Should my child learn common core math or a specific type of math process?

The short answer is: maybe.

Homeschooling?
Find yourself schooling at home?
Do you have to teach common core math or can you teach the "regular math"?

Ask yourself two questions:
​
1. Are they learning it for a test (and you care about the test score?) - then yes.

2. Does the child want to learn it? Is common core–or the type of math you are talking about–a process that helps them really "get" it in ways other processes don't? - then yes.

Otherwise, no.

Stick to the bigger goal. If your child wants to have a career in a field that requires a specific type of math that will be evident in their desires. If they don't do a math-related field how much math does an adult actually do throughout the year?

​Be honest.