When you walk into a foreign language class for the first time, most likely, you are not fluent in that language. After the first week, you may only know a few phrases and vocabulary words. The ability to read and speak that language is built over time by practicing - hearing, writing, conversing - using the new information in a variety of ways. No one expects to go from new learner to translator overnight, or even in a year.
Why then, don't we treat learning math the same way?
Math is expected to be mastered the day, week, or year after being introduced to a concept. Typically, it is not allowed to be developed over time because many do not consider it to be a language. But, I’ll let you in on a little known secret: math is a language, it is not solely computation. In fact, computation is only one small part at mathematics. And once you can “speak math" you can problem solve in any situation.
If we truly want students to understand the language of math, it starts with the teaching and learning of math vocabulary. Students must be able to "use their words" when working to comprehend mathematics. The majority of students are unaware of this and end up treating math as a purely computational subject. They spend time trying to memorize equations, routines, and methods of problem solving - the "what" - instead of using the language of math to understand the “why.”
Once students know and believe that math is a way of communicating relationships and structure, they can make connections that lead to real, long-term, conceptual understanding. I always say “If you can speak math, then you can do math.” The language of math should not be considered foreign.