Hi Dan, Thanks for getting back to me. I had my students do the Desmos Activity “Smiley Face” where they learned to restrict the domain and range and they learned that what they typed effected their picture. Computers are picky about reacting to directions that we type. This was a great lead into the importance of being able to express our ideas in math symbols, and I talked about Set Builder Notation. But…my “wonder” here is this: Does Desmos have a way to type in set builder notation to restrict a domain (or a range) to only “Integer” values as we would in a sequence, or to restrict it to “rational numbers” as we would in a context where values deal with money (which are always rational numbers). Is there a way to connect Fawn Nguyen’s Visual patterns website to a Desmos activity where they have to restrict the domain to integer values? This would allow them to really see how the graphs are either discrete or continuous. If there is already something in Desmos that can do that, can you let me know. Thanks for all the amazing things you do!

It all depends.

I have used DragonBox Algebra with students that haven’t mastered solving complicated equations (i.e. their Dragon Box interest outpaced their math studies) and have been able to flash up, in the middle of instruction, a screen from DragonBox Algebra and ask “why did the DragonBox program prompt look like this?” or “What would Dragonbox prompt you to do?”

I personally play DragonBox Algebra as a leisure activity much like I do Suduko puzzles. I don’t think anyone thinks DragonBox is going to replace mathematics education but I think of it as laying the ground work for math education…..the way picture books set the ground work for teaching reading.

Regarding DragonBox math…..a simple reality that all developers need to understand…. is that many school computers aren’t running Microsoft 8 or higher yet. I have purchased personal Apps for interested students to use on their personal electronic devices but too many times their devices do not have enough space to use the App with all the other images/videos they have on them already that they “simply can’t live without.”

But I will forever fully support any video games that support student engagement!

Actually, I don’t think you’ll need to make any kind of a priori assumptions at all. Rather than assuming that all humans make good judgments, you should be able to use your data stream to identify the teachers who have the best judgement. Then you can train your algorithm just on their decisions. Very exciting–I wish your team all the best.

Should humans adapt to input devices? It’s the other way around and the pen will make a comeback.

+1

But until it thinks like a human, could it be a far better approach to connect people and give them better communication/sharing tools?

Do we overinvest in autonomy and not enough in collaboration between peers? I have that feeling.

Love these values. I’m curious how you put them to work in BuzzMath, Carl.

Kevin:

Could you add a feature to Desmos that lets teachers advance all students through a lesson synchronously?

On the way, and for exactly the use case you’re describing.

I think the intervention itself could have lots of closed-ended question-answer loops, ideal for automated feedback, as long as a human teacher certifies that this intervention is the one that’s needed.

I like your faith in humans. We share it. Over time, I’d like those tutorials be suggested automatically, but right now we just don’t have faith that computers are smart enough to make the right suggestion.

Taking the future you’re describing and running with it:

We’d know every intervention that a teacher ran, and when she ran it, and what student work preceded that intervention. At whatever point we feel confident enough to train a computer to suggest the intervention, we can run that suggestion algorithm back through all those interventions and see how many times the computer gets it right. Which is an a priori assumption that the teacher got it right originally. I feel more comfortable making that assumption, though, than the a priori assumption that computers will get it right out of the box.

Let me back up and say that as I see it, there are two very diferent types of Desmos lessons: 1) conceptual explorations like Central Park, Function Carnival, Penny Circle; and 2) skills practice that’s more open-ended than a typical worksheet, like Des-Man, Polygraph, and the Marbleslides. You might think automated feedback would fit best in the latter category, but I think it would run into all the problems your blog post describes.

Instead, I’ve longed for little tutorials that I can turn on to assist specific groups who are stuck during conceptual explorations. For example, lets say a group is stuck making the mistake I mentioned above: writing w-3p/4 when either they need to write (w-3p)/4 or they need to hit the “division” button first to create numerator and denominator textboxes before starting to enter their expression. As teacher, I’m busy going around to different groups when I notice that Sammy’s group is stuck on this. I type in a little teacher code and activate the Desmos tutorial that intervenes for precisely this misconception; then I skitter off to the next group with a plan to circle back to Sammy’s group later. I think the intervention itself could have lots of closed-ended question-answer loops, ideal for automated feedback, as long as a human teacher certifies that this intervention is the one that’s needed. In fact, I think teachers wouldn’t mind writing the interventions themselves in the activity builder…you could probably crowd-source them!

In the future, computers will connect me to humans when there is no added value in guessing me.

In the future, humans will learn when a computer can add value to a task. I like Audrey Watters on that topic.

I love how handwriting is getting interesting again. People are still clamoring “you don’t need to learn cursive writing, we are in a keyboard world”.

Some think they are even more progressive, saying “you don’t need to learn the keyboard, we are in a touch keyboard world”.

Should humans adapt to input devices? It’s the other way around and the pen will make a comeback.

And next year, No UI is the New UI:
https://medium.com/swlh/no-ui-is-the-new-ui-ab3f7ecec6b3

And the following, it’s going to be teaching with VR. And after that, they are going to wire your brain. Etc. etc.

But until it thinks like a human, could it be a far better approach to connect people and give them better communication/sharing tools?

Do we overinvest in autonomy and not enough in collaboration between peers? I have that feeling.

Thanks for the generous posting Dan!

Will Desmos be trying to integrate some feedback into its activities? I think Central Park could be made much better by making it a little adaptive.

Thanks for the suggestion, Kevin. We’re starting to make some tentative steps into computer feedback. We are just really skittish about making false claims about student learning. We’d rather our system make no evaluation at all than make a false or misleading evaluation of the sort you see in this video.