I used to train people to work as cashiers. There was a marked difference between people who could do math and people who understood how math works. My “test” to categorize them was asking what happens when you divide by a (positive) number less than one.

And they would reply (and pass the test) “There are no positive numbers less than one”

Well, integers anyway.

Why would you think, in the context of that question, that “positive numbers” have to be integers?

Congratulations, mister confidentially incorrect. You failed.

“confidentially” ?? a typo I guess.

How about just asking what is 10 divided by 1/2?

Unless those percentages are volume of constituent divided by volume of mixture. 6% ABV beer is more than 94% water by volume.

one-and-a-half thirds of 100 - throws off a surprising number of people

You guys sure think everyone has as easy a time with math as you do.

I got a B/C in Math 101 in college thanks to the best TA **ever** and stopped there. Math is not my thing. I sincerely doubt I am alone.

Are you perpetuating the “fixed mindset” idea that people either are or are not “math people,” and there’s nothing you can do to get better or develop math skills?

Really, math is hard for everyone. We all had to put in work to get good at it. I think the biggest difference is, for some people, it’s fun. It’s a lot easier to put in the necessary amount of work if you enjoy it.

These aren’t opposing ideas. Anyone can work to improve their math skills, yes, but also some people will have an easier time in doing so, just as with music or language, etc.

Having an easier time in a pursuit naturally makes it more fun, which amplifies initial predispositions over the many years of skill development. That is: yes, it takes work to progress with a skill (such as math) so it has to be somewhat enjoyable, but it’s going to be more enjoyable if you’re at least sorta decent at.

Really you are wrong. I loaded up on math courses when I was working my way through college because that was the easiest way to get credits without having to do any work (except go to class and listen). As a grad student, there was only one course I ever took where I actually had to do some work. If you care, that was called algebraic geometry and I still don’t fully understand the Riemann-Roch theorem.

And you don’t do things like, for instance, mentally work through math problems to pass the time when you’re bored? It might not seem like work to you, but it would to many folks.

The guy at the drop/add table at my college was very confused that I was adding “Topology” (and dropping something else) - he said that he’d only ever seen “Topology” dropped before.

No. I am saying for some of us trying gets us to just over basic and no more.

It’s like I can train like crazy for a swim meet but practice and natural talent will only make me middle of the road at best.

Everyone can’t be good at everything, no matter how much they try.

I still don’t fully understand the Riemann-Roch theorem.

That makes two of us. At least.

I remember older generations had intuitive math skills. My grandad born 1902 never got past 7th grade. He was lucky to stay in school that long. He had to work on his dad’s farm. He left to work in the oil fields at 17.

Yet he was good with basic numbers. He helped my mom with her high school math homework. My mom told me that he couldn’t explain how he got the answer. But she’d work the problem and use his answers to check her solution.

I’ve heard similar stories of people’s grandparents and great-grandparents. They didn’t get cheated on their paychecks or in stores. Understanding numbers was a life skill. If they were hired for 65 cents an hour, they knew 55 hours in a week meant $35.75 in the pay envelope.

Maybe it was knowledge they learned from years of working. But the lack of a formal education didn’t mean they were ignorant.

I don’t think you can extrapolate from the fact that your grandfather was good at mental arithmetic to conclude that “older generations” in general had the same skills. My mother was abysmal at practical math. I remember my son once left her house and took a taxi to a location about 40 miles away, then called us about an hour and half after he left. She didn’t know he had taken a taxi and said that he must have walked. I said, “he couldn’t possibly have walked that far.” She insisted, saying “he’s been gone a long time.” She really thought someone could walk 40 miles in an hour and a half.

I remember older generations had intuitive math skills. My grandad born 1902 never got past 7th grade.

in the old days, by the 7th grade, you had been drilled in arithmetic for years. The old “3 R’s” were reading, writing and 'Rithmetic. These were the skills deemed necessary to succeed in life for most kids, and the schools did not coddle kids.

They learned the “Times Table” thoroughly, and would be able to calculate their salary (65 cents times 55 hours= 35.75. in your example) faster than we can.

The teaching methods were based on rote memorization. and people were good at it. There was no TV or radio to distract people, paper was expensive, pen and ink was inconvenient to write notes with*, so people had better memories than today.

*( kids used chalk on slate in school, not notebooks)