While there has been a rapid increase in the use of data science and the related field of big data, there has been minimal discussion on how teams using these techniques should best plan, coordinate and communicate their activities. To help address this gap, this paper reports on a mixed method qualitative study exploring how a big data science team within a Fortune 500 organization used two different agile process methodologies. The study helps clarify the concept of agility within a big data science project, as well as the key process challenges teams encounter when executing a big data science project. Specifically, three key issues were identified: (a) the challenge in task duration estimation, (b) how to account for team members that might be pulled onto other tasks for short bursts and (c) coordination challenges across the different groups within the big data science team. Our findings help explain how different process methodologies might mitigate or exacerbate these challenges and supports previous research showing that big data science teams would benefit from an increased focus on their process methodology and that adopting an Agile Kanban methodology, which focuses on minimizing work-in-progress, could prove beneficial for many big data science teams.