I'm going to skip the academic argument. If you've read any math-education blog in the last twenty years, you've already read it. People I respect have strong opinions on both sides. I'm not here to add to that pile.
Here's the practical reality, which the academic argument tends to miss:
Reasoning is what keeps a kid from being stuck
If a kid is asked 9 × 7 and they don't know it cold, you don't want them to freeze. You want them to have a path. Counting up from zero for the first digit, down from nine for the second — there it is, sixty-three. The reasoning rule isn't a substitute for knowing the fact; it's a safety net for the times the fact hasn't loaded yet.
The eight rules on the tips page are the safety net. They're eight small patterns that cover most of the table. Once a kid has internalized them, they're never out of options.
Rote is what makes the table get out of the way
Reasoning is great until you need to do something else with multiplication.
Picture a fifth grader meeting fractions for the first time. The teacher writes 3⁄4 × 2⁄3 on the board. The conceptual lesson is about how fractions multiply — top times top, bottom times bottom, simplify. That's the lesson. That's what the kid is supposed to be learning.
If the kid has to mentally compute 3 × 2 and 4 × 3 from scratch — counting fingers, working from rules — most of their attention goes to the multiplication and only a sliver goes to the actual fraction lesson. The teacher explains it once, the next problem comes, and the kid is still somewhere on the previous one.
A kid with the table on automatic looks at 3⁄4 × 2⁄3 and instantly sees 6⁄12 = 1⁄2. The multiplication is free. All of their attention is available for the new thing. That's what rote is for. Not to win an argument with a progressive educator. To free up the kid's attention for the next lesson.
The order: reasoning first, rote follows
The protocol does both, in this order:
Day one through day three, when the kid hits a fact they don't know, they fall back on a rule (or guess, or use the calculator). The rules are doing the work. They're getting familiar enough with the eight rules that the rules feel natural.
Day four through day seven, the rules are still there but they're getting used less. The facts are loading. By the end of day seven, on most facts the kid recognizes the answer before they've consciously chosen a rule. That's automatic recall, and it's the rote half kicking in.
You don't have to choose between reasoning and rote. The protocol gives you both. The reasoning is in the rules; the rote is in the daily repetition.
If your kid only gets one of them
If your kid only gets reasoning — they know the rules cold but the table isn't automatic — they'll do fine on a quiz that's only about multiplication. They'll struggle every time multiplication shows up inside a different topic, which in real math is most of the time.
If your kid only gets rote — the table is automatic but they have no rules to fall back on — they'll be fast right up until they hit a fact that hasn't loaded yet, and then they'll be stuck.
Both. In that order. One Kata a day for a week. That's the deal.