Cellphone video obtained by a Detroit TV station and aired Tuesday shows the boys slugging it out in a Pershing High School ninth-grade classroom.
The video also shows the teacher — who is smaller than both boys — hitting one across his back to stop the altercation.
Education Achievement Authority spokeswoman Chrystal Wilson said the district has recommended the teacher's firing to its board after the incident last Wednesday. She said the teacher can appeal and go before the board when it meets in June.
The teacher was hired in January. Her name was not released.
The boys, ages 15 and 16, received suspensions.