I recently wrote to a homeschooling mom about avoiding an error in math documentation called stream of consciousness math notation. This is basically the equivalent of a run on sentence or no punctuation. You can probably understand the gist, but it would be inappropriate for formal writing. Here’s an example:
Let’s say I have 3 apples and you give me 2 more. Now I have 5. Then a third person takes 4 away from me. Here’s the stream of consciousness version of events:
Here it is as if the equality is meant to say, “and then what happens is…” In reality the equality sign indicates that whatever is to the left is the same as whatever is to the right. A chain of equalities means that everything between the equals signs are all equal to each other. In the example above, I am writing that 
This is no big deal with such small numbers because we can all see past the error to what is going on. But I’m convinced that it leads to muddied thinking as the problems become more complex.
This is no big deal with such small numbers because we can all see past the error to what is going on. But I’m convinced that it leads to muddied thinking as the problems become more complex. If you see this kind of notation, then gently–preferably with humor–encourage your students to use correct logic.
Math Problem Solving Skills 