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If this is correct (and I hope the Cleveland Clinic webpage and similar sources are reasonably reliable), I can see the point immediately: the traditional curriculum involves many "drill to kill" and "let's remember this for now without full explanation" techniques and just as many routine computations. So, if your ability to keep numbers in your head and manipulate them speedily is limited, you'll struggle a lot. One of the middle school kids I helped with math could follow the full explanation of why the total number of different ways to get dressed for rollerscating (the conditions are that you have 3 operations: putting the shoe on, tying the laces, and buckling the shoe latch. The last two can be done in any order, but only on the shoe that is on the foot already; the left and the right foot are distinguishable and you can switch between them as many times as you want in the process; try to figure the answer out in your head before reading further to evaluate the level of conceptual difficulty here) is what it is, but was getting C's or even F's on the multiplication tests because she was still in the middle of the exercise sheet when the whole class finished and because she occasionally had trouble remembering if five times three is twenty five or tventy three and had to resort to adding 5+5+5 to get the correct 15.

Removing all that entirely or almost entirely and just asking if a big number times a big number is big or small, if the sum of a few positive numbers can be negative, if the number of leaves in a healthy deciduous forest in the summertime is bigger or smaller than the number of tree trunks, how to organize the river crossing for a wolf, a goat, and a cabbage head, etc. (the questions many "normal" students have severe trouble with because no memorized algorithm helps much with them, forget about graphing calculators) in addition to clearly defining all terms and operating at the level requiring nothing beyond common sense (but, at least occasionally, a fairly refined and sophisticated common sense) can make these students feel like the robot character in Azimov's "Stranger in Paradise" when he finally gets to Mercury after being trained and tuned up in the Earth conditions (reread it if you forgot the plot).

"John Lennart Smale, a Texas farmer in the 9th generation, whose grand-grand-grandparents escaped Ireland after the Portadown massacre and found the new home in the faraway continent of North America, was sitting in the town saloon drinking rum and talking to the sheriff about strange disappearance of several cows from his herd a couple of weeks ago, the cows that have never been found despite Johns whole family was searching for them day and night"

"For every positive epsilon and every point $x$, there exists a positive delta such that for every $y$ whose distance to $x$ is less than delta, the deviation of the value of the function at $y$ from that at $x$ is less than epsilon"

Cows: disappeared. Belonged to John. Search useless, Sheriff getting ivolved
John: farmer, 9th generation, Irish ancestors. Ancestors: immigrants, escaping religious persecution. Location: saloon; drink: rum State: Texas. Persecution: Portadown massacre. Johns family: searching for cows. Search duration: 2 weeks. Johns full name: John Lennart Smale.

That is all I could recover after 5 minutes without looking at the sentence and I placed it exactly in the order it arose in my head when trying  . Now try to run this experiment on yourself and see how you think.

The point is that abstracting and establishing logical cross-references seems to work for people with discalcula as a primary compensation mechanism for the normal linear memory handicap when processing any information in their life from the early age, and they get as good at it as some blind people with their sense of hearing and touch, which, in the absence of the normal sight become the primary navigation means. So when they deal with highly abstract math, they just find themselves in the situation when their natural way of thinking is exactly what is needed for the maximal efficiency (in both processing and communicating) after many years of suffering in the environment that forces them to convert

If this is correct (and I hope the Cleveland Clinic webpage and similar sources are reasonably reliable), I can see the point immediately: the traditional curriculum involves many "drill to kill" and "let's remember this for now without full explanation" techniques and just as many routine computations. So, if your ability to keep numbers in your head and manipulate them speedily is limited, you'll struggle a lot. One of the middle school kids I helped with math could follow the full explanation of why the total number of different ways to get dressed for rollerskating (the conditions are that you have 3 operations: putting the shoe on, tying the laces, and buckling the shoe latch. The last two can be done in any order, but only on the shoe that is on the foot already; the left and the right foot are distinguishable and you can switch between them as many times as you want in the process; try to figure the answer out in your head before reading further to evaluate the level of conceptual difficulty here) is what it is, but was getting C's or even F's on the multiplication tests because she was still in the middle of the exercise sheet when the whole class finished and because she occasionally had trouble remembering if five times three is twenty five or tventy three and had to resort to adding 5+5+5 to get the correct 15.

Removing all that entirely or almost entirely and just asking if a big number times a big number is big or small, if the sum of a few positive numbers can be negative, if the number of leaves in a healthy deciduous forest in the summertime is bigger or smaller than the number of tree trunks, how to organize the river crossing for a wolf, a goat, and a cabbage head, etc. (the questions many "normal" students have severe trouble with because no memorized algorithm helps much with them, forget about graphing calculators) in addition to clearly defining all terms and operating at the level requiring nothing beyond common sense (but, at least occasionally, a fairly refined and sophisticated common sense) can make these students feel like the robot character in Azimov's "Stranger in Paradise" when he finally gets deployed to Mercury after being trained and tuned up in the Earth conditions (reread it if you forgot the plot).

"John Lennart Smale, a Texas farmer in the 9th generation, whose grand-grand-grandparents escaped Ireland after the Portadown massacre and found a new home in the faraway continent of North America, was sitting in the town saloon drinking rum and talking to the sheriff about the strange disappearance of several cows from his herd a couple of weeks ago, the cows that have never been found despite John's whole family was searching for them day and night."

"For every positive epsilon and every point $x$, there exists a positive delta such that for every $y$ whose distance to $x$ is less than delta, the deviation of the value of the function at $y$ from that at $x$ is less than epsilon."

Cows: disappeared. Belonged to John. Search useless, Sheriff getting ivolved
John: farmer, 9th generation, Irish ancestors. Ancestors: immigrants, escaping religious persecution. Location: saloon; drink: rum State: Texas. Persecution: Portadown massacre. Johns family: searching for cows. Search duration: 2 weeks. John's full name: John Lennart Smale.

That is all I could recover after 5 minutes without looking at the sentence, and I placed it exactly in the order it arose in my head when trying. Now try to run this experiment on yourself and see how you think.

The point is that abstracting and establishing logical cross-references seems to work for people with discalcula as a primary compensation mechanism for the normal linear memory handicap when processing any information in their life from the early age, and they get as good at it as some blind people with their senses of hearing and touch, which, in the absence of the normal sight become the primary navigation means. So when they deal with highly abstract math, they just find themselves in the situation when their natural way of thinking is exactly what is needed for the maximal efficiency (in both processing and communicating) after many years of suffering in the environment that forces them to convert

Removing all that entirely or almost entirely and just asking if a big number times a big number is big or small, if the sum of a few positive numbers can be negative, if the number of leaves in a healthy decidous forest in the summertime is bigger or smaller than the number of tree trunks, how to organize the river crossing for a wolf, a goat, and a cabbage head, etc. (the questions many "normal" students have severe trouble with because no memorized algorithm helps much with them, forget about graphing calculators) in addition to clearly defining all terms and operating at the level requiring nothing beyond common sense (but, at least occasionally, a fairly refined and sophisticated common sense) can make these students feel like the robot character in Azimov's "Stranger in Paradise" when he finally gets to Mercury after being trained and tuned up in the Earth conditions (reread it if you forgot the plot).

"I'm not an expert, of course, but 25+ years of teaching of students of all levels of brilliance and observing their struggles and successes, I am pretty sure that what I'm saying now may have some bearing on what's really going on here"

Removing all that entirely or almost entirely and just asking if a big number times a big number is big or small, if the sum of a few positive numbers can be negative, if the number of leaves in a healthy deciduous forest in the summertime is bigger or smaller than the number of tree trunks, how to organize the river crossing for a wolf, a goat, and a cabbage head, etc. (the questions many "normal" students have severe trouble with because no memorized algorithm helps much with them, forget about graphing calculators) in addition to clearly defining all terms and operating at the level requiring nothing beyond common sense (but, at least occasionally, a fairly refined and sophisticated common sense) can make these students feel like the robot character in Azimov's "Stranger in Paradise" when he finally gets to Mercury after being trained and tuned up in the Earth conditions (reread it if you forgot the plot).

"I'm not an expert, of course, but after 25+ years of teaching of students of all levels of brilliance and observing their struggles and successes, I am pretty sure that what I'm saying now may have some bearing on what's really going on here"

If this is correct (and I hope the Cleveland Clinic webpage and similar sources are reasonably reliable), I can see the point immediately: the traditional curriculum involves many "drill to kill" and "let's remember this for now without full explanation" techniques and just as many routine computations. So, if your ability to keep numbers in your head and manipulate them speedily is limited, you'll struggle a lot. One of the middle school kids I helped with math could follow the full explanation of why the total number of different ways to get dressed for rollerscating (the conditions are that you have 3 operations: putting the shoe on, tying the laces, and buckling the shoe latch. The last two can be done in any order, but only on the shoe that is on the foot already; the left and the right foot are distinguishable and you can switch between them as many times as you want in the process; try to figure the answer in your head before reading further to evaluate the level of conceptual difficulty here), but was getting C's or even F's on the multiplication tests because she was still in the middle of the exercise sheet when the whole class finished and because she occasionally had trouble remembering if five times three is twenty five or tventy three and had to resort to adding 5+5+5 to get the correct 15.

If this is correct (and I hope the Cleveland Clinic webpage and similar sources are reasonably reliable), I can see the point immediately: the traditional curriculum involves many "drill to kill" and "let's remember this for now without full explanation" techniques and just as many routine computations. So, if your ability to keep numbers in your head and manipulate them speedily is limited, you'll struggle a lot. One of the middle school kids I helped with math could follow the full explanation of why the total number of different ways to get dressed for rollerscating (the conditions are that you have 3 operations: putting the shoe on, tying the laces, and buckling the shoe latch. The last two can be done in any order, but only on the shoe that is on the foot already; the left and the right foot are distinguishable and you can switch between them as many times as you want in the process; try to figure the answer out in your head before reading further to evaluate the level of conceptual difficulty here) is what it is, but was getting C's or even F's on the multiplication tests because she was still in the middle of the exercise sheet when the whole class finished and because she occasionally had trouble remembering if five times three is twenty five or tventy three and had to resort to adding 5+5+5 to get the correct 15.