Interesting ideas & compelling illustration. Thanks, Jonathon.

The evolution of the challenge is critical to player learning the challenge. Because not only does it allow the player to interpret the results of their actions, but the player understands how the game changed because of their actions.

Here is an example.
Here is a gif of a Mario fan game granting Mario the use of a portal gun.
https://i.imgur.com/Htssq.gif
When presented with an obstacle (Hammer Bro), Mario uses the portal gun to have the hammers thrown at him come right back to the Hammer Bro. The Hammer Bro. is defeated, but the lethal hammers are still in play being thrown over and over again in a similar arc through the leftover portals. Bringing about a new challenge for the player to solve.
If the game were to just “interpret” the player’s actions in this situation, the Hammer Bro. is defeated. However, we think in terms of how the game “evolved,” the player has defeated the Hammer Bro. BUT, because of the specific action the player took in defeating the Hammer Bro., a new problem presented itself. Allowing the player to understand more of their own technique and problem-solving method.

There are not many math subjects that may allow for this type of “evolutionary interaction” in their current state. But developing a teaching style or game with this in mind will allow for students to better understand the subject matter.

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The “Instant Replay.”
Student: Solving some equation divides both sides by x, arriving at a dead-end..

Commentators: “Oh. So close… Let’s look at that again in slow motion…”

I would slightly change the Dan’s answer by plugging in the actual number instead of “c”. For example, “I see where you’re going. But let’s take c=2 for example. Then your expression 9c results in 18. And 18 is not a quotient of 9 and 2, it’s their product.”

Both of those essays are canon. Thanks, John.

This page collects a bunch of his demos and ideas related to math. The idea of scrubbing is especially related to this idea of being a cause.

http://worrydream.com/KillMath/

But note this very thoughtful rebuttal: https://www.evanmiller.org/dont-kill-math.html

While I agree that PE has a solid feedback mechanism – I would argue that the site is geared toward mathematically inclined learners who are intrinsically motivated to get answers to obscure math questions, and the feedback fits the needs of this audience. Would a more general audience get tired of being wrong and just rage quit? How do we cultivate the persistence to keep at a problem and try multiple solution pathways before giving up?

It has become a more common social mechanic to open up discussion for folks that get the answer correct (or in some cases, who opt to see the solution, eg HackerRank or Brilliant.) I agree that this is effective and seems to promote more discussion.

I’ve come to feel that the feedback offered in typingclub is ideal feedback for deliberate practice. It shows me the expert model as I attempt to perform in real time. I can refer to it if I get stuck, but I can keep moving forward if I make a mistake. It is both non-intrusive and immediate. I am not sure how to mimic that with something much less mechanical and rote than typing – namely problem solving, or even particular skills like adding fractions… but I hope it illustrates a contrast to the feedback on PE, that in my opinion, more reluctant learners need in order to eventually build the confidence to hit ‘b’ with their left pointer finger and ‘x’ with their left ring finger… and by kludgy analogy, properly distribute the negative when multiplying polynomials, or find a common denominator when adding fractions.

After writing that out, it really doesn’t seem a fitting analogy. Now I am wondering why multiplying polynomials or finding a common denominator are different in structure than simply remembering which finger to use for a keystroke… thanks for getting me to ponder this William.

Always woven into the question is a simpler particular case of the question with an answer that allows you to check your own reasoning as you work. It’s marvelously effective at allowing a mathematician to work towards an answer from a place of discovery.

The reward for answering correctly (!) is access to a discussion forum where other people who have answered the question correctly can discuss their answers.

Socially it’s totally different from most online (and classroom) pedagogies, and marvelously effective.