Every time we teach calculus we discover that a significant portion of our students never understood arithmetic. I don't mean that they can't multiply numbers, but rather that they don't know intuitively that a car going 15 miles an hour goes 1 mile in 60/15=4 minutes (i.e. that division is the arithmetic operation corresponding to this problem).

It would be entirely inappropriate to teach them as if they were 10 years old, even if we had 3 months to teach them arithmetic.

Usually these are fairly intelligent individuals considering that they managed to get through high school mathematics well enough to get into a good college or university despite this handicap. In most cases, this happened purely because none of their elementary school teachers understood arithmetic either. They are likely to be able to pick up arithmetic quite quickly, and figure out from that why they have been a little befuddled through all of high school math.

I would hope this problem has been studied and ways to help these students have been proposed.

I am looking for references either to resources for these students or resources for instructors trying to help these students in the context of a calculus (or precalculus) class.

Every time we teach calculus we discover that a significant portion of our students never understood arithmetic. I don't mean that they can't multiply numbers, but rather that they don't know intuitively that a car going 15 miles an hour goes 1 mile in 60/15=4 minutes (i.e. that division is the arithmetic operation corresponding to this problem).

It would be entirely inappropriate to teach them as if they were 10 years old, even if we had 3 months to teach them arithmetic.

Usually these are fairly intelligent individuals considering that they managed to get through high school mathematics well enough to get into a good college or university despite this handicap, and this deficiency in their background is not their fault in any way. They are likely to be able to pick up arithmetic quite quickly, and figure out from that why they have been a little befuddled through all of high school math.

I would hope this problem has been studied and ways to help these students have been proposed.

I am looking for references either to resources for these students or resources for instructors trying to help these students in the context of a calculus (or precalculus) class.