What are the differences between writing and speech?

When do we use spoken words, and why?

Think of the characteristics of the written form - it has longer, more involved sentences, because we can see what's there and revise it. We use complex sentences in writing and we don't usually do that in speaking. After all, we have time to think about how we are going to say something when we write it, whereas we don't often have that time and brain space when we are talking. It's a one-way method of communication, for the most part.

Think of the characteristics of the spoken form - we think on our feet, so we're colloquial, we use idiomatic expression, and are not always grammatical - just as long as we get the point across. We often repeat ourselves for emphasis, and we stop and start, and say and um and ahh! Why is this? Because there are different processes going on and we are usually having a two-way exchange of ideas. (Not always, but think of the different things going on when we read something rather than hearing it.)

Notice when someone reads aloud a speech that's meant to be read - or from a history book or a formal letter - you have to concentrate hard - why? Because the form is complicated and the ideas don't flow in the way we speak. In fact, think of the rhythms in formal writing that put you to sleep when someone reads a boring speech!

Notice when someone writes a script for a movie or a radio play - it looks much different from a piece of formal writing - much more interaction and short sentences, etc. That's because the script writer is deliberately mimicking spoken communication. A script writer writing for TV or radio writes things because she or he knows they are going to be communicated verbally. Perhaps you might listen to someone on TV in a drama and write down what they are saying. Then try to put that into a formal, written style.

In any case, provide examples of written style and spoken style. Maybe you can find a complicated sentence in a book, and then try to think how you would say it if you were talking to someone, and put that down. Your assessor would like that, and you could use these to make the comparisons and contrasts.

Another idea might be to write all of your essay except for one paragraph in a formal essay style, and use that paragraph to show how different it looks and would sound if spoken.

You may also like to consider how the Shakespearean style is a mixture between styles of written and spoken media, often poetic. It could be worth finding a passage or two from a Shakespearean play and commenting on it from this point of view. Also, it would add to your explanation, I think, if you could find examples of very formal writing such as you see in the nineteenth or even eighteenth century and show how very different they are from colloquial speech today. You could go to a web archive of classical writing to look at examples - the Gutenberg Project, e.g.. Something like "Gulliver's Travels" would be useful as an example.
You may notice that I've written this to you in a fairly colloquial style, even though it is written. The reason why it seems colloquial is that I've used contractions such as "I'll", and "can't". These are characteristic of spoken rather than written styles.

You now have enough points to consider to write a good essay. Create a plan for the essay, and then construct a paragraph around some of these points, and any others that might come to you when you read this.

It shouldn't be too hard! Enjoy it. Remember to check it thoroughly for spelling and grammar, as these things always count. Happy writing!