One in four public elementary and secondary school teachers believes that he or she is likely to leave the teaching profession in the next five years, including many of the best and brightest teachers, according to a Harris survey.

The poll of 1,846 teachers, sponsored by Metropolitan Life Insurance Co., found that half the public school teachers seriously have considered quitting teaching at some time and a quarter are "likely" to leave, while three in 10 who have received teaching awards are "likely" to leave.

The findings come at a time when demographic shifts and teacher attrition point to a severe teacher shortage in the future, with researchers projecting a need for a million new teachers by 1990.

Already in this school year, many districts have had trouble finding teachers to fill classrooms, particularly in mathematics, science and foreign languages.

Six in 10 teachers considering leaving teaching mentioned low pay as a chief reason and four in 10 cited such conditions as excessive paperwork, nonteaching duties and overcrowding.

Other factors included the lack of prestige accorded the profession, dissatisfaction with students and the administration, boredom, stress and lack of parental support.

Other findings from the survey, which was conducted by telephone from April 25 to June 8, include:

*Teachers reported working an average of 51 hours weekly, including 13 hours on paper work, administration and nonteaching tasks.

In return, 70 percent said the total income they derived from teaching was $25,000 or less in 1984.

*Half said that educational reforms had been implemented in their school districts and 42 percent said those reforms in their school districts have had a positive effect on students.

Twelve percent said the reforms have had a negative effect and44 percent said there was little effect. Half the teachers said that the reforms do not reflect their views.

*Six in seven teachers said they have benefited from across-the-board salary increases in the past two years.

Overall, 12 percent said that they are "very likely" to leave teaching and 14 percent said they are "somewhat likely," while 26 percent said they are "not too likely" to leave and 47 percent said they are "not at all likely."

Among teachers who said they had received awards, citations or special recognition for their teaching -- making them among the best and brightest in their profession -- 29 percent said they are very or somewhat likely to leave.

Thirty-three percent of those who had other job options when they started teaching said that they intend to go into other professions, as did 36 percent of teachers in urban settings.

Disgruntled teachers said they are attracted to a variety of white-collar occupations.

Asked to rate teaching as a career, 44 percent described themselves as very satisfied, 35 percent as somewhat satisfied, 16 percent as somewhat dissatisfied and 5 percent as very dissatisfied.

"This level of dissatisfaction could lead to an ongoing attrition that will sap the strength of the profession and carry away some of its best elements," the pollsters noted.