Should multiplication be taught before addition and subtraction?
The obvious answer for most people is 'no'. However, I think there are a few valid points that could change the way students approach and respond to higher level mathematical concepts.
- The human brain is inherently logarithmic. We perceive light and volume in orders of magnitude, i.e. candela and decibel. Sources include Weber Fechnel law, and https://www.scientificamerican.com/article/a-natural-log/
This would help students gain an intuitive sense of numbers, which would help them gain a deeper understanding of advanced concepts.
Multiplication rules are easy. . It is easy for students to learn that anything times 1 is itself, everything times 0 is 0, everything times 10 is the same thing followed by a 0 (moved a decimal place over), etc. In contrast, when 100 is added to something it must be added to the hundreds place, which is further abstraction.
Though children are taught that multiplication is iterated addition, there are other methods of teaching it such as geometry or counting rectangular arrays.
When students reach algebra, logarithms could have more meaning. Rather than being taught at the end and hardly understood, logarithms could be a valuable tool to teaching concepts such as order of operations, exponents, powers, and more.
The skills and intuition developed by multiplication tend to be more used in daily life (when am I going to us this) and are more beneficial as a whole.
However, there are reasons why not to. For example, addition can be done on fingers so it is simple and then addition can be used to help teach multiplication (though I dislike this because students use this as a crutch through secondary education instead of actually memorizing the dang multiplication table, though I don't know if this would make multiplication any less labor intensive or accessible)
Let me know your thoughts, just be sure to include examples and backing instead of isolated opinions :)