Why does this innovative method of subtraction from a third grader always work? My daughter is in year $3$ and she is now working on subtraction up to $1000.$ She came up with a way of solving her simple sums that we (her parents) and her teachers can't understand.
Here is an example: $61-17$
Instead of borrowing, making it $50+11-17,$ and then doing what she was told in school $11-7=4,$ $50-10=40 \Longrightarrow 40+4=44,$ she does the following:
Units of the subtrahend minus units of the minuend $=7-1=6$
Then tens of the minuend minus tens of the subtrahend $=60-10=50$
Finally she subtracts the first result from the second $=50-6=44$
As it is against the first rule children learn in school regarding subtraction (subtrahend minus minuend, as they cannot invert the numbers in subtraction as they can in addition), how is it possible that this method always works? I have a medical background and am baffled with this…
Could someone explain it to me please? Her teachers are not keen on accepting this way when it comes to marking her exams.

I think this method is awesome, it might even be easier than the classical method in some cases. Consider the following 'easy' subtraction, where the digit of the first number is bigger than the corresponding digit of the second number.
\begin{align}462-231&=(400+60+2)-(200+30+1)\\
&=(400-200)+(60-30)+(2-1)\\
&=200+30+1\\&=231\end{align}
Anyone would do this sum with little thinking. You would normally write it down without any steps inbetween. The method of your daughter extends this method to work with numbers that don't have this nice property.
\begin{align}431-262&=(400-200)+(30-60)+(1-2)\\
&=(400-200)-(60-30)-(2-1)\\
&=200-30-1\\
&=170-1\\
&=169
\end{align}
This could also be extended to larger numbers. To compare this to the usual method of borrowing tens I think that the regular method would be better if you have a pen and paper at hand and the numbers are relatively large, if you have no paper at hand this method might be easier.
