There’s no onus on either of us to do anything. We are just strangers posting on the internet without pay or other compensation. Your experience and knowledge about teaching help me to decide the merits of your beliefs. It appears from my perspective that you know quite little about what you are posting. I know slightly more by having a lot of anecdotal evidence but this certainly doesn’t imply that I’m more likely to be right.

As stated in my original comment I’m quite liberal. In education we talk a lot about social conditions and their effects on education. It’s why teachers’ unions strongly support universal healthcare, school lunch programs, etc.

After 20 years on the job I’ve come to the conclusion that some can’t learn it. This isn’t controversial in some sense since we know retarded people can’t learn algebra. So what level of capability is necessary to learn it? I don’t know but I suspect it’s well above being mentally retarded.

I could be completely wrong but given your lack of experience in the topic my experience ought to at least make you pause a bit. In another comment you wrote about me:

… you're more likely ignoring the real-life circumstances your students find themselves in, and your colleagues are not.

Talk about making an assertion with no evidence! At least I waited 20 years before stating my absurd assertion.

It's clear to me that this belief has wormed its way into your identity somehow, and you're unable to discuss it in a detached and curious way. I'm sad for you that such is the case, but I am now more empathetic towards your colleagues who have to deal with your false assertion that some people are too stupid to learn the math you teach.

Also not for nothing, but "retarded" hasn't been a medical term for some time now, with institutions such as the AMA and SSA both replacing the term with "intellectual disability". The only remaining reasons you'd use it are either because you are thus uninformed, or you're signaling something...

It’s easier to type retarded than intellectually disabled on an iPad. I wrote the modern version in my original comments. Clearly I have been discussing this topic in a detached way. You’ve formed an image in your mind about me that isn’t supported by the evidence.

I’ll read whatever response you have but won’t comment further. I wish you well. Keep up the good fight!

You can use "cognitively impaired" as a more neutral and factual descriptor than either (and "cognitive impairment" as the generic term). It's also more broadly applicable. (I.e. If you got whacked in the head once too many while playing rugby, that might not count as "intellectual disability" according to some since it's not developmental. But it might interfere with learning math, so it's pretty indistinguishable in a practical sense!)

That’s a better term to use. Thanks for the suggestion.

Thanks, I appreciate you taking the time to talk about a view you've held that's been unpopular with your colleagues.

I think you, and everyone who thinks like you, need to take a very hard look at what you've done to eliminate the environmental factors related to your viewpoint that some people aren't smart enough to learn something, because its extremely easy to trick yourself into thinking someone is incapable when in reality other factors abound.

As the article explains, if society refused to educate/feed/raise/nourish red-headed children, there would be a genetic correlation between red-headedness and intelligence.

How absolutely confident are you that you've accounted for every explanation besides the genetic one in determining why some people can't learn algebra?

Its kinda crazy how casual people are with their constraints on explantion when the topic is intellectual disparity. Person you're replying to claimed they weren't arguing for a gentic component to another reply but also doesn't do anything to filter any other factor than a congential threshold for learning math. This is absolutely why the Left is generally leary of this type of discussion because it is so easy to use the information for all sorts of ill-informed or cross purposes.

It's pretty clear you've never instructed a remedial math class.

My university would conditionally admit students who had a math score below a certain threshold on their ACT, I think it was 19 or something. Anyway, as part of their admittance criteria, they had to attend an after class lab for an additional hour an a half for a total of three hours per week dedicated to learning pre-algrebra. There were four modules where they would do some reading, work through some example problems through interactive software, and then have some homework to work through that was almost identical to the examples. Students would try and try and try and try to learn the material, and they would take days to work through the problems on their own (often with my guidance, giving pointers on how to think about the problems) to finish the module so they could take the quiz and pass the module. Near the end of the semester many students made appreciable progress, but for others the inability to retain and apply what they've spent so much time on results in tears, especially because they don't know if this requirement will keep them from being able to graduate.

Given infinite time, could these guys all have figured out pre-algrebra enough to pass? Maybe. But the amount of time it takes them to learn math concepts that are very easy for us means that it's entirely impractical to expect them to ever achieve proficiency in advanced mathematics.

It’s interesting reading the responses of people who never taught in the classroom.

> There were four modules where they would do some reading, work through some example problems through interactive software, and then have some homework to work through that was almost identical to the examples.

This just does not look like a universally effective way of teaching to me, irrespective of the topic. It's hardly any wonder that some people fell through the cracks if they were unfamiliar with the subject in the first place. What about leveraging stuff that's actually been tried and tested, like the Khan Academy videos and their automated interactive, school-like environment?

They used Pearson software to learn to modules. I didn't explain that part in much detail, but it was highly interactive and had instructional videos.

To take a step back for a moment, what is it you think I'm saying that's so objectionable?

> And to be clear, I don't doubt that many people "can't" learn calculus in the same way I "can't" run a marathon; we don't have the desire, discipline, and free time necessary to do the work required. This does not speak in any way towards our capacities to do so, only our desire.

Your VO2max, max heart rate, and other factors appear to be significantly determined by genetics, and will absolutely contribute to your capacity to run a marathon. If it takes you a year of hard training, but it takes me a few practice runs a few weeks before, it's not fair to say we required the same amount of desire, discipline, or free time to succeed. I would instead say we had a very different capacity to run a marathon.

Are you saying that similar things could not possibly be true for learning math? Or really anything else that humans do?

I don't think any of those things contribute to whether or not I could complete a marathon, though they do contribute to how pleasant the experience would be. The same holds for learning calculus, or doing anything intellectually taxing. It's differing in difficulty for people, however it's not unachievable for anyone who isn't experiencing some kind of mental (or physical, in this marathon example) impairment.

All healthy people can learn calculus and run marathons, with varying degrees of success and effort, due to genetics and environmental factors.

I don't see how if you can agree that it requires varying degrees of effort for different people to run a marathon or learn calculus, that you then think it is impossible that some people won't be able to do those things. Just like the amount of effort required will be small for some, it will be impractically large for others. Even in the theoretical sense, there is only so much time in a day.

I also don't think "healthy" and (presumably) "not healthy" are useful categorizations. There are many people in that fuzzy in between area between "healthy" and "not healthy", for both physical and mental health.

Is it really worth so vigorously arguing the semantics of "some people are incapable of learning algebra" and "it requires an impractically large amount of effort for some people to learn algebra"?"

Yes, I think it's absolutely worth arguing the difference between "it's hard" and "it's impossible", because those are two fundamentally different things.

You can overcome difficulty, you cannot overcome (by definition) impossibility.

What you keep ignoring in what I'm saying however, is that I do think certain things are impossible for some people. I will never play in the NBA, for example, but that's a far cry from being "very good" at basketball.

Learning calculus and completing a marathon are not the point at which "healthy" (and yes, it's fuzzy, but precision is impossible on this topic) people are sometimes unable to do things. Winning a marathon and getting a Ph.D. in mathematics, I would acquiesce to your argument.

In other words, I think anyone can dabble in anything, but you do need an alignment of genetic and environmental circumstances to be in the top 1% of something. I could be argued into top 10%, but below that, it appears the data supports almost anyone being able to do almost anything, or at least well beyond whatever artificial lines we might draw to discourage people from achieving.