1. Comma Splice
Avoid and correct

2. What is a comma splice?
A comma is used to splice together two complete sentences when that isn't the function of a comma.
Sara obviously named that one, she was a sucker for those old “Happy Days” reruns.
This is an example of a comma splice.
Corrected: Sara obviously name that one. She was a sucker for those old “Happy Days” reruns. (Or use a semicolon.)

3. Correct the Comma Splices
The cat jumped from step to step, it gracefully landed with each jump.
The professor stated that he especially favors personally connected papers, these papers reflect the most emotion.
Anthony did not agree with the method he was taught, he found other means to solve the problem.
I learned the song on the piano, I chose to never play it.
The Revolutionary War was a triumph, it was also a struggle.

4. Answers may vary
The cat jumped from step to step; it gracefully landed with each jump.
The professor stated that he especially favors personally connected papers. These papers reflect the most emotion.
Anthony did not agree with the method he was taught; therefore, he found other means to solve the problem.
I learned the song on the piano, but I chose to never play it.
The Revolutionary War was a triumph; however, it was also a struggle.