My explanation and preference is that if you want to learn Chinese you should also learn the reading and the writing.
In our school we teach speaking, reading writing, culture and interpretation/translation.
In the speaking and the listening part, we want the student to listening and understanding correctly and when speaking to pronounce correctly and be able to express in proper sentences.
In the reading part, we want the student to be able to read Chinese character and sentences. If you go to China or Chinatown, you should be able to understand the street signs, name of shops, restaurants, banks, hospitals, and etc.
When you pick up a newspaper you should be able to read the headlines. When you are given a form, you should be able to understand the written information.
In writing, you should be able to write your Chinese name, fill out a simple immigration entrance form when you visit China. When you learn to type Chinese with your computer, you should be able to read and write Chinese e-mails with your friends or for work purposes.