In my inquiry class, we are sorting through a surplus of observations about what happens when we stack various colored transparencies. I decided to narrow the focus down from all transparencies to just CYM, so that we can try to pin down some things in a certain arena without having to worry about everything all at once.
We have (at least) 3 ideas about how colored transparencies work. Here’s is what I think those theories are:
Theory #1: Transparencies are Color Activating (or Enhancing)
White light has all the rainbow colors available (ROYGBIV), but white light by itself is mostly colorless. It is colorless because none of those colors are activated. When white light hits a yellow transparency and then goes through it, the yellow component of white light becomes activated (or now visible). All the different colors of light get through, but only the yellow light is activated. Transparencies work by activating some portion of the rainbow colors but not all of them.
How this theory explains and accounts for other phenomena: This theory explains why we see green when we stack Yellow and Cyan transparencies in the following way: After enhancing the yellow light, all the unactivated light continues on where it reaches the cyan filter. The cyan filter activates both Blue and Green. So now, both green, blue, and yellow are activated. Green is obviously present from being activated by by Teal, but the blue and yellow activated light blend to make more green. Thus, yellow, blue, and green give the overall appearance of green. One group says this theory can also explain other CYM combinations, by noting that magenta must enhance much more red more than blue.
Theory #2: Transparencies are Color Changing
Transparencies work by changing the color of light. For example, white light is white. But white light upon a yellow transparency causes the white light to undergo changes which make it yellow. Of course, different colored lights upon the yellow filter will change the color in different ways. For example, the magenta light on yellow the transparency changes the light to be green light. Different colors have different rules.
I’m not sure if hidden in this idea is a “blending” or “averaging” idea–meaning that maybe we could come up with some rules. But it seems like the idea is “colors mix in weird waya” and you just have to go observe every combination to learn each rule. I think what I can appreciate about this idea is that it doesn’t assume that there should be simple rules: Why should we expect a yellow filter to have the same behavior when different colored lights shine through them? Can’t the change it induces be particular to the kind of light we shine on it?
One limitations of this theory (so far) is that it has a difficult time making predictions because it sort of says, “Go out in the world and find out what all the rules, because the rules are different for all the different combinations”. It’s feels almost anti-theoretical.
Theory #3: Transparencies are Color Filters
This idea also focuses on white light having all the rainbow colors. Transparencies work by blocking some colors and letting other colors through. For example, many groups decided that we know both Magenta and Cyan must let a good amount of blue light through, because Magenta stacked on Cyan make blue. So a lot of blue light must be getting through. Most groups thought that Magenta must let mostly red and blue (and maybe purple, orange and yellow), and that teal must let through mostly blue and green (and maybe purple and yellow). They explain that blue light results from stacking Cyan and Magenta because it’s the only color that doesn’t get filtered out. I’m interested to see what these groups say about yellow as a filter.
The Big Picture: Assessing student theories? Assessing disciplinary knowledge?
Most of the time, we assess student ideas in terms of correctness. Most of you know which of these theories is more closely aligned with current scientific understandings. However, without correctness, how do we assess the “goodness” of a theory or of an explanation. I think the only refuge is to think about how the scientific community assesses scientific theory, because in science we don’t have the answer key to tell us what scientific theories are correct. Surely there are some criteria for judging some theories to be better than others. Surely we must have ways of assessing scientific explanations in light of the current ideas and evidence we have.
I’d say that right now, I think the “activating color theory” is the best theory… It has the most specificity (details which filters enhance which light), coherence (tells a consistent story for each situation), and has explanatory power (explains all CYM combos). #2 is almost simply a statement of observations at this point. #3 has some good beginnings, but at this point, it still needs some fleshing out. Yellow in particular is going to represent some serious hurdles. We’ll see where this leads us, and I’m happy to keep all of theories along, pressing upon them in different ways that I think will nudge us all along together.
Of course, to be fair, I also have reason to believe that not everyone has well-distinguished theories. I think many hold some combination of #1, #2, and #3 and they certainly aren’t well articulated or committed theoretical frameworks. So Where do we go now? They have a homework to write about their theory for transparencies (how they work in general for CYM in particular), and how their ideas explain stacked CY, YM, and CM.
This is also an excellent description of how many students view mathematics courses. These courses exist to list out all the rules; students cannot be expected to develop ideas about what those rules will be in a new situation because every situation has different rules.
One more thing to consider…do these students’ theories predict CY differently from YC? Perhaps activating and/or filtering suggest different results; that the order of transparencies matters.
It’s a good question. I think their theory does explain CY = YC, because all colors always get through, and the order in which they get activated shouldn’t matter. But I’d have to ask the students.
I was thinking today that the theory probably has a hard time explaining why CYM filters all stacked together is dark.