Three persons were shot to death in Washington yesterday -- including a 15-year-old youth and a 43-year-old science teacher -- as January ended with a single-month record of 37 homicides.

The death of 15-year-old Reginald Small, who lived in far Southeast, was described by police as drug-related, underscoring two deadly trends in the District: the increase in killings connected with illicit drugs and the increase in killings of juveniles.

The shooting of Fred Parris, who taught at the private Sheridan School in Northwest, came during a robbery attempt outside his home at the edge of the Adams-Morgan and Mount Pleasant areas, police said. Parris was described by his friends and colleagues as a gentle man and dedicated teacher.

In a third homicide, the body of an unidentified woman who had been fatally shot was found about 7 a.m. on the sidewalk at the intersection of Holbrook and Levis streets NE.

There was no immediate indication of any motive in that shooting. Police and neighbors said drug activity has been reported in the area, but they said they had established no clear link to drugs in the case.

Yesterday's three killings came two days after police announced the 33rd homicide of the month, which broke the record for the largest number in any month, set in December 1971.

They also raised the total in the past two months to 67, a rate that, if continued, would bring this year's total to almost 400. That number would dwarf last year's total of 228 killings, and would far exceed the figure for 1970, the District's deadliest year ever, when 280 persons were killed.

The present pace, more than double the rate of 1985, when 148 persons were killed, reflects an explosive growth in drug sales, which police say is linked to 60 percent of District homicides. The number of juvenile victims also has soared, rising to 19 last year from six in 1986.

Small, an eighth grader at Frederick Douglass Junior High School who was living with his grandmother, was gunned down about 5 p.m. in the 800 block of Bellevue Street SE in an area where police and neighbors said the drug trade has been flourishing. Police said the youth died at the scene of the shooting.

Family members said Small had lived off and on since he was 11 at his grandmother's house on Condon Terrace SE and his mother's on Atlantic Street.

They said they knew nothing of any involvement in drug activity.

"He was a good son," said his mother, Linda Small, a psychiatric attendant at St. Elizabeths Hospital. "He had no problems."

But, she added, "there's a lot of drug traffic here and he could have been involved with some kids who were not the best kids and who influenced him."

At the time of his death he had been staying with his grandmother, Mary Riddick, on Condon Terrace, a few blocks from where he was shot.

"He was a good boy," said Riddick, adding that Small spent much of his time with her because of affection for his grandmother rather than any family difficulties.

Investigators and friends said that Fred Parris was shot about 2:25 a.m. as he returned to his home in the 1600 block of Argonne Place NW with a friend.

They said the friend had begun to walk up a short flight of steps to the door when two men approached Parris from behind and demanded money.

One of the robbers fired a shot. Parris fell onto the sidewalk, fatally wounded.

"He took a couple of breaths . . . and he was dead," said Parris' housemate, who was in the house when the shooting occurred. "I came down and felt his pulse. He was gone then."

The woman who had been walking with Parris was unhurt. The robbers fled. Police said they took nothing.

A native of West Virginia and a graduate in civil engineering from the West Virginia Institute of Technology, Parris had taught science for 13 years at the Sheridan School on 36th Street NW.

"This was a guy dedicated to teaching and to children," said Hugh Riddleberger, headmaster of the 60-year-old school, which enrolls about 200 students in classes from kindergarten through eighth grade.

The headmaster characterized Parris as a meticulous man who "cared a great deal about trying to develop the discipline of science for students . . . . He developed his own courses" for fifth through eighth grade children.