While looking up something on the internet, I came across a blog written by a young person who recommended students focus on learning the steps involved in solving problems.
He said a person should carefully look at the steps and determine the exact number of steps needed to solve a particular type of problem.
He went on to tell people to use those exact same steps when solving the same type of problem. Practice using those same steps and eventually, you'll become a whiz at solving problems.
Toward the end of the blog, the author admitted that he did well in calculus even though didn't always understand what he was solving or why it worked. He was proud of the grade. I mention this because it supports the need for students to understand what they are solving and why it works.
His advice means a student is learning the mechanics of solving problems without having to understand anything more. Unfortunately, we are expecting students to know when to use certain problems or why they are applied in certain situations so his advice may not work as well today as it did when it was originally written.
According to a page on Understanding Mathematics at the University of Utah, you understand math if you:
a.) are able to explain mathematical concepts using simpler concepts and facts.
b.) make logical connections between different facts and concepts.
c.) see a connection between something new and something in math you know.
d.) can identify the principal of any math you do.
It is suggested that if you miss a point in the process, get clarification immediately because math builds on previous concepts. Its like building a house with one joist missing. Your house may begin sagging and eventually fall.
Memorization only takes you so far but developing an understanding leads to so much more. So the author of the blog provides a good reason for learning to understand mathematics. Let me know what you think.