A big part of my job as teacher is to not just record and notice ideas, but to see connections, and see across the landscape of ideas, and to use those insights to nudge us forward. On Monday, I just scrambled to get down all our ideas, but I’ve been thinking about where we are and where we are going. So, here is some of what I see us doing right now, in the big picture.
Basically, I see we are struggling with two questions.
First Question: What causes the image to be upside?
I see that we have four kinds of ideas:
Our Brain Causes the inverted image. Some talk about this like it has something to do with the box playing a trick on us (somehow), so our brain doesn’t properly correct for what we are seeing.
Light Bouncing Causes the Inverted Image. Some seem to like the word “refraction” for this. Others are noticing how a spoon is concave just like the box, thinking that light bends off the spoon in some way to make it upside down, maybe the bouncing off the box is having the same effect.
Light Crossing Causes the Inverted Image (and this is due to how hole limits what angles of light can get it box)
The distance (or time) that light has to travel affects whether the light straightens out or flips
** All of these are relevant, some more proximal to the phenomena of our personal box theaters than others, but they are all relevant to phenomena of optics, and how and whether images are inverted or not. Right now our idea space is huge, and there are some many connections, I feel we need to spend some time really digging into a smaller idea space, and then pull our heads up again once we can say something more about that smaller space. **
Second Question: What does it mean to be upside and left/right backwards?
We have lots of ideas:
Mirrors seem to make things left-right backwards from our view, but not upside down
Turning anything clock-wise or counter-clockwise, 180 degrees also flips L and R. So, one “flip” creates both kinds of invertedness.
A Painted Wilson Ball bouncing off a wall will leave a right-left backwards imprint (once again left-right backwards, but not up-side down)
Perspective: What is or isn’t left-right backwards depends on which way you are looking
* I really let this conversation go for a while on Monday. I wasn’t sure where it was going, but (at least some) students were really excited about this. There’s something very deep here we are making contact with concerning the nature of transformations (i.e., rotations, inversions, reflections) and perspective-taking. What I like about all of this is the realization that if something is upside down or left-right backwards, there are different ways it could have gotten that way, and it might be important for us to figure out what kind of transformation we are dealing with **
Some Other Notes:
I got a chance to read students’ notebooks the last two days. Lots of students are writing about how they are dissatisfied with all this talk about the Brain, because it seems too psychological. One student remarking, “Shouldn’t there be a physical reason its upside down?” Others, students, however, are quite intrigued by the whole brain possibility. The brain and our minds is intriguing–and makes me wish I had a biologist to co-teach with! (wink wink).
And, we also started a more-structured inquiry later in class on Monday with students investigating what happens with various bulbs shining through holes onto a screen. Lots of students are seeing connections between what they are seeing there are the crossing light idea. One student old me on Monday while doing the investigation that they are absolutely fascinated. I’ll tell you that in years I’ve taught or watched video of students observing bulbs shine through holes (from PBI and Tutorials), I’ve never had a student say they were fascinated in the way this student did. Anyway, Students will continue that investigation Today, and we’ll see where that gets us.
Based on the searches that have found their way here to the blog, some students have certainly found the blog. (Hi!) Deciding whether to just share the blog with whole class, or just let it become know on its own time.