Teachers who teach subtraction and multiplication to elementary-school children this way should be placed in public stocks, and the students and their parents supplied with rotten eggs and rotten cabbage to throw at them. Colleges of education that taught future teachers to teach this way should have their doors wrapped shut with crime-scene tape!
I have a master’s degree in mathematics, and I will admit that the number line is an important concept that links geometry and algebra, and the lattice method works. But these have no place in an elementary school. It does not matter that students are allowed to use calculators and will use these concepts only in theory and not reality. Each student should be able to do the arithmetic on paper and use the calculator as a tool only for efficiency and speed.
Our arithmetic is based on the decimal (base-10) system. Elementary students must be taught the structure of a decimal number with hundreds, tens, units on the left of the decimal; and tenths and hundreths on the right. Other number bases are important, but that also is a subject for higher-level work.
My favorite example is “one plus one equals one zero” (1+1=10). This is base-2, and allows us to use digital devices such as calculators, computers, smart phones, etc. Teaching this to a normal elementary student also should be a crime!