as a) bumpy square. We can always make the square right, by bending it, see?...except putting everything on the inside of it (instead of around the outside)."

Kaiya "Yeah, the square way! Then it could be a square of the whole school (campus), and the whole forest could be on the inside!"

a circle...the 4 trailers are upside down

Now that the girls have had more time to draw and think about their map, they have a few more things to say...