What kind of language do you speak?

So we often think that texts are broken into paragraphs which are broken into sentences and then into words.  But what are words broken into?
We know that a word can be broken into syllables but that is a practice for dividing the sounds up; if we are looking at meaning, we need to break it up into meaningful chunks where the word unbreakable for example becomes un (not), break and able (possible).

These are morphemes. 
A word is broken up into the chunks that add meaning to the word.  Now we can understand a way that linguists use to classify languages.

Isolating languages
These languages add the meaning to the word by surrounding it with other words.

Polysynthetic languages
These languages use affixes to add on to the base word.

So which one is English?  Neither.  And both.
Actually, we need to think of it more as a spectrum into which most languages fall in the middle or tending toward one extreme or the other.

Take the word "sing".  If I want to show my ability to do this, I add "can".  This is a separate word.  But then if I want to show that this is my profession, I add -er to make "singer".  This is a bound morpheme (the -er cannot stand alone).

It is an interesting difference to note when you are learning a new language or trying to understand the errors of someone else.