Many English teachers often repeat the fake rule that an English sentence should not begin with the word and. The same rule is given for other words like so and but (all conjunctions). This rule banning the word and from the start of English sentences is an old Latin grammar rule that has been added to English classes by excitable English teachers. It is not real English.
Many respectable English writers use the word and at the start of a sentence. (Would you like to make a list? Just search electronic books for ".And". ) But if a student does it they lose marks. That is unfair. English should be the same for everyone. I dislike making a language point by waving a book at someone and shouting "See!" But in this case it appears to be the only way to convince some people that their grammar rule is fake. Some people really like grammar rules and want more of them.
Sentences that begin with words like and are mentioned in some well respected English style guides. English Professor William Strunk (1869–1946) published a famous writing guide book called Elements of Style (1918). He called sentences that begin with words such as and loose sentences. Loose sentences connect to the topic of the previous sentence. He instructed us not to have too many of these loose sentences. That is good advice. Because too many sentences, one after another, all with the same structure soon becomes very boring. He never said that loose sentences were wrong, which is what many teachers seem to believe.
Many other English writing style guides also allow and at the start of sentences, but offer another reason. They suggest that these sentences can be used for "dramatic or forceful effect", but again not to use too many of them. (www.oxforddictionaries.com/page/216)
Using the word and at the start of sentences is not modern nor slang. It was used in the old, formal and much respected Anglo Saxon Chronicle. All of these are examples of proper loose sentences. They are connected to the sentence before them by their first word.
A.D. 473. This year Hengest and Esc fought with the Welsh, and took immense booty. And the Welsh fled from the English like fire.
A.D. 1075. ...Some were punished with blindness; some were driven from the land; and some were towed to Scandinavia. So were the traitors of King William subdued.
A.D. 860. ...In his days came a large naval force up into the country, and stormed Winchester. But Alderman Osric, ..., fought against the enemy, and putting them to flight, made themselves masters of the field of battle.
The well respected British National Corpus, which is a large ordered and scientific sampling of British English, shows that the words and, so and but are commonly used at the start of sentences.
The King's English (2nd ed. 1908, by H.W. Fowler 1858–1933) is one of the most prestigious British English style guides. It uses the word and at the beginning of some sentences. (Chapter II. Syntax)
And perhaps it becomes so closely associated with....
An English teacher's professional magazine, called The English Journal, has published an article showing that this fake rule makes learning more difficult. [Herman R. Struck, The Myth about Initial Conjunctions, The English Journal, Vol. 54, No. 1 (Jan., 1965), pp. 42-44]
Words like and, so and but can be used correctly at the start of sentences. If every sentence in a paragraph began with the word and the whole paragraph would be sloppy. The word and tells the reader that the information in this sentence relates to the earlier sentence. Adding extra words onto the beginning of sentences for no reason would be a mistake. However when properly used and can appear at the start of a sentence. And at the start of a sentence is part of real English.
A native English speaker who has been teaching practical English in Hong Kong for more than a decade.
Note: When writing about words it is useful to put the word in italics, or use some other emphasis, to show that you are not using the word, just writing about it. Example: Words like and, soandbut can be used correctly at the start of sentences.