Language, Part 1

Just as a note, I definitely dropped the ball last week.  No updates?!  Geez.


I did write some stuff down and, when I'm running, I generally have amazing ideas...I just wish those ideas would flow automatically into this blog!!


All right, language.  For the past little while, we have been looking at what is math and what the math classroom looks like.  I would like to take a chance to look at what language is.

Definition: Language:

1. The method of human communication, either spoken or written, consisting of the use of words in a structured and conventional way
2. The system of communication used by a particular community or country
1. Computing a system of symbols and rules for writing programs or algorithms
3. the manner or style of a piece of writing or speech;
1. the phraseology and vocabulary of a certain profession, domain, or group of people

So there definitely is a good part of mathematics that is a language.  Last entry, we (watching way too much Tudors... "I") mentioned that Hersh said that math can’t be a language because there are certain things that you cannot express that you can in English, such as “I am bored”, or “I am happy.”  But now that I think about it, English cannot be used to describe many mathematical concepts.  We think that we’re speaking English, but we’re not; we’re speaking math.

First of all, there is symbolic language, such as:

a² + b² = c² 

The above formula describes Pythagorus’ Theorem.  In words, the formula is:

The sum of the squares of the two smaller sides of a right angle triangle is equal to the square of the hypotenuse.

Those seem like English words, like “smaller”, “sum”, “right”, “triangle”, “square”.  Little do you know (ever seen Stranger than Fiction?) that those are English words but you are not speaking English anymore; you’re speaking Math.

The words that seem like English are no longer English because you’re not stringing them together like an English sentence.  They carry different meanings suddenly.  Does this make sense?

So no, I can’t say, “I’m bored” in English; but you can’t describe properties of a right angle triangle in English either.  Hersh noted this difference between Math Lingo as well.

The second example (the long, wordy one) is much more clumsy than the first.  The symbolic version is much more compact and efficient and just easier to read, so we generally associate that with the mathematical language, but I believe both are.

The study of English in high schools (actually entitled ‘English Language Arts’) is not just the study of the English language, but the study of the use of language.  So let’s think of math that way; we’re not just teaching the language of math, but we’re teaching the usage of it by teaching mathematical concepts.

Where is the line?  What is a rule and what is a concept?  Well that’s a little more difficult to divide up (and something I’ll have to read a little more on).

More on this later.  It's time for bed.