What we mean by "Mathematics is a Language" (and why you still need to learn mathematics).

Particularly in the field of education, people say "mathematics is a language". There is a lot of thruth to this, and I will explain what we mean.

I am writing this because the anti-science folks here twisting this to say "language is mathematics". What they want to say is I don't need no education to understand stuff. It doesn't work that way.

If you want to understand Science in any depth, you are going to have to study mathematics. There are no shortcuts.

I spent a year or so working on a team with an expert on Algebra education. Our goal was to measure the trouble many students have with high school Algebra (particularly with abstraction) and design a curriculum that would have better results.

We used the phrase "mathmatics is a language" in two related ways.

1. We want kids to understand that the terms of a function could be seen as an "object", and that functions could be seen as an object. Much like in a normal language you can construct and understand mathematical expressions as "nouns"(that are an object) and "verbs"(that are a verbs) and "predicates" etc. This is particularly useful for understanding how young students think about math and correcting problems in their understanding.

2. We say "mathematics is a language" because we want kids to learn how to represent the real world in mathematics. This means word problems (which unfortunately seems to strike fear in the hearts of many students). In our program we would try to take real world issues, and show that mathematics is useful in daily life problems.

For example we had kids analyze and graph a set of confusing cell phone plans and turn this into a function estimating the cost per minute of each plan (including start up cost and monthly fees). Kids understand this and seem to enjoy turning this into mathematics.