Everyone thinks about concepts and abstract ideas differently. The more complicated, typically, the more ways there are to arrive at the same answer. Addition is simple, and I imagine most of us do mental addition in the same manner (or using a small set of similar approaches). Multiplication is much more complicated, same with division, and there are a myriad of ways we may go about it.. or not go about it!
I would hope teachers could be flexible enough to try to deal with students reaching the same, correct, answer using different mental approaches.
When it comes to these sorts of basic mathematical operations, the best method I ever had for learning them was a terribly strict math teacher who would make the entire class stand up 5 minutes before her class ended (stand up so that you couldn't use pen and paper or calculator) and then verbally go through a long series of operations: "5 plus 3 times 8 divided by four plus six subtract 2 and divide by 2), and whoever answered correctly first got to leave the classroom. There was no method involved, but there was motivation to get it right (since you got an extra long break to go talk to friends between classes or whatever!) and it made you work. I think class by class, week by week most of us got a lot better at doing math in our heads and that sort of improvement becomes ingrained and sticks with you.
I never found teaching me a particular method was as effective as making me just want to solve these problems in real time. Anyway, not really a useful anecdote, but something I always think of when the topic of math education comes up
I would hope teachers could be flexible enough to try to deal with students reaching the same, correct, answer using different mental approaches.
When it comes to these sorts of basic mathematical operations, the best method I ever had for learning them was a terribly strict math teacher who would make the entire class stand up 5 minutes before her class ended (stand up so that you couldn't use pen and paper or calculator) and then verbally go through a long series of operations: "5 plus 3 times 8 divided by four plus six subtract 2 and divide by 2), and whoever answered correctly first got to leave the classroom. There was no method involved, but there was motivation to get it right (since you got an extra long break to go talk to friends between classes or whatever!) and it made you work. I think class by class, week by week most of us got a lot better at doing math in our heads and that sort of improvement becomes ingrained and sticks with you.
I never found teaching me a particular method was as effective as making me just want to solve these problems in real time. Anyway, not really a useful anecdote, but something I always think of when the topic of math education comes up
![[Image: 21282370099_a814a08664_o.png]](https://farm1.staticflickr.com/590/21282370099_a814a08664_o.png)
