The acquisition of negative sentences by L2 learners follows a path that looks nearly identical to the stages of L1 language acquisition (* Please see p. 6).
The difference is that L2 learners from different language backgrounds behave somewhat differently within those stages.
Stages of forming negative sentences (see examples on pp. 77-78):
stage 1 – using ‘no’ before the verb or noun
stage 2 – using ‘don’t’
stage 3 – using ‘are’, ‘is’, and ‘can’ with ‘not’
stage 4 – using auxiliary verbs with ‘not’ that agree with tense, person, and number.