Warning - STEM professional post coming  .-)
To dignify grunge level arithmetic with the designation of mathematics is a stretch ! It is axiomatic, fundamental, the bricks and mortar of logic. If you have to "Discover" it every time before solving a problem no wonder the Ontario Liberals remain in power ! Nothing wrong with memorizing at this level.
As for teachers - most are clueless about the higher realms of the STEM universe, having carefully evaded its brutal realities in order to obtain their BA. ( My experience )