Is /ə/ "real"? "Is schwa a real phoneme?" asked a first year student, during a preliminary session preparing them for transcription in the second year. What an excellent question!
The issue arose because I had referred them to John Wells' standard lexical sets to describe English vowel sounds more easily. This is a list of English phonemes with keywords devised by Prof Wells and given in his three-volume book Accents of English(1982). Rather than trying to explain in articulatory terms what /ʊ/ is in comparison with /ʌ/, for example, they can be referred to as the FOOT and STRUT vowels respectively, and then discussion about them appearing (or not) in various accents of English can also be facilitated.
Via Shona Whyte