Connotations can be negative or positive, and are often subjective.
Example
'Thin' is more or less neutral, 'slim' may have a positive connotation, 'skinny' a negative one.
In the classroom
Teachers often teach negative and positive connotations along with literal meaning. It is important to raise learners' awareness of the connotations of a word if they are to use them appropriately, although it is a complex and changeable area.
Further links:
https://www.teachingenglish.org.uk/article/working-vocabulary
https://www.teachingenglish.org.uk/article/same-opposite-or-different-dictation