But with math minute you are not reasoning quickly. You are recalling facts quickly.
Reasoning and recalling a fact from memory are two different things
Well, yes and no. Why is the 10 times table easier to memorise than the others? Because you don't really memorise it - you understand the numbers well enough that you can work it out very fast. Hands up all those who still don't feel as though they truly recall times table facts from memory, but rather, work them out every time fast enough that it looks to everyone else as though they're recalling them from memory? (My hand is raised, even though as I said elsewhere I think of myself as a slow processor.) [ETA: on second thoughts, this is less true than it used to be before I helped DS learn his tables, actually! I am now wasting several more synapses on this task than I used to ;-) ]
Reasoning and remembering are really intimately entwined. When you solve a novel problem, you never approach it
completely from first principles: part of what you're doing is allowing your memory to bubble up possible approaches that have helped with similar problems in the past. To over-simplify, there are two ways to be bad at problem solving in maths:
1) too much reliance on memory: being unable to solve any problem that isn't extremely similar to something you've solved in the past
2) too little reliance on memory: being overwhelmed by the need to work out anew a strategy for doing every tiny piece of arithmetic that comes up in the course of doing the problem.
Times tables and other number facts are about as far on the memory end as it's possible to go, but even there, I bet if we had the neuroscience to be sure, we'd see that logical reasoning plays a role even there for many people. And a key thing for mathy children who hate memorising is: this is fine. If you can get the answers fast enough and easily enough that it looks as though you have them memorised and working them out doesn't slow you down, that's OK. And practising strategies so that you get that fast is worthwhile in that it deepens your understanding of how numbers work, in a way that "dumb" memorising isn't.
