Two New York City public school teachers were recently fired, having been caught working at other jobs while collecting sick pay. Presumably, among the 80,000 or so teachers who work in the school system, something like this is bound to happen. What made these cases noteworthy is what the double-dipping teachers were doing during the time they should have been in the classroom.

The first case involved a fellow named Matthew Kaye, a social studies teacher at Benjamin Cardozo High School in Bayside, Queens. Mr. Kaye, 31, by all accounts a popular and particularly effective teacher, was pursuing a mildly successful career as a professional wrestler, using the alias “Matt Striker.” While the incident made interesting tabloid reading, I concluded that Mr. Kaye’s wrestling exploits added no particular value to his ability to teach history.

I will leave it to the judgment of my readers as to whether the Department of Education overreacted in banning Mr. Kaye from ever teaching again, the same punishment it would have meted out to a teacher accused of sexually molesting a child. It could be argued that he might have been disciplined and ultimately allowed to return to the classroom. Good teachers are hard to find.

The second case was more interesting, at least to me.

This incident involved a music teacher at the Bayard Rustin High School for Humanities in Manhattan, Dorrit Matson, 51, who, on two occasions, called in sick and collected sick pay for a total of eight days.

Ms. Matson is the founder, music director, and conductor of the Scandia Symphony, an orchestra highly regarded for its performances of Scandinavian classical music. On the days she called in sick, she was actually performing with her orchestra.

Reviews of the orchestra’s performances and recordings suggest that Ms. Matson is an extraordinarily talented musician. Now, for all I know, she may be an awful teacher. But this incident raises larger questions, and suggests potential opportunities.

New York is filled with talented artists and musicians. A few have enormous talent and make a good deal of money. But many, perhaps most, just struggle along. Even musicians of some note, such as Ms. Matson, who has found a small but presumably unprofitable niche in the world of classical music, need a regular paycheck to put food on the table.

One area in which the public schools fail miserably is the teaching of music and art. When money is short, these are the first programs to be cut. During the municipal budget crisis in the mid-1970s, many of these programs were gutted and have yet to be restored. Since nobody requires standardized tests in these subjects, they are very much at the end of the line when it comes to allocating time and resources.

In the first column I wrote for The New York Sun, nearly three and a half years ago, I discussed how money earmarked for arts programs in the schools, $75 million allocated annually by Mayor Giuliani and the City Council, was routinely skimmed by central office educrats, shortchanging thousands of children.

Today, with huge blocks of classroom time mandated for “literacy” and math, the arts are still very much a back-burner enterprise in our schools.

While there are a number of programs to put musical instruments into the hands of students in many schools, this is the least of the problem. There is plenty of private money around to provide the hardware. There are even schools where existing instruments are locked away in storage closets, gathering dust for years, simply because we don’t have teachers qualified to teach the children how to play them.

When negotiating a new teachers’ contract, much attention is paid to the so-called “work rules” that, depending on the perspective from which you view them, either protect teachers or strangle the system to the detriment of the children. Even more attention is paid to money. Both of these are contentious issues.

Lost in the shuffle is how we can use the contract creatively to allow for a degree of flexibility in recruiting and retaining music and art teachers. We should figure out some new and clever ways to use the contract to tap into Gotham’s creative community so that a Dorrit Matson would be legitimately given the time off to conduct her orchestra, an activity that potentially adds to her instructional value, without resorting to deceiving and scamming the city.

Many of the city’s private schools already do things like this. I know of some schools that require their music and art teachers to be active practitioners of their craft. In one instance, a talented jazz musician was given two weeks off to play in a group touring Japan. The school hired a substitute during this period.

There are enormous benefits to establishing a program that would subsidize the city’s artists and musicians. It would certainly add to New York’s creative energy. The added bonus is that while we do this, we are creating a homegrown audience of future consumers of music and the arts, while enriching their lives today.

But most important, among Gotham’s children are a few of special and unique talent. Since many of these children are unlikely to find the resources elsewhere, we need to find ways for them to discover their own potential in our schools.