Often students arrive at my doorstep with sad childhood tales about tone deafness, when they were refused entry into the school choir because they were "tone-deaf". Sometimes a student will say: "I can't carry a tune."
My experience as a teacher is that "tone deafness' is usually the term given to people who are unable to match a pitch played. It is also used to describe a person who is unable to sing a series of musical notes in their correct relative pitch - in other words, they are unable to "carry a tune". For many people this comes naturally and for others the placing of the pitch is something they never learned to do.
The good news is that tone deafness can be corrected. At first it will take some concentrated and consistent supervised practice. I have designed a systematic, step by step approach: simple exercises to educate a person how to listen carefully and then physically match the pitches heard.
These potential singers should not be discouraged. However each student needs to have patience and faith in the process. It will happen.