If you and I have had a conversation about math education in the last month, it’s likely I’ve taken you by the collar, stared straight at you, and said, “Can I tell you about the math lesson that has me most excited right now?”
There was probably some spittle involved.
Evan Weinberg posted “(Students) Thinking Like Computer Scientists” a month ago and the lesson idea haunted me since. It realizes the promise of digital, networked math curricula as well as anything else I can point to. If math textbooks have a digital future, you’re looking at a piece of it in Evan’s post.
Evan’s idea basically demanded a full-scale Internetization so I spent the next month conspiring with Evan and Dave Major to put the lesson online where anybody could use it.
That’s Do You Know Blue?
Five Reasons To Love This Lesson
It’s so easy to start. While most modeling lessons begin by throwing information and formulas and dense blocks of text at students, Evan’s task begins with the concise, enticing, intuitive question “Is this blue?” That’s the power of a digital math curriculum. The abstraction can just wait a minute. We’ll eventually arrive at all those equations and tables and data but we don’t have to start with them.
Students embed their own data in the problem. By judging ten colors at the start of the task, students are supplying the data they’ll try to model later. That’s fun.
It’s a bridge from math to computer science. Students get a chance to write algorithms in a language understood by both mathematicians and the computer scientists. It’s analogous to the Netflix Prize for grown-up computer scientists.
It’s scaffolded. I won’t say we got the scaffolds exactly right, but we asked students to try two tasks in between voting on “blueness” and constructing a rule.
- They try to create a target color from RGB values. We didn’t want to assume students were all familiar with the decomposition of colors into red, green, and blue values. So we gave them something to play with.
- They guess, based on RGB values, if a color will be blue. This was instructive for me. It was obvious to me that a big number for blue and and little numbers for red and green would result in a blue color. I learned some other, more subtle combinations on this particular scaffold.
This is the modeling cycle. Modeling is often a cycle. You take the world, turn it into math, then you check the math against the world. In that validation step, if the world disagrees with your model, you cycle back and formulate a new model.
My three-act tasks rarely invoke the cycle, in contrast to Evan’s task. You model once, you see the answer, and then you discuss sources of error. But Evan’s activity requires the full cycle. You submit your first rule and it matches only 40% of the test data, so you cycle back, peer harder at the data, make a sharper observation, and then try a new model.
The contest is running for another five days. The top-ranked student, Rebecca Christainsen, has a rule that correctly predicts the blueness of 2,309 out of 2,594 colors for an overall accuracy of 89%. That’s awesome but not untouchable. Get on it. Get your students on it.
TomMay 23, 2013 - 5:49 pm -
Dan, will this website be live for an extended period of time? Or just for the duration of the contest?
I’m starting up two computer science classes next year (one for 8th graders – a very intro level, and one for high schoolers – a pre-AP CS type class called Foundations of Computer Science).
I would LOVE for this to be my first day (or second day) activity for my high school Foundations of Computer Science class.
Dan MeyerMay 23, 2013 - 7:09 pm -
Hi Tom, none us have talked about what will happen to the project after this week but I think we’d all like to keep it up indefinitely. In the other thread, Dave was talking about wiping out the database every week to give a new crop of kids a chance to be the weekly winner. You should head over there and weigh in on that idea or offer a different one for how this could be useful to you and yours next year.
MaryMay 24, 2013 - 4:30 am -
Is this best viewed in a certain browser? I don’t have any buttons to slide the colors up and down in Firefox for Mac (21.0). Some random clicking does some random changing of the colors. In Chrome I still couldn’t see any sliders but clicking above the color boxes made the numbers go up and clicking below made them go down but I found this by randomly clicking on the screen.
BhavikMay 24, 2013 - 4:45 am -
What is the formula?
BertMay 24, 2013 - 5:34 am -
Dan: matching the color would be a lot easier if you tracked the relative distance, not absolute position. Currently, the first click already changes the color to a value depending on the click position. It would be nicer if the color did not change when you click, but only when you dragged up and down. That would make it a lot simpler to set a particular value (especially on a touch screen).
Matt EMay 24, 2013 - 9:25 am -
I second Bert’s comment.
GladysMay 24, 2013 - 9:49 am -
I could not get the color boxes to work. maybe don’t completely understand how it suppose to work. If I could use it with kindergarten explain how it would work.
Jason DyerMay 24, 2013 - 9:58 am -
I’d be all over this if it was earlier in the year, but my students all just left yesterday.
Cindy MedeirosMay 24, 2013 - 3:21 pm -
Love this. You could also use Photoshop’s Adjust color function.
Mr. SteveMay 26, 2013 - 7:10 pm -
Another nice follow up on this would be can you tell and Orange from a Lemon, where they are given width and length of each. Then they have the kids plot the values on an X-Y plane. After they have done this ask them to draw a line that would separate the oranges from the lemons. You could also ask them to think about how to draw a line to maximize the “margin of safety.”
I think I will try this with my kids over the next few weeks.
Thanks to my friend Joseph for the idea
NicoraMay 27, 2013 - 10:38 am -
I love this. What a neat idea. Are you planning on doing any research on it?
Evan WeinbergMay 28, 2013 - 3:13 am -
I want to publicly thank Dan and Dave for pushing this idea forward. It was a lot of fun doing it with my students, but the excitement they have had around making this an interactive activity for any student with a web browser has really opened my eyes to the potential of the medium.
If you haven’t yet been convinced to learn to code, consider the fact that doing so might lead to making this sort of experience for your own students the way you want it. There are so many great ideas out there that deserve to built and shared. The technology and the people to help you learn are all out there. Take advantage of it.
Dan MeyerMay 28, 2013 - 7:47 am -
@Nicora, no plans at the moment. What research questions do you have about it?
Nicora PlacaMay 29, 2013 - 9:18 am -
I study student learning, so I’d be interested to learn more about how the students are learning as they go through the activity. It would probably require interviewing the students in some way. It would also be interesting to look at how teachers are using the lesson with their classes.
KlausMay 31, 2013 - 6:58 pm -
loved the project.
Started to wonder though if everything is properly coded.
I used an approach via HSV, creating an inequality that kept the Hue value H between 180 and 260. This worked for 87% of the given examples, but my score was only 57% when the formula was tested on all 4000 combinations. I redid it with another sample of 30 colors. same thing. Strange.
another things that was odd, was that among the examples there were no colors that were judged not blue between 60% and 100% of the time.
and one judged not blue 100% of the time was so close to blue (to my eyes) that i had a hard time believing the data.
Joe BoyerJuly 2, 2013 - 6:19 pm -
I loved this and used it with several classes, but now it seems broken and won’t load. Was it just a temporary thing?
Joe BoyerJuly 4, 2013 - 8:17 pm -
It’s great that it’s working now, but it’s not really working properly. The “Or” function is broken, and without that it’s pretty difficult to get a score above 80%. Any function with “OR” just gives a blank value.
Feature request: I also wish there was a way to jump straight to the challenge bit of coming up with the rule, so when we revisit it in class the next day the students don’t have to go through all the intro bit.