Conversational text-to-SQL aims at converting multi-turn natural language queries into their corresponding SQL (Structured Query Language) representations. One of the most intractable problems of conversational text-to-SQL is modelling the semantics of multi-turn queries and gathering the proper information required for the current query. This paper shows that explicitly modelling the semantic changes by adding each turn and the summarization of the whole context can bring better performance on converting conversational queries into SQLs. In particular, we propose two conversational modelling tasks in both turn grain and conversation grain. These two tasks simply work as auxiliary training tasks to help with multi-turn conversational semantic parsing. We conducted empirical studies and achieved new state-of-the-art results on the large-scale open-domain conversational text-to-SQL dataset. The results demonstrate that the proposed mechanism significantly improves the performance of multi-turn semantic parsing.