BODMAS + BIDMAS
One thing that jumps to my mind now is mathematics. BODMAS was introduced to schools in my local area in 1988, a few years after I left school. It was only until I decided to return to night classes in 2014 that I discovered that the BODMAS method of calculating existed. The very first class that I took had four older adults, including myself, and fifteen to twenty youngsters on the course.
The teacher wrote a very basic equation on the board and asked us all to calculate it. Thereupon the teacher asked us all individually to call out our answers. We four adults had one answer and all of the youngsters had another answer. The teacher then said that we were all correct, which caused arousal in the classroom, at which point we four adults looked at each other with twisted faces and shrugging our shoulders in bemusement, as did the younger classmates to each other.
The teacher went on to explain why this was, which was when we, the older students, discovered the existence of something called BODMAS. I had an epiphany at the time as I realised why so many people that I knew had income tax bills that they couldn't fathom.
I had a vision thereabouts of an upstairs office full of forty to fifty year old administrators calculating and tallying using the old method and an office downstairs with younger staff who were using BODMAS to do their calculations. Both groups believed that they were doing what they were supposed to do, and believed that they were right, which, to a high degree, they both were. However there is an obvious conflict between the two different methods that speaks for itself.