What does it mean to "do mathematics?"

According to Van De Walle, "doing mathematics" means that students are engaging in the science of pattern and order, and doing mathematics is effortful and often takes alot of time (13). I think that in order to be able to"do mathematics" children should be actively involve in the process of understanding how the problem works, how they can connect it to their lives, and how they can solve the problem in not just way but in maybe several ways. We are taught in school that there is only one way to do a problem, but in all reality there could be several ways to solve the problem and get a probable solution. "Doing mathematics" also means that it shouldn't always be easy, we should be able to dig into it and struggle a little bit. According to Van De Walle there are many verbs we can correlate to "doing mathematics." For example, we can correlate explore, investigate, conjecture, solve, justify, etc (13). When students are engaged in these verbs it is very impossible for them to be passive learners or observers (13).