I just finished doing my own toaster experiment. I went through each setting three times. You can check my results here.

My middle school students had immediate concerns regarding the non-linear nature of the line. Their collective conversation mirrors the conversation here and on a few other blogs.

Some were not bothered with the flaws, some wanted to draw trend lines (not by name as they don’t know much about them yet) and still others, most others had complaints as to the flawed nature of the work. Ha!

Their complaints started at the beginning where the time that the toast was reported. Some felt it to be inaccurate in respect to their own observations. Finally, their complaints ended with the questions talked about on this blog regarding heat and regularity of practice in the experiment.

Never the less, they became rather good at working with y=mx+b during the process. The test results from this unit showed that it was the highest tested set of skills among the rest from the same unit. The inquiry, I hope, helped attach this learning in a solid location in their minds. my blog has a little bit of evidence of their work on it.

Thanks for the idea.

The only “deep food-chemistry principle” I can think of is the Maillard reaction. This is the reaction that causes meat to sear, and bread to turn into toast. Apparently this is reaction combines the outer layer of carbohydrates and protein, creating the “golden brown and delicious” crusty goodness we know and love. Your question intrigued me enough to hop online and see what I could find about it. I discovered this gem on Wikipedia:

“The rate of Maillard reactions increases as the water activity increases, reaching a maximum at water activities in the range of 0.6 to 0.7. However, as the Maillard reaction produces water, further increases in water activity may inhibit Maillard reactions.”

Could this be the cause of the change in the graph? I don’t know, but it sounds good.

Uninteresting?! I’m shocked at how flawlessly piecewise-linear the setting vs. brightness graph looks! I wouldn’t expect the literal darkness of the toast to be related in such a simple way to the toaster setting. And what’s going on at setting six? Is the slope change an artifact of the processing method? A manifestation of some deep food-chemistry principle?

This stuff is really neat! Thanks for looking into it.