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"Schwarzwälder Kirschtorte" by Mikel Ortega is licensed under CC BY-SA 2.0

The conclusion paragraph, like any other paragraph, needs a point or topic sentence. The point of the the conclusion paragraph is the answer to the essay question. You already stated this as the first sentence of your introduction paragraph as a bold claim which you then needed to persuade your reader was true. This time you are stating it as the logical and (hopefully) irrefutable outcome of all the evidence and arguments you have been putting forward in the essay.

For example, if the essay question was "Children are active and creative in their relationship with new media technologies. Discuss." then the first sentence of your conclusion paragraph might be "In conclusion, we can see that children can certainly be active and creative in their relationship with new media technologies"

The remainder of the conclusion paragraph will then expand on and elaborate the point or topic sentence (just like any other paragraph would). One way to do this is to succinctly restate the key points you have made in your essay so far. This is a perfectly valid way to write a conclusion paragraph.

A stronger, but more difficult way, is to attempt a synthesis. I like to think of synthesis as being a bit like making a cake from scratch. You start out with flour and eggs and butter and sugar and maybe some other ingredients like flavourings or raisins or chocolate chips. But after you have mixed and bake them, they turn into something new and unexpected - a cake. Synthesis is about putting together the ingredients in a new and original way so that your conclusion doesn't simply re-state the points you have made, but provides a new way of looking at them. Like baking a cake, it requires you to be a little bit creative.

It sounds hard, but it doesn't have to be so hard. One way to attempt a synthesis is to ask yourself "Can all of my points be collected into categories?". For example, do you have a number of points which are in favour of a certain view and some other points which are against? Or can your points be grouped into e.g. internal vs external factors, or alterable vs unalterable factors, or arguments based mainly on direct evidence vs arguments based mainly on theoretical considerations? Or maybe your points break down into three different categories, or even four (although it is harder to have many categories if you only have a few paragraphs as in a typical undergraduate essay of 2000-3000 words).

Or perhaps you notice that the essay question has different answers depending on how you look at it. Maybe you can argue that girls are creative and active in their use of new media technologies, but not boys. Or that wealthy children are, but not poor children. Or that children in the global north are but not in the global south.

Whatever your conclusion, it shouldn't come as a complete surprise to the reader. You should have already stated your answer to the essay question in the introduction paragraph, and your paragraphs should have been structured so the reader always undertands where you have gone and where you are going. The conclusion must never contradict the essay, but sometimes it might put a delightful new spin on it.

"apple peel" by Clara T is licensed under CC BY-ND 2.0

A tried-and-true structure for an academic essay paragraph is PEEL:

P for Point or topic sentence

E for Example

E for Explanation

L for Link back to the question

The point or topic sentence spells out simply and clearly what the point or topic of the paragraph is going to be. It helps the reader know what to expect. The point or topic of the paragraph must be related to the essay question (if it isn't, delete that paragraph and find another point or topic which is related to the question). So your topic sentence is likely to include some key words and phrases from the question itself. It's a good idea to include a signposting word or phrase in the topic sentence to help the reader understand how this paragraph fits into your argument. Signposting words and phrases include "The first factor which influences....", or "Another example of...", or "On the other hand...." or "Finally,....". 

If you were writing an essay on the question "Describe how caregivers can influence children's psychological development", then one example of a topic sentence might be "Additionally, caregivers can influence children's psychological development by the way they talk to their children".

Most of the rest of the sentences in the paragraph will be example or explanation sentences which expand on the point or topic of the paragraph. 

The final sentence of the paragraph links back to the essay question. Like the topic sentence, this sentence probably includes key words and phrases in the essay question. It clearly states how the ideas in this paragraph help to answer the question. For example "This shows that caregivers can positively influence children's psychological development by talking to their children as much as possible".

The convention when writing student essays is to forget you are writing for your tutor or lecturer. After all, they already know all this stuff - they are probably the one who taught it to you. Instead you imagine you are writing for someone else.

Your imaginary reader is intelligent and educated, so you don’t need to dumb down your writing. But they are not expert in this field, so you do need to explain any concepts or jargon terms to them. You need to describe any experiments. They haven’t watched the module videos or read the textbook or the articles you have been given, so you need to summarise those in your own words.

You could imagine that your reader is a fellow undergraduate who is studying a different subject. Or you could imagine that you are writing for a past version of yourself, shortly before you began studying this module. So anything you didn’t know before you started the module will need to be explained.

When editing your essays, put yourself in the shoes of this imaginary reader and ask yourself "Would I understand this essay if I hadn't studied this module already? Or am I assuming the reader already knows the things I know"? You may need to rewrite some parts to make it clearer.

The best way to check whether your writing is clear enough is to get someone else to read your essay, and ask if it made sense to them. If they couldn't follow what you wrote, you may need to do some rewriting.

(I had this page bookmarked and used to share it with students to help them write better introduction paragraphs. But it was taken off the internet, so I saved it here. I believe it was originally written by Sean Evans of Union University)

Writing More Persuasively

Your essays will be more persuasive if you focus a spotlight on your main message. Here’s what I mean. 

A strong opening paragraph that clearly states your main point does wonders for your persuasiveness. When you open a paper by previewing your basic argument you do your readers a favor. You set the terms of the debate and tell them what they can expect to find. They will then judge you on how well the rest of the paper delivers the goods. You have saved your readers the trouble of hunting for your point. And why wouldn’t you want them to hunt for it? Because they might not find it. 

Many undergraduate papers don't open with strong paragraphs. Most opt instead for one of two openings: (a) the lofty sounding throat-clearing paragraph, or (b) the roadmap paragraph. Neither of these openings works terribly well. Here’s why. 

The Lofty Sounding Throat-Clearing Paragraph. This paragraph indulges in empty rhetoric that does not advance the argument of the paper. Here is an example of what I mean: 

The history of American foreign policy has had many influences, and over the years American presidents have had to confront many different challenges. In addition to economics and institutions, one of those challenges is geography. America is a country of great abundance that spreads from sea to shining sea. Diversity is a hallmark of the United States, a source of our greatness. It is the complex combination of these facts that has played a role in American foreign policy.

Geography has played a long-standing role in American foreign policy. In this essay, I will do two things. First, I will discuss the nature of American geography. Second, I will explain how geography has affected American foreign policy. In sum, I will analyze and discuss the impact of geography on American foreign policy.

The roadmap paragraph improves on the lofty sounding throat-clearing paragraph because it tells the reader the topic to be discussed, i.e., geography and U.S. foreign policy. The problem with the roadmap paragraph is that it tells readers the wrong thing about the topic. It tells readers how you are going to proceed and not what you’re going to say. Readers care about the latter much more than the former.  

What Should You Do? Again, a strong opening paragraph previews the main argument for the reader. It not only names the topic, it specifies the paper’s thesis. Here’s an example of what I mean: 

Napoleon once remarked that "geography is destiny." The history of U.S. foreign policy bears out his maxim. The United States was blessed with weak neighbors as well as a large ocean separating it from the major powers of Europe. As a result, the United States --unlike most other countries -- came to view foreign policy as discretionary.