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The article laments a disconnect between learning and work force skills. On the other hand, they claim a high school diploma makes $260k difference in life time earnings.

So what value does a high school diploma provide? What's the reason for the $260k increase?

Social approval, socialization expectations, etc.

As far as capitalists care, your productivity, predictability, and sociability are what's important. HS diplomas are not uniform. Institutions that are permitted to discriminate based on high school attendance do so to an extreme degree. So while legally the diploma is a commodity, in practice it's a highly differentiated good.

If you are lumping in University High School graduates from SF in with graduates from Compton High School, you will be mislead.

Because that $260k figure isn't explained, it should be ignored. 'Cause life's too short to be bamboozled by unexplained numbers. If this author had access to the study, there's no reason that it couldn't be linked to or at least footnoted.

The TV tells us that we have millions of college-educated people who are eager and engaged but still can't find a sustainable job.

Do high-school dropouts really have a chance in such a competition if they need gamification to become re-engaged?

As soon as high-school dropouts learn marketable skills that do not require credentials or formal education, sure they have a chance. Some of those skills are: coding, design, copywriting, UX/UI design, etc.
Wait, wait - learning any of those skills can surely be done, but it naturally requires motivation, time and engagement.

That's the whole point - if we're expecting employers to use gamification to engage them after hiring, then can we expect them (the majority of them, not the best of them) to learn nontrivial marketable skills on their own before getting that job?

Well, programming and coding education is already gamified (codeschool, treehouse) so if gamification works for that target audience it will work at the education stage, too.
I think there is a bit of merit to this - part of the problem of schools (which i've read about off and on for years) is the expectation that students sit there and absorb lectures without any actual interaction with the information they are supposedly learning. I find this would be a decent bit of solution if it were used in conjunction with other changes. But considering in some places they make a fairly grand issue about whether or not students should learn cursive writing (Indiana has had this) and there are people that think education should go back to "reading, writing, and 'rithmatic", I doubt schools are going to consider this approach, let alone others that try to solve a number of issues with people dropping out of high school.
Gamification is great, but from personal experience I find it only works when I'm already engaged. e.g. I'm interested in what's going on HN and the karma points help motivate me to contribute, or get a sense of whether my comments are valuable to the community etc. Same with StackOverflow etc.

Gamification won't convince me to do something I'm not already interested in doing, and to some extent, even things I would like to do (e.g. learn a new language), but which are hard - gamification helps, but won't be enough to keep me learning.

That's just my personal observation. I do not know if it applies to others.

Gamification can play a role in a program for dropouts, but it by no means is suitable as the sole treatment: It just patches over the underlying problems[1], among others lack of robust archivement motivation in combination with lack of learning competence. To worsen things, working class students (who have a higher probability of being a dropout) also attribute bad performance in school with lack of talent rather than lack of effort more often than middle class students. A treatment in a school context that has been shown to be both sustainable and effective is continuous feedback on the relative improvement in archivements of the specific student (school marks comparing the individual performance to the class usually make the percieved talent-mark correlation worse as the high-performing students often didn't need much effort to get their marks). Luckily this is one of the seldom cases where a treatment has stronger effects on the students with learning problems compared to the high performers, too (thats usually a big problem in pedagogy).

[1] Leaving out the the sociological context. I really doubt "boredom" was a real reason, boredom sounds too much like self assessment.

edit: typos

Many people believe Gamification is the key to the problem of motivation. But only in a few cases it could be applied successfully up till today. Posting the same post 5 years ago might have resulted in a lot of positive discussion and feedback, but nowadays people are already a little disappointed of how Gamification performs in general. It's still a good argument but it shouldn't be the only one and it should have some examples from successful applications by the author.

The same goes for the software that 26gems plans to implement. Gamification should not be its main selling point, but it can be an awesome finishing.

I agree - we are only now coming to where we understand gamification enough. I do believe that gamification is very important for some of the rote, but necessary, aspects of educations. It's not a cure-all, but perhaps it's good for drilling basic math, building vocabulary, and learning grammar.