Like other English words derived from the same Latin root, fragment has to do with breaking. Fracture, as a noun or verb,means break (a fractured skull); a fraction is a “broken” number, less than a whole; a fragile object is easily broken; diffract means to break apart or bend — for example, light.

A fragment is a piece of something broken. Think of the Chinese artist Ai Weiwei dropping a Han Dynasty urn. The broken pieces that results are fragments. (Another word for pieces of broken ceramics or glass: shards.) 

Grammatically speaking, a sentence fragment is a piece of a sentence — an incomplete one that lacks a crucial element, most often a verb. Consider the fragment above: Another word for pieces of broken ceramics or glass: shards. No verb.

Student and professional journalists alike often write in fragments, sometimes for effect. But that assumes the writer knows how to write complete sentences and has chosen a fragment deliberately (as I did above), not accidentally, as I presume CUNY international students did this semester in these examples:

I hate sports. At least, the kind of sports you watch on television.

The first three words form a simple but complete sentence: subject (I), verb (hate) and direct object (sports). The rest is a fragment, since it has no verb. For an easy fix, connect the two with a dash:

I hate sports — at least, the kind of sports you watch on television.

The Scandinavian welfare system has been a continuing reference in Sanders’s campaign. A reference that has obviously received a lot of coverage in the Danish media.

Here a dash could make the fragment a stronger version of an appositive.  (Dashes, which should not be overused, make pauses more emphatic than commas do.) So:

The Scandinavian welfare system has been a continuing reference in Sanders’s campaign — a reference that has obviously received a lot of coverage in the Danish media.

Or, to avoid repeating reference:

The Scandinavian welfare system has been a continuing reference in Sanders’s campaign — one that has obviously received a lot of coverage in the Danish media.

If the fragment enumerates what precedes it, a colon often works better. A fragment:

To increase educational awareness, I would like to create four workshops. Two in Spanish and two in Chinese.

A complete sentence:

To increase educational awareness, I would like to create four workshops: two in Spanish and two in Chinese.

Similarly:

It’s three o’clock and the jolly bunch is well entertained. For two reasons: Hernandez could be a comedian, and the day has started over four hours ago and the group has visited three breweries and one distillery before coming here – and there has been no lack of refreshments.

With different punctuation and tightening:

It’s three o’clock and the jolly bunch is well entertained, for two reasons: Hernandez could be a comedian, and the group has already visited three breweries and one distillery. There has been no lack of refreshments.

A social journalism student wrote:

Out of so many social platforms to choose, they prefer to use mainly Facebook and WhatsApp. Facebook to feel that they are still part of their family back in their home country.

She could have used a dash, but a little editing makes a complete (and tighter) sentence

Facebook helps them feel they are still part of their families back home.

In TV news, it;s become conventional to introduce stories with fragments. An anchor on a local New York newscast introduced a story this way:

A mystery on Long Island: a man is shot twice in a barbershop early this morning.

That sentence is a technically a fragment: even though the part after the colon is a full clause with a subject and a predicate, the part before the colon is not. Another example, from mid-2015:

Vice President Biden, tonight considering a run for the White House.

This construction may have evolved from the conventions of headline writing for print, in which the present continuous (the -ing form of a verb) lends immediacy. A first-semester international student echoed it this fall when she led a Craft story with a fragment:

Crowded trains at rush hour, hot cars in summer, accidental subway delays. Still, 19 times as many New Yorkers take subways as buses on an average weekday, according to the MTA.

In this case, I think it works. (Her Craft professor may or may not have agreed.) But it’s a device to use sparingly.

Last year another international student stretched a little too far:

Of about 500 children born to mothers kidnapped and killed during the dictatorship and then illegally adopted, only 109 have been traced. A story yet to be written by resuming memories, connecting dots and, in some cases, rebuilding identities. A story Videla, bringing his secrets to the grave, did not want to be part of.

Better:

The story of the others has yet to be written by resuming memories, connecting dots and, in some cases, rebuilding identities. It is a story Videla, bringing his secrets to the grave, did not want to be part of.

Fragments may be incomplete, but they aren’t necessarily short. That social-J student rightly retained the fragmented constructions when quoting a speaker at a news conference, no doubt following his phrasing and emphasis:

“It is critical, near-impossible, for police officers to be in the street anywhere in the city and represent safety — represent law and order — and yet be part of an institution that practices the opposite,” he said. “That hides behind a wall of secrecy. Where its own members are not held accountable and are not disciplined for what they do. For how they murder people, for how they destroy communities, for how they harm people, and how they don’t obey a certain line of discipline. And that is what this is all about.”

Think how the quote would have read if punctuated as one sentence:

“It is critical, near-impossible, for police officers to be in the street anywhere in the city and represent safety — represent law and order — and yet be part of an institution that practices the opposite,” he said, “that hides behind a wall of secrecy where its own members are not held accountable and are not disciplined for what they do, for how they murder people, for how they destroy communities, for how they harm people, and how they don’t obey a certain line of discipline. And that is what this is all about.”

The mind boggles. The speaker may have been not have had a prepared text, and thus gone on and on, as we all tend to do when talking off the cuff. He needed to take a breath every now and then, and so does the reader. In this case, using fragments did them both a favor.