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"I was just wondering why all of the homework has to be verbally explained. The homework takes me a really long time as it is and it is difficult to find the words to explain numbers."

The answer to the above question:

"The earlier the students understand what the instructors mean by explanation, the better. The students' writing is not to show that they know the answer, it is to communicate the answer together with argument for its correctness.

Without words

- a grader might not be able to guess what your writing has to do with the problem

- a grader might not be able to guess whether you know WHY your steps are correct

- your formulas tend to float around on the page without clear order in which they should be read

- you are more likely to make mistakes and be unorganized

Words are used

- in general to explain nontrivial steps that concern the main point of the problem: not ALL has to be made verbal, only the main things!

- to connect steps and to relate your text to the question, e.g. "therefore", "so", "from this we obtain", "the limit does not exist", ...

- to cite theorems, e.g. "by the quadratic formula", "by the limit principles", " equality hold by the continuity principles", ...

- to explain the meaning of numbers or formulas for the problem question

- circumvent using formulas, if you don't know how to put it in a formula

- say something else to the grader "It seems to me that...", "I did something wrong here, but cannot figure out what", ... ."

May be if you try to see through the eyes of an independent grader you'll have an idea of what exactly you should write. You can also try to read aloud your solutions and then think if that made sense to a person listening to it. And you should not be much concerned with the time taken since even if you do not write out the words, most of the times you are speaking these words in your mind and writing it out would not take very long. As for "finding the words to explain the numbers", I believe from above points, it should be clear to you that we are not looking for words for numbers but we just want you to express your thoughts on paper in a proper manner.

The solutions to the worksheet 1 should give you an idea how to write out the solution to a problem. We will post more examples soon.