Did Americans, before new math came in to schools, really say, 'three from two is nine carry the one", instead of borrowing ten from the tens column?

Question

Tom Lehrer claims and the audience seems to agree with him that the 'old way', before new math to do subtraction was to say, for example, 'three from two is nine carry the one'. I never heard of this method. Does anyone still use it? What is it called? https://www.youtube.com/watch?v=UIKGV2cTgqA is the video showing Tom Lehrer's bit. Does it really not involve understanding what you are doing as the new math activists claimed (I presume).

Is it known what Lehrer really thought about this part of new math?

Lehrer's example is 342 - 173.

Edit: Also, when was the borrowing method of teaching subtraction invented?

Answer 1

It sounds like a variation of subtracting that I learned in high school (1968). My instructor called it European subtraction.

\begin{array}{ccc} & 3 & 4 & 2 \\ - & 1 & 7 & 3 \\ \hline \end{array}

You start by saying $9$ plus $3$ is $12$. You write the $9$ as shown and "carry" the $1$, of the $12$, as a subscript of the $7$ as is shown below.

\begin{array}{ccc} & 3 & 4 & 2 \\ - & 1 & 7_{\color{red} 1} & 3 \\ \hline & & & \color{red} 9 \\ \end{array}

Then $7$ and $1$ is $8$ plus $6$ is $14$.

\begin{array}{ccc} & 3 & 4 & 2 \\ - & 1_{\color{red}1} & 7_1 & 3 \\ \hline & & \color{red}6 & 9 \\ \end{array}

Finally, $1$ and $1$ is $2$ plus $1$ is $3$.

\begin{array}{ccc} & 3 & 4 & 2 \\ - & 1_1 & 7_1 & 3 \\ \hline & \color{red}1 & 6 & 9 \\ \end{array}

The big advantage of this method is that you can do many subtractions at once.

\begin{array}{ccc} & 5 & 3 & 4 & 2 \\ - & 1 & 9 & 2 & 3 \\ - & 2 & 9 & 4 & 5 \\ \hline \end{array}

$5$ and $3$ is $8$, plus $4$ is $12$.

$5$ and $2$ is $7$, plus $7$ is $14$.

$10$ and $9$ is $19$, plus $4$ is $23$.

$4$ and $1$ is $5$, plus $0$ is $5$.

\begin{array}{llll} & 5 & 3 & 4 & 2 \\ - & 1 & 9 & 2 & 3 \\ - & 2_2 & 9_1 & 4_1 & 5 \\ \hline & & 4 & 7 & 4 \\ \end{array}

I think this is a wonderful way to subtract, but, I would not teach it to grade school students.