Badge Designs
Recently I've been programming a few different badge icons and ideas. My first one was Aspen.
Aspen was meant to be a badge that user would earn for being a member for 5+ years on Khan Academy. As of right now, there is a badge for 1-4 years of membership, but none for 5. Personally, I think a 5 and 10 year member badge should be put in place.
Aspen: Remain a member of Khan Academy for 5 years
The next badges are for the Unit Mastery system that is, I think, in beta form right now. I decided why not make badges for each category? Apprentice is for 0-24% mastery, Explorer is for 25-49%, Pioneer is for 50-74%, Adventurer is for 75-99%, and Sage is for 100% mastery. These are terms made by the KA team, I simply designed the badge concepts. Now I'm not sure how they would be earned since if you truly mastered all the math skills on KA, you'd get a crazy amount of these badges. So they would probably have to be a different way these were awarded than a set for every single section.
Apprentice: Achieve 0-24% mastery in a given section
Explorer: Achieve 25-49% mastery in a given section
Pioneer: Achieve 50-74% mastery in a given section
Adventurer: Achieve 75-99% mastery in a given section
Sage: Achieve 100% mastery in a given section
Another thing I've wanted for a while is Question badges. Now currently, there are two Question badges put in place (Investigator and Detective) But Answers have Excellent Teacher, Guru, Incredible Teacher, Sensei, and Oracle. I think badges for questions should also have that amount. So, that being said, I believe three badges should be added.
Excellent Thinker: Post 5 questions that earn 3+ votes
Incredible Thinker: Post 25 questions that earn 3+ votes
Curiosity: Post 50 questions that earn 3+ votes
I've only designed a badge concept for Curiosity since finding a "thinker" badge icon that doesn't already go along the lines of other badges out there, is very hard. I was thinking light bulbs, gears, a head with brain, question marks, etc. But all those have already been taken. Nevertheless, here is the Curiosity badge I came up with:
Finally I thought about some rare badges that are real badges, but not many users have them. These are Special Project, Support Advocate, and a more well known Rave Reviewer. Now a small disclaimer, I'm not very happy with my designs for both Rave Reviewer and Special Project but they'll have to do as concepts.
Special Project: Go above and beyond! Contribute to an officially recognized special project that will live on in the KA community.
Support Advocate: Become a Support Advocate who responds to posts in the support community and helps users escalade technical issues.
Rave Reviewer: Evaluate 150 projects
Last, but not least are two badges that have icons, but another user had asked me to make new icons for. I'm not a big fan of them as they have a pretty gross color scheme but they were fun to make.
Documentation Doctor: Create documentation for our programming courses
Trusted Tester: Review our programming courses before we release them
These are just some of the badges I have come up with but I have many other ideas I think KA would benefit from. I won't post them due to length reasons but I might post them in a different request later down the road.
Thanks to all who read, I hope you feel inspired to go out and make your own designs and try new ideas! I certainly had tons of fun while making these badges and am excited to go on to make more later on. Let me know if you have any questions about any of the badges above, I'll be more than happy to answer them :)
All these badges were designed on Khan Academy.
Special thanks:
I want to thank Jett for helping me perfect the gradient inside the badge. Before, they just looked really plain and didn't pop as much. But since he was able to figure it out, they were able to become much more colorful and vibrant.
Another thanks goes out to Legolas. He helped me with the inspiration for Curiosity. I was originally going to just do a hand holding a magnifying glass, but he suggested I put a finger print in there.
-Light Runner
The user profile widget could have a similar look to either the badge counts or the showcase:
It could, as you suggest, show the amount of mastery in subjects that you have. (Along with the lower levels of mastery) 
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