Has anyone used the math in *How to Tutor*? What do you think of the author's warnings that "New Math has smothered arithmetic". The current wide and conceptual math curriculums are pretty much the same as the old "New Math" right?

Depends on which curricula you have in mind. Everyday Math and Connected Math, yes, same nonsense. AoPS? Conceptual yes, but absolutely not New Math.

"New Math" was designed to produce more scientists for the cold war, and there is the same goal to produce more scientists now due to global competition? Am I oversimplifying this or just wrong?

No, that was the basic motivation. They just got scared of the success of the Russians.

The author says that arithmetic is the "tool of economic man" and "practical everyday living" and that mathematics is more closely allied with the sciences and philosophy. He says that arithmetic is best taught in isolation and "in a very orderly way" **with memorization before understanding.**

I agree that arithmetic should be the foundation and needs to be taught before higher math and conceptually more abstract topics. I utterly

**disagree**, however, that it should be taught with memorization before understanding.

It is perfectly possible to teach arithmetic with conceptual understanding, and in fact, this will lead to better retention, because students who know why they do what they do do not have to rely on memory, but will be able to derive anything they have forgotten.

This conceptual understanding becomes more crucial the harder the math is. Students who simply memorize operations with fractions will inevitably make mistakes because they misremember, whereas students who understand the concepts behind the procedures can think critically, can spot mistakes, can evaluate their results and see if they are meaningful. (Typical subject: dividing fractions, The student who understands WHY the divisor fraction is flipped will know exactly when to do this. OTOH, I have seen students without this understanding remember vaguely that they "must flip" and do this for addition and multiplication. Ouch.)

The author, Samuel Blumenfeld, says that arithmetic "is one of the most useful tools a child can learn to master" and "is vital to an individual's economic survival and success" and "should be given top priority". "Once the child has mastered the arithmetic system, he'll be in a much better position to deal with the often confusing theories and concepts of New Math."

Absolutely. Without arithmetic, students can not function in daily life: they need it to budget, balance accounts, figure percentages...

But I would say the confusing New Math curricula should not be used at all in math education.

Is there anything wrong with STARTING with a narrow focus on arithmetic for below average students that are not going to compete for STEM jobs? What about average and above average students?

No. In fact, it is necessary to start like this. Typically, elementary education is almost entirely devoted to arithmetic with positive integers. Only after this has been thoroughly mastered, the student can be taught arithmetic with fractions and negative integers.

Aside from some geometry topics (which are interesting, useful, and fun for students), students study arithmetic until they are ready to move on to algebra. I would not advise skimping on arithmetic mastery for

**any** student, be he below, at, or above, average. But I would encourage the teaching of the "why" alongside the teaching of the "how". This does not require "new math".

**Edited by regentrude, 26 August 2012 - 08:05 PM.**