There is a common view among students who have struggled with arithmetic that the times tables — single-digit addition, multiplication facts, fraction rules, order of operations — are low-level busywork. The real math is the algebra, the calculus, the interesting stuff. The arithmetic is just the annoying part before you get there.
This view has consequences. And they are not good ones.
What cognitive load actually means in math class
Your working memory has a capacity limit. When you are learning a new concept, that capacity is being used to hold and manipulate the new information. There is only so much room. If a portion of that capacity is being consumed by effortful basic arithmetic — stopping to think about what 7 times 8 is, laboriously working out fraction multiplication from scratch — there is less room for the new concept you are trying to learn.
A student who is not fluent in multiplication facts will make errors in algebra not because they do not understand algebra, but because the cognitive load of the arithmetic is crowding out the working memory they need for the algebraic reasoning. The errors look like algebra errors. They are arithmetic errors wearing algebra's clothes.
Which foundations actually need to be automatic
Not everything needs to be memorized. But some things do — specifically the operations that appear constantly as subcomponents of larger procedures. These include single-digit addition and subtraction facts, multiplication tables through at least 10x10 and ideally 12x12, fraction operations (especially finding common denominators and reducing), and order of operations.
These are not arbitrary. They are the operations that appear as subcomponents of almost everything else. If they are slow, everything built on top of them is slow. If they are automatic, that cognitive capacity is freed up for the harder work of understanding the concept being taught.
How to build it
Fluency is built through repetition in the right conditions. Not passive repetition — active, slightly pressured repetition where you are trying to produce the answer quickly and checking yourself. Flashcards work. Timed drills work. The interactive times tables flashcards on this site are built exactly for this purpose — they recycle your misses so you drill what you don't know, not what you already have.
Five minutes a day of deliberate fluency practice, maintained over several weeks, will produce genuine automaticity. That is a small investment for a significant reduction in cognitive friction across every math topic that follows. Do not skip it because it feels like low-level work. It is the foundation the higher-level work is built on.