Miss Mason on the Math
The child may learn the multiplication-table and do a subtraction sum without any insight into the rationale of either. He may even become a good arithmetician, applying rules aptly, without seeing the reason of them; but arithmetic becomes an elementary mathematical training only in so far as the reason why of every process is clear to the child.
from Home Education, Vol. 1, Section 15 Arithmetic
I was one of those students Miss Mason is talking about here. I could follow the rules and get the right answer without understanding anything of the mathematical principles.
To this day, I don’t consider myself “good” in math despite my good grades and even a short stint as a math tutor in college. Why? Because I know that I never grasped the concepts of the math. I simply parroted the progression of steps.
Understanding math is just as important as getting the right answer.
I have seen this time and time again in Emma’s math lessons. She will make strong scores in her Teaching Textbooks lessons. And then in the middle of a unit, she will come out saying, “I finally get it! It clicked!” Instantly, what was just following steps becomes an understanding of the math. Her scores may improve a little or they may be the same after that revelation, but that doesn’t matter to me. My concern is that she has that Eureka moment when she grabs hold of a math principle and adds another layer to her math confidence structure.
For younger students, math must be taught with concrete objects so that the understanding happens. Do not be in a hurry to put aside the counting bears. They are important learning tools not crutches.
This quotes series is part of the iHomeschool Network Quotation Link-up.