Michael Alison Chandler, in Washington Post May 20, 2012 has the article:

Today’s math vocabulary exposes generational divide

The term borrowing in subtracting is called the B-word. They also don’t like the word carry. However, these terms are embedded into math and technical and computer language.

The technical literature of mankind has already adopted these terms. Carry is a perfectly fine word. So is borrow.

The purpose of some of these terms may be not to give precision but to shift from one method of teaching to another. Some of the Chicago Math type approaches that emphasize different algorithms may be more suited to the new terms. The standard place value algorithms are suited to the current terms. But the alternatives may not work as well with the standard words. So to change the algorithms they change the words.

There has been substantial resistance to these alternative algorithms. By changing the words that are suited to explaining the standard algorithms to words suited to the alternative algorithms, the reformers make the standard algorithms harder to understand and the alternatives easier. This sounds like a Frankfurt School style march through the institutions. The result is lower math skills according to the critics.

They claim in the article the reformers do it this way to teach the real concepts. However, if one examines their materials they are somewhat short on doing this. The book Pre-Algebra New Math Done Right Peano Axioms is an actual explanation of the basics of addition starting from the Peano Axioms.

That book goes over place value notation and place value addition of 1 to 3 digit numbers using distinct letters for each digit and each carry. Nothing like this is done in books on arithmetic. I went through the books on arithmetic at University of Maryland’s EPSL Library and none of them did this in much detail or at all. A few sources will go quickly over this with a subscript notation. But they don’t give it an extensive effort with many practice problems. An example is the Wiki article:

Wiki Positional Notation article

Pre-Algebra New Math Done Right Peano Axioms spends 30 pages just on place value notation addition for 1, 2 and 3 digit pairs of numbers. As mentioned, this uses letters for the digits, carries and the final result. The point of this was not to teach that as much to show that place value notation is recursive math.

The reform math being pushed with these words as in the Chandler article about DC area schools is not teaching that place value notation is recursive. The word recursive is not taught to students in K-12 except rarely. Yet place value and all its algorithms are recursive.

Nor do the schools teach the Peano Axioms nor proof by induction for natural number addition. So the claim they have to stop teaching the standard algorithms to teach the concepts is undermined in that they don’t teach that place value is recursive, they don’t teach the Peano Axioms, and they don’t teach mathematical induction as the basis of proof. These would be what teaching the concepts would mean. This is pointed out in some of the other articles on this blog. See the Asmuth and Rips work for this from a psychological point of view, they are in the psychology department not math. See R. James Milgram from the point of view of a math professor, as well as Alexandre Borovik. In Germany they teach the Peano Axioms to pre-service teachers. See the *Christian Spannagel* references.

The traditional terms for arithmetic are the ones most closely tied to the standard algorithms. They go back for a considerable period of time. They are likely used in other languages. They are used in technical documents at the patent office, computer code, etc. The reason to use them is not to teach the concepts of math as in the Peano Axioms and so on, but to make the standard algorithms harder to understand and push students into alternative algorithms. This is part of the NCTM reform math agenda. Parents should not be taken in by what are essentially Marxist tactics.

The new words are not being pushed by math professors. This is a false impression if anyone gets that impression. They are not being pushed by computer science professors. They are pushed by a math ed group that is not pushing the connection to the standard terminology of math, technology, computer science or of practice. They are simply trying to disable the standard algorithms of arithmetic by taking away the terminology for the standard algorithms so that the standard algorithms don’t have the proper words to explain them. This is an assault on knowledge. It is a deliberate attempt to make it impossible for children to learn the standard algorithms of arithmetic.

The article references Linda Gojak of the National Council of Teachers of Mathematics as pushing the new terms and the elimination of the old words that are standard in all technical literature including patents, computer code, and math texts. The NCTM is at war with the standard algorithms and is trying to eliminate them from widespread human knowledge. It is already known this results in children not learning.

The article also mentions foreign speaking students have trouble learning the new words. This suggests that words like carry and borrow have been used for centuries and are already the same in different languages. The NCTM words don’t come from math textbooks. They come from their disinformation campaign on the standard language of math. This is to disable math learning and to prevent children understanding the language of math, computer science, patents, technology, etc.

That parents are confused by the new words is intentional. The parents are being bullied into silence while the Chicago Math is introduced into the schools and the children’s actual math skills fall. America is low on international comparisons of math education. This is because of the assault on the standard algorithms.

This is supposedly to teach the concepts. But the concepts are Peano Axioms, recursive algorithms, and proof by mathematical induction. That these are the concepts of natural number arithmetic was proven by Grassmann, Dedekind and Peano in the 19th century. These are never mentioned in the reform math nor their results used. Thus the reform is not to teach the concepts based on math, it is to disable the teaching and learning of the standard algorithms. The result is children learn neither the standard algorithms nor the concepts of natural numbers.

If you want to teach the concepts, you go with Peano Axioms, recursive functions, and mathematical induction. If you want to teach the standard algorithms you go with carry and borrow and other terms suited to the standard algorithms. If you want to teach neither the concepts nor the standard algorithms, you introduce new words not used elsewhere for the sole purpose of confusing parents while you push the Chicago Math and Reform Math, which is neither conceptual nor skill based. This is what NCTM is doing. This is misdirection and bullying of parents to achieve their covert agenda of avoiding teaching the concepts or the skills. That is why the US ranks so low on education comparisons across countries.