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Comment by kulahan | Hacker News Reader

I recently read something that stated we've never really had more than 30% of students in the US at a level of mathematical understanding where they can tell that 3/4ths and 0.75 are the same thing, conceptually.

I cannot stop thinking about this; it honestly explains so much.

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The third-pound burger flopped because consumers failed to understand that one third is bigger than one fourth.

https://en.wikipedia.org/wiki/Third-pound_burger#Marketing_f...

Thanks for this, wow.

Should have promoted a quarter-plus-twelfth burger! That's about 37%!

Why complicate it: just advertise a fifth

With a price markup.

Thank you! I heard that on the radio decades ago but never saw a source to point people to. Wikipedia, who knew?

I would hope fervently that HackerNews would be subject to selection bias and would be an exception, but who knows.

Indeed, one thing I keep in mind is that almost all progress, social, technical, political, etc. are wrought by an exceedingly small proportion of people. These are usually the people derided as deviant, nonconforming, abnormal.

Left to the vast majority of "normal" people who want to half-ass everything, there'd be absolutely no progress whatsoever, and what is more, society might actually fall apart.

I like Kandinsky’s metaphor of a flying pyramid with progressors at the tip and more down-to-the-earth people at the base. Such a good idea.

Even harder to understand that 1 part vinegar and 3 parts olive oil isn't 1/3 vinegar.

One cup vinegar and three cups olive oil will give you four cups salad dressing.

That’s probably one of those cases where they use two different statistics to assume a conclusion, e.g. maybe only 30% of students pass a particular profiency test, and then add to the fact that that test is the minimum level where fractions/percentages are expected to be known, and combine it to make a scary sounding headline.

You might be right but, citation needed.

Sure: https://www.nagb.gov/naep/mathematics.html

Additionally: https://www.nationsreportcard.gov/

22% of 12th graders are considered proficient in Math. This means:

NAEP Basic - Apply single-step percentages to solve real-world problems.

NAEP Proficient - Analyze information to solve real-world problems with proportional reasoning.

NAEP Advanced - Solve multi-step, real-world problems using percentages.

Specifically, for 12th-grade math, the cut scores are 141/300 for NAEP Basic, 176/300 for NAEP Proficient and 216/300 for NAEP Advanced. https://nces.ed.gov/nationsreportcard/mathematics/achieve.as...

The score is an aggregate over questions testing many different skills, so while getting a low score suggests that a student is less skilled, it doesn't immediately tell you which skills they're bad at in particular. So this is exactly the scenario that 'ninkendo was talking about. If you want to know how many students correctly answered a specific question testing a certain skill, you would need the raw disaggregated data, which I don't think NAGB publishes.

I'd like to add that it's intentional that there are substantial numbers of students in each of the four buckets defined by the three thresholds, since the goal is to track the performance of the overall population, not just a few very bad or exceptionally good students.

I should've clarified it was an example, not that literally that one highly particular thing is what all American students are bad at, or that knowing .75 == 3/4ths == 75% somehow causally affects your future or whatever.

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