Taking courses at WGU not part of my degree program? And credit by examination

[Merlin]

I want to take them with WGU because they are competency based courses.
I already asked them if I could change my major if I wanted to later on and they said I could.

Changing majors is not a problem... people do it all the time. They just usually do it because they are unhappy with one major or because of other issues. Most people don't do it in order to take a few courses in one degree and then complete a different degree. The process is a bit cumbersome and time-consuming. I would never recommend that someone do it just to pick up a few extra courses that won't even factor into their degree.

If you want to take competency-based courses you don't have to take them at WGU. I don't know which math and science courses you want to take, but there are several competency-based options out there depending on your reasons for wanting to take the courses.

Considering that you won't be able to apply them towards a WGU CS degree, you might as well take the free option and go with a Coursera course or just bone up on the skills at Khan Academy.

If you want ACE recommended (college credit) courses, you could take a look at the credit-recommended courses from StraighterLine and Study.com. Those are all competency-based and can be transferred to WGU. However, since they are not required for a CS degree they would not be used. You might be able to use them for a second degree if you wanted to go back to get a teaching degree though.

Beyond that, you can look at community colleges or other RA schools to pursue these courses. It is harder to find competency-based options that don't require you to sign up for a minimum term length, but you may find something that meets your needs.

But if I changed my major, would I still have those competency units on my transcript that I got from taking those classes for if I wanted to transfer those units to another college?

WGU may only show the credits required to meet the requirements for the specific degree you graduate with. I'm not entirely sure if they will show credits that are unused for a degree.

If you're looking to take extra classes to transfer to another college, then you might as well just take the courses from the destination college. Once you complete your bachelor's degree, a destination school will probably not care about any secondary courses taken. Though that depends on the program and entrance requirements.

If you are doing this for a graduate degree and you have a specific grad school in mind, it may be easier trying to work backward from the school's entrance requirements to figure out your best approach rather than try to switch degrees, etc.

What are you trying to do?