Traditional approaches for ensuring high quality crowdwork have failed to achieve high-accuracy on difficult problems. Aggregating redundant answers often fails on the hardest problems when the majority is confused. Argumentation has been shown to be effective in mitigating these drawbacks. However, existing argumentation systems only support limited interactions and show workers general justifications, not context-specific arguments targeted to their reasoning. This paper presents Cicero, a new workflow that improves crowd accuracy on difficult tasks by engaging workers in multi-turn, contextual discussions through real-time, synchronous argumentation. Our experiments show that compared to previous argumentation systems which only improve the average individual worker accuracy by 6.8 percentage points on the Relation Extraction domain, our workflow achieves 16.7 percentage point improvement. Furthermore, previous argumentation approaches don't apply to tasks with many possible answers; in contrast, Cicero works well in these cases, raising accuracy from 66.7% to 98.8% on the Codenames domain.