One way humans are rational is when they "reason on paper". We write down most of the initial conditions and then use an algorithm (that's also written down) on them to get to the next step. We write down the result we got. Then we use an algorithm again on this result to get to the next step etc. This is how mathematics and science works. Obviously this is cultural - we learn to do this by learning to write, to do mathematics etc. It's not something ingrained to us.
I think humans can do something similar in their head, but it is greatly limited. The limiting factor is memory - an even remotely complex algorithm will eat up all your memory and you will forget about the results you had already got.
Eg adding 419875 + 87458284 uses the same algorithm as 356 + 472. We can easily do both on paper, but the former is difficult to do in your head, whereas the latter is fairly easy. You give someone an external memory (eg notes) and they both become easy again.
An external memory keeps our reasoning rational.