Memorizing is a "small but mighty" part of mathematical fluency.
While number sense is developed by practicing many modes and strategies of learning, memorizing remains an important component of mathematical competency.
Fluency in math facts frees up working memory so students can devote their cognitive energy to problem solving and learning new concepts.
A child who has working memory overload will struggle with word problems because the attention they have to give to the basic facts clutters up the brain, making it harder to understand not only what is being asked but how to work the problem.
Fluency means less confusion as they learn new concepts.
The more time a child spends calculating basic facts the more likely they are to get confused with the processes and get lost in their calculations.
Automaticity affects performance.
If a student does not have their math facts committed to memory, they will spend a disproportionate amount of time figuring out the smaller calculations. This can translate to not completing tests etc. and contributes to overall feelings of poor performance in the subject.
It lessens anxiety around math.
Math anxiety starts when children fall behind and can’t keep up. Focusing on understanding and memorizing during the early elementary years lays the foundation math skills needed for later years. While it could be said that memorizing is a practice which can also cause anxiety, I would propose that if memoization is well designed (using helpful tools, like Math Songs) and not burdensome (meaning, it’s not valued as the be-all, end-all or your math skills) then memorizing should not be anxiety producing.
This article by Kate Snow from The Well Trained Mind gives a great apologetic for memorizing facts in the early years.
“Imagine trying to make spaghetti sauce if you didn’t know how to chop an onion, brown ground beef, or measure spices. Even with a recipe, you would find yourself puzzling over every single step: “Do I need to take the skin off the onion first? How high should the heat be when I cook the meat? What’s the difference between a teaspoon and a tablespoon?”
This is how math feels for kids who never master the basic facts: painstaking and hard. Whether they’re learning how to divide decimals, subtract fractions, or multiply polynomials, they spend so much of their working memory on simple calculations that they have no brain space left for understanding new concepts.
That’s why it’s so important that children master the math facts during the elementary years. Once they’ve learned these basic number relationships, they’re much better prepared to tackle challenging topics in their middle school and high school math courses.”
Kate goes on to discuss strategies that teach and reinforce the concepts behind the facts.