Will things never change? When I taught math in "antiquity" I taught, among other class, a class on the slid rule. Many outside the colleges felt it was not a good thing as it hindered the students development and ability to think. In fact one time I took a slide rule to a test for a electrical licence and was told it could not be used, as it had all the answers on it. My response was yes, but you find them. And as you all know it was widely used by engineers and did not hinder their math.

Then near the end of my teaching days calculates started to come out (very expensive and were only able to add, subtract, multiply and divide, but did that well and were better than a mechanical adding machine). Soon the calculators were adding all the other math functions and slide rules were a thing of the past. It would be hard to even find one today.

I was asked if I could do anything for high school students that were found to be retarded in math. I evaluated them and found they were not dumb, but had trouble learning the addition and multiplication tables. Because of this they had mental blocks toward anything mathematical and these blocks were reinforced by every teacher insisting on them memorizing the math tables. Some to the point that they would punish there students for using their fingers, as if that was not a good memory assistant.

Somehow we had, and have, the idea that is something magical or mysterious about the Math tables and surround them with an importance far greater than they deserve. In the days before the ten digit number system they were a must, did you ever try to multiply MCMXXII times XCVII. As every problem had to have a table there were too many tables in those days to make it possible to memorize them all, so books were kept for that purpose.

All these tables really are then, are records of the solution of a multiplication, or addition problems, so we do not have to work them out each time. Even teachers forget this. It makes no difference whether these tables are stored in our minds, in books, in mechanical devises, or electrical devices, except that in the mind we can access them a little faster in some cases.

I had about 30 of the students that seemed to have mental blocks bused to the college every day for a one hour class and the first rule was they had to use the calculators to work all problems. Even if they knew the answer they had to use the calculator. Hopping to brake the mental block by removing its cause. I received a lot of heat for this by the math department as "it watered down math and weakened the students". They had to pay their dues and learn the old way even if it meant they never learned.

The result of this approach was that in one semester most of them were working math at the highschool level as well as other highschool students. Some had overcome their problem with the math tables (which, after all, are just pure memory) and were asking to drop the calculators unless they got stuck. So in the second semester I made the calculators optional. Some never got away from the calculator, but all were working math at about the same proficiency as other highschool students. But! Despite the fact that they had to admit that the class was a success the math department voted against continuing it as they felt it was wrong to allow students to use a calculator.

Today students are forced to learn to use the calculator in their math classes. The calculator removes so much drudgery and time-consuming memory drills from the learning of math and the student's mind is free to do the real math-the reasoning. And, without even knowing it the students learn the memory part by repeated use.

We had the same problem when computers first came out, but fortunately they are now in almost every classroom.