I can get around this by brute forcing the numbers into the formulas on paper and going through each step slowly but surely, even steps that people can do mentally. I just need significantly more time than my peers to finish.
Taking stimulants and increasing my dopamine levels across my synapses alleviates much of the working memory deficits I outlined.
I wonder how many of these students that struggle were just undiagnosed ADHD and not deficient in an low IQ mental handicap sense.
I've got ADHD that was undiagnosed until a decade after finishing my degree, and maths was my favourite - and best - subject all the way from age 4 through to doing solutions to Einstein's equations involving 10+ A4 pages (both sides) of tensor mechanics for my final year project. My results across that time showed the more maths in a subject the better I did, the more writing it had the worse I did.
Doing maths is like reading is for me - an external cognitive structure that I can follow to make my own brain calm down while in that process. While I don't do much maths nowadays, I literally read whenever I'm not actively doing something else - I read a page or two of my book in-between clicking reply to your comment and starting typing this reply.
Maths involves a lot of "muscle memory" once you get past the initial hump. But it's often poorly taught at an early age to the level of inducing near-phobic levels of discomfort with it which to me seems strange. But I don't think there's any extra issue with having ADHD and maths
ADHD is very comorbid with dyslexia, dyspraxia, dysgraphia and dyscalculia - around 20–60% of people with ADHD also have one or more learning difficulties. Dyscalculia affects as many people as dyslexia, but dyslexia is far more well-known and more likely to get diagnosed and helped with. There's a nice summary box of typical symptoms of dyscalculia in this paper:
Interestingly, testing myself with the Wechsler reverse-digit-span test, I found very large improvements in working memory from taking 20-minute afternoon naps and from modafinil. I'm not claiming everyone is alike, of course, but working memory is definitely not as fixed as height and eye color.
Specifically with regard to mental math, I find I can do a lot more when I'm lying in bed in a dark room than when I'm in an uncomfortable chair in a noisy cafe with people talking to me. Or, for that matter, classroom.
> Many of these students grew up in rich neighborhoods with good parents. They had most advantages you can imagine, seem reasonably intelligent when you talk to them, but Algebra will always be beyond them.
I tried marijuana once and found the opposite effect: when I was high, by the time I got to the end of saying a sentence, I couldn't remember how it had begun. But people report that I seemed like I was conversing normally; if they didn't know me, they wouldn't have realized anything was off. I wonder if these folks were experiencing something similar all their lives?
Sure. My ability to do anything also drops to near zero if I don't sleep enough. Yet I have not found unlimited increases in capability if sleep more and more...
> modafinil
Yeah, drugs are a quite different beast. Doping happens when individual athlete realizes they have hit the limits what their "natural" biology can do and yet still are not going to win the competition.
If you are functioning at the optimal point - stimulants will only make your performance worse.
You are likely sleep deprived, for whatever reason. That's all.
Wait, are there mainstream schools of thought where working memory isn't considered valid? I'm a layman but I suffer from ADHD, and very much notice that my working memory fluctuates with my attention span (from lack of sleep/stress/etc).
Google's of no help to me, but I remember a story of some educators, looking at some kids who didnt go to school but worked selling concessions, but in turn, were actually quite good at math. They couldn't answer math questions when written out on a worksheet, but they could do the exact same questions when presented in the form of a complex order. (Double digit multiplication and summation isn't the same as algebra, but being able to do that implies a large working memory, which is claimed is the barrier to learning algebra.)
But I did make paper sort of my working memory and when doing algebra I felt that I was just the very resource limited CPU that executed the instructions from paper-memory.
Algebra always made me feel like I was doing some mindfull exercise where I had to empty my mind, follow the paper script and hope I didn't mess anything while switching from row to row of calculations.
Even today, as a programmer, I struggle to remember class or function names, I just empty my mind and am really good at searching stuff in code.
> There is also evidence of domain-specific cognitive deficits that contribute to specific learning-related disabilities. For example, phonological processing difficulties have been found in children with poor reading performance, whether or not they also exhibited problems with ADHD symptoms or math, but not in children with deficits in ADHD symptoms or math only. Similarly, both with and without a reading deficit, children with ADHD symptoms exhibit significantly impaired object naming and behavioral inhibition, and math-disabled groups demonstrate visuospatial and numerical processing deficits, while those with only reading problems sometimes do not.
There's significant co-morbidity between learning disorders and ADHD, and despite dyscalculia being as common as dyslexia (~3-7% of the population) it's a lot less well-known, isn't as frequently diagnosed and there are fewer tools to help people with it. It would be very possible to have both ADHA and dyscalculia, given you used symptoms listed for both that are almost word-for-word identical with those in the paper...
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7079676/
(paragraph 3 of the main discussion)
My problem was that oftentimes I would screw up calculations for a math problem and only get 7/10 score on it (the reasoning was mostly right, but the answer was not).
You sequenced the genomes of your students and correlated their performance against their genes?
I haven’t performed any genetics tests but brain composition is partly determined by genetics so genetics might play role, right?
I got the feeling as a kid that a lot of my classmates would just give up. I mean they're sitting there acting like they're concentrating on math, but they aren't. In other classes intermittent attention is enough, you pick up social cues and repeated stories that you've heard, and poof you have a history essay. With math there's a need to have all the steps.
How do you control for that as a teacher observing the kids? How do you know whether a kid has actually tried to learn stuff at home?
I still remember my brother was baffled at how I got top grades in math when he never saw me studying. Of course I tended to do that when he wasn't around.
The only solution I ever found was not having more than 3 students at a time, not an option for most teachers; I spent most of my career working with 1-3 students as a result. With that few students you can carefully observe the mistakes students are making and ask individual questions about their mental state. Experience will eventually tell you to differentiate students not putting in effort from students who are so lost that they're just flailing and hoping something sticks.
With more students, my experience was that both my attention became too split to give students the kind of careful diagnosis to control for effort.
I have. Some people are dumb.
You try teaching these people (anecdotally they're less than 1% of the population, with no obvious markers, so you have to actually find one first) and then come back and tell me how it's like "getting algebra to run on someone with less working memory". If I wanted to continue that analogy, I might say that the task is like getting algebra to run on someone whose brain has a power supply that randomly shorts out and spends half its time browned out.
Because some people out there are just not easy to teach.
A week of playing Kerbal Space programm gave me better understanding of orbits than years studying calculus, physics, general and special relativity.
It has poor applicability in everyday life - we learn all the biology of a cell but kid's don't know the difference between aspirin and ibuprophene.
To start, I believe that the idea of "working memory" is largely valid. Think of it as the number of distinct ideas you can hold in your head at once, sort of like trying to hold a phone number in your head when you've just heard it for the first time.
The general consensus in psych is that this number for the average person is in the single digits and is relatively static in adulthood till a decline in old age. It's been my observation that people with really incredibly small working memory cannot do algebra. The amount of numbers/ideas held in their head is too large, and multiple students in this group described the experience of attempting an algebra problem as feeling like sand constantly slipping through their fingers.
Many of these students grew up in rich neighborhoods with good parents. They had most advantages you can imagine, seem reasonably intelligent when you talk to them, but Algebra will always be beyond them.