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The biggest difference between what I do now and what I was taught to do in school is that when I do mental arithmetic I mostly work from the largest (leftmost) digits first. I think this is much better than the alternative. It builds the important mathematical habit of getting an order-of-magnitude answer before getting a more precise answer. For example, just eyeballing the most significant digits I know that the final answer has to be about $-20000$, so if I get something much different from this I know I did something wrong.

The idea of analyzing the biggest contribution to the final answer first is also a foundational habit for learning, for example, real analysis, where to analyze a complicated sum it's often crucial to identify the largest few terms and analyze those terms and then the sum of the rest of the terms separately.

Finally, I hate subtracting bigger numbers from smaller numbers, so instead I always do it the other way and take the negative. So first I'd compute $78954 - 65465$ as follows:

$$78954 - 60000 = 18954$$ $$18954 - 5000 = 13954$$ $$13954 - 400 = 13554$$ $$13554 - 60 = 13494$$ $$13494 - 5 = 13489.$$

Next I'd compute $13489 + 12356$ as follows:

$$13489 + 10000 = 23489$$ $$23489 + 2000 = 25489$$ $$25489 + 300 = 25789$$ $$25789 + 50 = 25839$$ $$25839 + 6 = 25845.$$

Then I'd negate to get the final answer. Of course I wouldn't be saying this all out in my head; I'd just be keeping track mentally of which digits I have and haven't used yet.